Travels in a Mathematical World Blog

Apparently Gauss got in this bar fight with Hilbert...

2012-01-27T08:21:00.000Z

The title is silly, of course, but is meant to refer to a problem with historical accuracy. I have had this blog post in draft for a long time and I am struggling to finish it. I would like to talk about an area in which I appear to have cognitive dissonance. I'm intending to ask a bunch of questions to which I do not have answers. I hope you will help me come to some.

I firmly believe that what is published on the history of mathematics should be correct. The history of mathematics is full of misconceptions and apocryphal stories and to propagate these is a terrible sin. Call this Principle A.

Now, from time to time I see someone who has had a good go at producing something on a historical topic which is mostly correct but repeats a few common errors. This work (or person) is then picked apart by those in the know, or the piece of work is roundly dismissed as entirely without merit. I've heard this in the case of very popular books - "it's written well and tells a good story but it has this fact wrong so nobody should ever read it".

I'm not talking about someone who copies wholesale from some website nobody has ever heard of without checking any of the facts. Nor am I talking about a serious academic history of mathematics work. Nor silly errors. I'm talking about cases where an enthusiastic amateur has put in the effort; they've read fourteen sources for a particular piece of information and when they publish it they are picked up for not having read the fifteenth - a recent research paper in a journal they can't access - which debunks the fact.

I believe popularisation is good. Mathematicians would do well to know more of the history of their subject. I value the use of history in teaching as a way to engage students with the curriculum. I also believe history can be useful in outreach, the use of engaging stories to bring in more people to study of mathematics or its history. When I see someone having an honest attempt at telling some historical story, and they have done a reasonable level of research, I think it is bad to tear them apart or dismiss their effort. Instead we should encourage their keeness and perhaps gently steer them towards a better understanding (and they, in turn, should be pleased to learn). Sometimes this might mean you overlook a series of small errors to work, for now, on the major one. Pointing out everything that is wrong with a piece of work in minor detail can be very discouraging and, since popularisation and keeness are good, we hope to encourage this person not put them off from trying again. Call this Principle B.

You see the problem? Principle A tells me nothing should be produced with errors, but Principle B suggests work with minor errors should be taken in good faith. Both cannot hold. This is particularly a problem when I might be the person naively committing the sin (as I will be more often than the expert spotting the error). The fear of what might happen makes me feel very uncomfortable and hesitant to publish content on history.

There is another issue running along with this one. Perhaps the minor errors were not through ignorance but by choice, either due to restrictions of the format (word count or time available for a performance) or out of an attempt to keep the momentum of a story without getting sidetracked. This is like a piece of historical fiction where a character's sister and cousin are amalgamated into one character because it would confuse the main thread to introduce a new minor character for some small interaction with the plot before they disappear. If the main story is basically being told correctly but a few peripheral details are being ignored or muddled to keep the momentum, is that a bad thing? We want an audience for our story, after all; is it possible that too much accuracy (or too many caveats) can make the story uninteresting?

This puts me in mind of a piece of advice I was once given about writing popular mathematics. I was told that nobody should write a popular mathematics book unless they are a researcher in the topic of the book. I don't agree with this at all. Sometimes the researchers are too close to the topic to explain it well, or to make it interesting, or perhaps there isn't a talented writer researching a particular area but it should still be popularised. I wonder if people hold the same view - people should steer clear of history unless they are professional historians of mathematics? Won't this lead to less history being told?

There are also cases where someone learns or remembers something, or builds confidence, as a result of a historical story. I can't think of a better example right now but say for example I meet a twelve year old who was really struggling with mathematics when they were eight until a teacher told them that Einstein had failed mathematics in school and gone on to be a great physicist. A lot of ability in mathematics comes from perseverance which comes from confidence. Was the person who told the eight year old this story to boost their confidence wrong to do so? (There are surely cases where less decidedly wrong misconceptions apply to more nuanced situations but this will do as a placeholder; please don't get too hung up on Einstein or my imagined twelve year old.)

I really don't know the answer to these questions. I am asking them here in the hope that you might share your views. I really am interested to hear arguments either way.

Puzzle from Maths Jam Nottingham: Jon's coloured balls

2012-01-25T08:56:00.000Z

At Maths Jam Nottingham January 2012, Jon brought this puzzle.

You have three pairs of coloured balls - 2 each of red, white and blue. Within each pair one ball is heavy and one is light but you do not know which. All three heavy balls are equally heavy and all three light balls are equal weight too.

Q: What is the minimum number of weighings needed to identify each ball?

A: 1 is fairly clearly impossible. 3 is trivial (weigh each pair separately). So, in order for us to have an interesting puzzle the answer must be 2.

Q: How can it be done in 2?

For a while Christian Perfect has suggested that Maths Jam local organisers write blog posts based on what went on at their meetings. Rather than write a wholesale account of what happened at each meeting once a month I have decided to drop occasional puzzles from Nottingham Maths Jam meetings into this blog. I will tag these posts so you can search for "mathsjam" and find them.

It is important in problem solving that you have an honest attempt before reading a solution. Once someone has shown you the solution you are forever robbed of the chance to have that experience (in future you will half-remember the solution rather than reason it out) so it is important that you attempt this puzzle before reading the solution. For this reason I will post the solution separately. I will post this as a 'Page' since I don't think they appear in the blog stream so you have a reduced chance of inadvertently stumbling upon it. Jon's coloured balls solution.

N.B. I assume the puzzles written about are old puzzles. They are brought to Maths Jam meetings, or half remembered at the time, by attendees. If I have done something wrong by posting a puzzle here please tell me and I will be happy to correct the mistake.

Maths Jam Conference talk write-ups

2012-01-23T08:05:00.000Z

I have attended the two Maths Jam conferences - 2010 near Stone and 2011 near Crewe. At each I gave two talks, one of each I have written up over at Second-Rate Minds, the mathematics writing blog Samuel Hansen and I share over at ACMEScience.com.

Most recently I wrote up my 2011 talk Why the hot light bulb annoys me. In this I describe a puzzle which annoys me and explore why this is the case through a couple of other puzzles:

The light bulb puzzle presents you with three switches, one of which controls a light bulb inside a closed room. You are permitted to flip switches as much as you like, then you must open the door and say which switch controls the light bulb.
You don’t seem to have enough information. You can flip one switch and open the door. If the light is on then you have found your switch. However, if the light is off you can’t tell which of the other two switches controls the bulb.

My first post over at Second-Rate Minds was a write-up of my 2010 Maths Jam conference talk Moving on a strange diagonal. In this, I describe a puzzle I have given to students and why I like what it reveals about their thinking.

Given a 4×4 grid of sixteen dots, draw six straight lines that form a continuous path passing through all of the dots. Here, continuous means you must be able to draw over your six lines in one go without taking your pen off the paper.
This task is easy to complete with seven lines and impossible with five. Six is where the interesting puzzle lies.

The way Second-Rate Minds works each of these posts was written by me with Samuel Hansen providing editorial direction.

Favourite popular mathematics books

2012-01-19T17:06:00.000Z

I consider popular mathematics writing to be a good thing. I even tried a little myself and would be keen to try more. I am not, however, an expert in this genre. I certainly read popular maths and science books as a teenager and I remember fondly, along with a couple of physics books and biographies, the mathematical stories told in James Gleick's Chaos, Ivars Peterson's The Mathematical Tourist and Simon Singh's Fermat's Last Theorem. I'm not sure this is sufficient qualification to have a strong critical opinion. I have a copy of Alex Bellos' Alex's Adventures in Numberland that I was bought last birthday and, although it is on the top of my pile and I feel sure I will enjoy this when I get chance (perhaps someday I'll spend a holiday not worrying about my PhD), I haven't quite got around to reading it.

This week Guardian Books offered Ian Stewart's top 10 popular mathematics books in which, the description promises, "the much-acclaimed author chooses the best guides to 'the Cinderella science' for general readers". Why Cinderella you ask? Stewart means this in the sense at the start of the story, "undervalued, underestimated, and misunderstood", and perhaps intends popular mathematics to take mathematics to the ball, saying:

Popular mathematics provides an entry route for non-specialists. It allows them to appreciate where mathematics came from, who created it, what it's good for, and where it's going, without getting tangled up in the technicalities. It's like listening to music instead of composing it.

It will be no surprise, after the opening paragraph, if I admit that I neither own nor have I read any of Stewart's choices. I've heard of several of them but by no means all. I was surprised by the inclusion of Newton's Principia. In the back of my mind I have collected the 'fact' (citation needed) that Newton is a difficult read and I felt this made it a strange choice against the aim to bring "the best guides to 'the Cinderella science' for general readers" (though I'm aware the description will have been added later, possibly without Stewart's knowledge). Stewart justifies its inclusion as "a great classic" saying that although this is "not popularisation in the strict sense", this "slips in because it communicated to the world one of the very greatest ideas of all time: Nature has laws, and they can be expressed in the language of mathematics" and claims "no mathematical book has had more impact".

On Twitter, Tony Mann confirmed my half-remembered notion that "Principia is hard, very hard. Even in English". As to the claim of impact, Tony suggested Stewart should have chosen the Latin version as having more impact. Thony Christie agreed this is "a very hard book to read and comprehend", though Christian Perfect suggested that he found the scans of Newton's college notebooks which were recently made available online to be "quite readable".

Reading what Stewart wrote about Newton's Principia and its impact in the history of science, I wonder if the book was chosen more to tell the story in the article than out of a serious suggestion that it might be read. Christian Perfect makes this point more generally about the list over on my Google+ page:

I think he's chosen 10 books about his favourite mathematical ideas rather than 10 books which most effectively communicate mathematical ideas to a member of the "populace".

To include a classic, I wondered if something like Euler's Elements of Algebra, which I had heard travels fairly well to a modern reader, might be a more appropriate choice. On my G+ page, Sarah Kavassalis suggested "one of Poincaré's popular books instead though, for readability".

I asked people for their thoughts on the list and what else they would include. It's quite noticeable that several respondents report not having read many on the list (the same is true of the comments under the original article). Alex Bellos, on G+ expands on this:

I guess there are two types of "popular" - 1) something accessible for people who know no maths and 2) something fun for the math literate. I'd say Ian's list is very much the latter. If a lay friend asked me for a maths book suggestion they might understand and enjoy, I would only recommend the first two on his list [Robert Kanigel's The Man Who Knew Infinity and Douglas Hofstadter's Gödel, Escher, Bach].

Given the popular medium and Stewart's introduction to the article, in which he talks about popular mathematics as "an entry route for non-specialists", it is strange to see the list being regarded in this way. There's nothing wrong with a list of fun books for maths folks, with something to surprise us rather than just the obvious choices, but if that was what was intended then this probably should have said so. I worry about someone using this list to build a 'must-read' list and perhaps being put off popular mathematics as a result.

I also asked for your suggestions and these follow. It may not be fair but I have listed these in the order they were suggested. I've included descriptions, except where stated these are those given on Amazon UK.

Thank you to everyone who played along with this little game. We've got more than ten and I can't vouch for which would suit "people who know no maths" or "the math literate", but I've enjoyed looking through the suggestions. Further suggestions are, of course, welcome via the comments.

Alex Bellos' Alex's Adventures in Numberland (US title: Here's Looking at Euclid)
Suggested by Vincent Knight and Singing Hedgehog on G+.

In this richly entertaining and accessible book, Alex Bellos explodes the myth that maths is best left to the geeks. Covering subjects from adding to algebra, from set theory to statistics, and from logarithms to logical paradoxes, he explains how mathematical ideas underpin just about everything in our lives.

Edwin Abbott's Flatland: A Romance of Many Dimensions
Suggested by Sarah Kavassalis ("very different approach to popular mathematics") and Singing Hedgehog ("strange since Ian Stewart wrote the follow up Flatterland!") on G+.

How would a creature limited to two dimensions be able to grasp the possibility of a third? Edwin A. Abbott's droll and delightful 'romance of many dimensions' explores this conundrum in the experiences of his protagonist, A Square, whose linear world is invaded by an emissary Sphere bringing the gospel of the third dimension on the eve of the new millennium. Part geometry lesson, part social satire, this classic work of science fiction brilliantly succeeds in enlarging all readers' imaginations beyond the limits of our 'respective dimensional prejudices'.

Ian Stewart's Cabinet of Mathematical Curiosities and Hoard of Mathematical Treasures
Singing Hedgehog, on G+, recognises that Stewart can't choose his own books for the list but would add Cabinet and Hoard, which he calls "fabulous repositories of interesting stuff".

A book of mathematical oddities: games, puzzles, facts, numbers and delightful mathematical nibbles for the curious and adventurous mind.

A new trove of entrancing numbers and delightful mathematical nibbles for adventurous mind.

Clifford Pickover's The Math Book
Suggested by Singing Hedgehog on G+.

Maths infinite mysteries and beauty unfold in this fascinating book. Beginning millions of years ago with ancient 'ant odometers' and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history.

Barry Mazur's Imagining Numbers: (Particularly the Square Root of Minus Fifteen)
Suggested by Singing Hedgehog on G+.

The book shows how the art of mathematical imagining is not as mysterious as it seems. Drawing on a variety of artistic resources the author reveals how anyone can begin to visualize the enigmatic 'imaginary numbers' that first baffled mathematicians in the 16th century.

Florian Cajori's A History of Mathematical Notations
Suggested by Singing Hedgehog on G+, who says this "covers the history of mathematics through the methods of writing it".

Described even today as "unsurpassed," this history of mathematical notation stretching back to the Babylonians and Egyptians is one of the most comprehensive written. In two impressive volumes--first published in 1928-9--distinguished mathematician Florian Cajori shows the origin, evolution, and dissemination of each symbol and the competition it faced in its rise to popularity or fall into obscurity.

Richard Elwes' Maths 1001: Absolutely Everything That Matters in Mathematics
Susan Turnbull insists this mustn't be forgotten over on G+.

Maths 1001 provides clear and concise explanations of the most fascinating and fundamental mathematical concepts. Distilled into 1001 bite-sized mini-essays arranged thematically, this unique reference book moves steadily from the basics through to the most advanced of ideas, making it the ideal guide for novices and mathematics enthusiasts.

William Poundstone's The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge
Suggested by John Read on G+.

In The Recursive Universe, William Poundstone uses Conway's Life as a vehicle to explore complexity theory and modern physics. Poundstone demonstrates how simple rules can produce complex results when applied recursively and suspects our own universe was created in a similar manner. (Description source)

Ivan Moscovich's Super-games
Suggested by John Read on G+, but of which I cannot find a description.

Benoit Mandelbrot's The Fractal Geometry of Nature
Suggested by John Read on G+.

"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature

John Allen Paulos' Innumeracy: Mathematical Illiteracy and Its Consequences
Suggested by John Read on G+.

Why do even well-educated people often understand so little about maths - or take a perverse pride in not being a 'numbers person'?
In his now-classic book Innumeracy, John Allen Paulos answers questions such as: Why is following the stock market exactly like flipping a coin? How big is a trillion? How fast does human hair grow in mph? Can you calculate the chances that a party includes two people who have the same birthday? Paulos shows us that by arming yourself with some simple maths, you don't have to let numbers get the better of you.

Martin Gardner's Mathematical Puzzles and Diversions
Suggested by John Read on G+ who says this is "the first I bought and the one I go back to most" but I can't find a cover blurb description of this.

Marcus Du Sautoy's The Music of the Primes: Why an unsolved problem in mathematics matters
Suggested by John Read on G+.

In this breathtaking book, mathematician Marcus du Sautoy tells the story of the eccentric and brilliant men who have struggled to solve one of the biggest mysteries in science. It is a story of strange journeys, last-minute escapes from death and the unquenchable thirst for knowledge. Above all, it is a moving and awe-inspiring evocation of the mathematician's world and the beauties and mysteries it contains.

Ian Stewart's Game Set and Math: Enigmas and Conundrums
John Read on G+ says "I'd also pick an Ian Stewart - probably Game, Set and Math". Again, I can't find a description.

William Cook's In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation
Mitch Keller on Twitter notes that only one book on Stewart's list focuses on a specific problem and suggests this as another.

What is the shortest possible route for a traveling salesman seeking to visit each city on a list exactly once and return to his city of origin? It sounds simple enough, yet the traveling salesman problem is one of the most intensely studied puzzles in applied mathematics--and it has defied solution to this day. In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today's state-of-the-art attempts to solve it.

On G+ Alex Bellos recommended the following three for an accessible list for "people who know no maths", saying "the challenge when writing a maths book is to find a strong narrative - and these three books do it better than any others".

Simon Singh's Fermat's Last Theorem: The story of a riddle that confounded the world's greatest minds for 358 years
Recommended by Alex Bellos on G+.

The extraordinary story of the solving of a puzzle that has confounded mathematicians since the 17th century... A remarkable story of human endeavour and intellectual brilliance over three centuries, Fermat's Last Theorem will fascinate both specialist and general readers.

Apostolos Doxiadis and Christos Papadimitriou's Logicomix: An Epic Search for Truth
Recommended by Alex Bellos on G+.

This brilliantly illustrated tale of reason, insanity, love and truth recounts the story of Bertrand Russell's life... An insightful and complexly layered narrative, Logicomix reveals both Russell's inner struggle and the quest for the foundations of logic. Narration by an older, wiser Russell, as well as asides from the author himself, make sense of the story's heady and powerful ideas. At its heart, Logicomix is a story about the conflict between pure reason and the persistent flaws of reality, a narrative populated by great and august thinkers, young lovers, ghosts and insanity.

Apostolos Doxiadis' Uncle Petros and Goldbach's Conjecture
Recommended by Alex Bellos on G+.

Uncle Petros and Goldbach's Conjecture is an inspiring novel of intellectual adventure, proud genius, the exhilaration of pure mathematics - and the rivalry and antagonism which torment those who pursue impossible goals.

For a list of "something fun for the math literate", Alex recommended the following three.

Petr Beckmann's A History of Pi
Recommended by Alex Bellos on G+.

The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

Tobias Dantzig's Number: The Language of Numbers
Recommended by Alex Bellos on G+.

A new edition of the classic introduction to mathematics, first published in 1930 and revised in the 1950s, explains the history and tenets of mathematics, including the relationship of mathematics to the other sciences and profiles of the luminaries whose research expanded the human concept of number.

Paul Hoffman's The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth
Recommended by Alex Bellos on G+.

The biography of a mathematical genius. Paul Erdos was the most prolific pure mathematician in history and, arguably, the strangest too.

For this group, Alex also recommends "the complete works of Martin Gardner".

James Gleick's Chaos and The Information
Recommended by Alex Bellos on G+. Alex says these are between the two lists as they are "both utterly brilliant but might lose the casual reader in parts".

Chaos: This book brings together different work in the new field of physics called the chaos theory, an extension of classical mechanics, in which simple and complex causes are seen to interact. Mathematics may only be able to solve simple linear equations which experiment has pushed nature into obeying in a limited way, but now that computers can map the whole plane of solutions of non-linear equations a new vision of nature is revealed. The implications are staggeringly universal in all areas of scientific work and philosophical thought.

The Information: We live in the information age. But every era of history has had its own information revolution: the invention of writing, the composition of dictionaries, the creation of the charts that made navigation possible, the discovery of the electronic signal, the cracking of the genetic code.
In The Information James Gleick tells the story of how human beings use, transmit and keep what they know. From African talking drums to Wikipedia, from Morse code to the ‘bit’, it is a fascinating account of the modern age’s defining idea and a brilliant exploration of how information has revolutionised our lives.

E-Learning in Mathematical Subjects

2012-01-17T11:00:00.000Z

In 2005 I was asked to attend a meeting at Nottingham Trent University with some fellow PhD students. I explained my topic, e-learning in university mathematics, to one student who said, "oh, you should go and talk to Mike in Physics; he's interested in that sort of thing". When I found him, it turned out Mike had a little interest in primary school teaching but he said "oh, you should go and talk to Dave downstairs; he's interested in that sort of thing".

Feeling like I was on a wild goose chase, I went downstairs and knocked on the relevant door. Dave turned out to be Dr. David Fairhurst, a physicist who had recently moved to Nottingham Trent University. Dave was indeed interested in university education and after a quick chat we agreed there are lots of subjects all trying to deliver mathematical content through electronic means who might benefit from getting together and a seminar series might be useful. I was keen on this; as a PhD student I was encouraged to attend departmental seminars but I hadn't even managed to understand the titles of any so far.

We booked a room and sent an email around whoever we could think of as an invitation to a general discussion on setting up a seminar series. Thirty or so people turned up and someone suggest Trevor Pull could give the first talk. Over the next three-and-a-bit years we held a total of 25 meetings which were attended by teachers of mathematicsfrom subjects such as mathematics, statistics, physics, chemistry, biosciences, environmental sciences, engineering, computing, social sciences, business and economics, as well as researchers from both computing and education and university learning technology developers. It was really pleasing to meet all these people and see how mathematics is taught in nearly every academic school in the university. We were joined in the organisation by Pete Bradshaw from the School of Education.

In 2006 we had a talk by Steve Maddox about his work supporting two blind physics students at the University of Nottingham. This was excellent and I felt a great sense of loss at having only made this available to the twenty or so people in the room who saw it live. Steve did write his talk up for MSOR Connections, but this only appeared a whole year later because these things take time. I applied for funding from the Institute of Mathematics and its Applications (I was a member but this is long before I worked for them) and received £600 towards speakers' expenses and refreshments at meetings in exchange for recording the talks and making them available online. The Maths, Stats and OR Network (long before I worked for them too) were kind enough to host the large video files on their web server.

For the first two talks I borrowed video cameras from the computing department and recorded and edited these myself. I wrote an article in MSOR Connections about this experience: A quick and easy (rough and ready) method for online video. From 2007 onwards, much to my relief, these were recorded and edited professionally by Chris Shaw of Nottingham Trent University.

Many of the seminar videos cover teaching, learning, assessment and support using specific technologies – wikis, podcasting, Logo, interactive whiteboards, GeoGebra, VLEs and interactive voting systems – a series of talks related to accessibility, particularly access to mathematics by students with visual impairments, and several related to more general pedagogy such as designing effective online questions and relevance of learning styles to e-learning. In the end we recorded fourteen talks as videos. These have been available for a while on the ELMS website and have been downloaded quite a few times (by unique ip addresses: min 30; max 176; mean 51; SD 38; median 37). Now I have transferred the videos also to a YouTube playlist. The website has downloads relating to talks (such as slides) where these are available.

I wrote updates on the availability of new ELMS talks in Mathematics Today (43(3), p. 85; 43(5), p. 164); 45(1), p. 11) and MSOR Connections (7(2), pp. 49-50; 7(4), p. 43; 9(2), pp. 29-30), and a final grant report in Mathematics Today (46(6), pp. 287-288).

ELMS seminars stopped when I moved to full time employment and couldn't get to Nottingham Trent very often to organise them. I'm really glad for this experience. I met a lot of interesting people doing these seminars and later ran workshops for the MSOR Network's Accessing MSOR group, staff development seminars for the School of Mathematical Sciences at the University of Nottingham when I worked there and in my current job for the MSOR Network we run seminars and workshops. ELMS was the experience that demystified this process for me and that alone was incredibly useful.

What is mathematics?

2012-01-12T15:53:00.000Z

This morning on Twitter Tony Mann asked the question: "This morning's class is "What is Mathematics?" Answers in a tweet please." Answers were collected via the #MATH1103 hashtag.

Some of the answers were what you might expect: patterns, abstraction, order.

Stuart Ravn sent a series of tweets giving his views:

Math is everything you can do with the abilities to count and deduce. There's literally no end to the fun you can have. No joke.
Math is the only thing which is truly universal; it underlies and makes it possible to understand and communicate with everything.
Everything, immediately or ultimately, is mathematical and arises from mathematics.
Ask yourself what isn't mathematics, and try to prove yourself right.
Noam Chomsky said of love, "I can't tell you what it is, but life's empty without it." The same is viscerally true of mathematics.
I don't just have enthusiasm for maths. I love it. It's the closest thing to my heart after my family. I'm emotional about it.

Noel-Ann Bradshaw noted that "What is mathematics?" is the name of "an excellent book by Courant & Robbins revised by Stewart". I have the tenth printing from 1960. Although this has a lot to say on the subject, it opens a discussion of historical development with:

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasise different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.

I was interested in a related question: When does mathematics become something else? At some point some topic is clearly applied maths and at some point it is physics, astronomy, engineering, economics, computer science, biology, and so on.

We struggle with this a little on the Math/Maths Podcast, where we try to report news from mathematics and its applications. On Twitter I said that I think I tend to stray a little further from that which is unambiguously mathematics than does Samuel Hansen. We both report applications but I think mine are often more tangential than Samuel's. This was quite noticeable on episode 80 this week when Samuel picked me up on an astrophysics story I was defending as involving statistical models. He said:

This is 'Math/Maths', not 'Stat/Stats', and it's definitely not 'Astronomy/Astronomies'. I'm assuming you put 's' at the end of every single science - you have 'Chemistries' and 'Physicses', right?

and later

Now you've turned us into 'Geology/Geologies'.

Answering my question on Twitter, Samuel said: "if an application has been around long enough to have own name, Physics astronomy or thermodynamics. It's not math". I don't fundamentally disagree with this and some disciplines, notably computer science, were born this way. However, Sharon Evans made a very practical (if teasing) counter-point: "so it's only maths if it hasn't got a name? You're not leaving much to report on in [the podcast]".

Clarissa Wornack replied to say "Well, when you start writing code; it's IT/software eng/comp sci; if you create something that is a material object; it's eng" and Charles Brain said "Applied maths becomes Engineering when it hits the real world and money becomes part of the equation!" I don't particularly agree with these. I know people who use high end computing to do mathematics and just because they are using computing as a tool (and writing bespoke code) this doesn't mean they are doing computer science research. I also don't agree that it stops being applied maths when it creates a material object. Defining mathematics as that which doesn't involve the real world or money seems very self-defeating.

Felipe Pait offered this definition: "Applied math interests mathematicians and non mathematicians. Otherwise it's pure math, or pure engineering. Math stops being applied math and becomes pure physics when it doesn't interest mathematicians. An operational definition."

There's something in this. When I think about "what is mathematics?" I am really thinking "what can mathematicians do?" I am particularly interested in what university mathematics graduates might become and would like this to be a broad as possible. I meet a lot of mathematics researchers working in different application areas. For example, back when I was doing the Travels in a Mathematical World podcast for the IMA I spoke to Paul Shepherd. I am much more naturally inclined to consider Paul a mathematician working in architecture than an architecture researcher who once did a maths degree. By extension, I am happy to include Paul's use of geometry in architecture as part of mathematics than to exclude it.

Daniel Colquitt suggested "a lot depends on the user" and "in many cases, the distinction is arbitrary". I think this may be the wisest view on the subject I have heard. From my point of view I am biased towards including topics on the edge within mathematics rather than excluding them, and maybe even collecting a little of the host subject along with them. I would rather cast the arbitrary net as wide as possible.

Have you used maths in the news in school?

2012-01-09T15:11:00.000Z

Later this year I am to give a session at a teachers conference on using maths in the news for enriching school maths lessons.

In my session, I intend to go over some recent maths news. I would also like to give some real examples of teachers having used some news in class.

Samuel Hansen and I keep track of mathematics news and mathematics in the news for our podcast. I am aware that people have written in from time to time to say they have used some bit or another in class but I haven't recorded these instances.

My plea, then, is this: Whether from the podcast or not, please could you send me your examples of how you've used current events in mathematics class for enrichment? I'd like to know what the news story was, what you did and how it worked.

You can leave a message in the comments of this post or send me a message various ways that are listed on the contact page of my website.

Thank you!

Card trick video from Christian Perfect

2012-01-04T14:26:00.001Z

A while ago Christian Perfect suggested the monthly local Maths Jam organisers might write up what happens at Maths Jams to their blogs so others can get a feel for what goes on. I regard this as a good idea I haven't got around to yet.

Luckily, Christian has just made a video showing a card trick we have played with at the Nottingham Maths Jam, so that makes this an easy post!

I was shown this trick by Matt Parker in a hotel bar in Coventry, who refused to say how it works. I went to the Nottingham Maths Jam in November 2011 having worked out how to do the trick but having spent no time at all considering how it might work, saving this for Maths Jam. I showed John Read, Kathryn Taylor and Sharon Evans and together we worked out the details given in Christian's video.

I made a joke on Twitter based on Gauss' reaction to Bolyai's work on non-Euclidean geometry: "Enjoying video by @christianp. However, 'to praise it would amount to praising myself' ;)". Gauss is reported to have written to Bolyai's father:

To praise [Bolyai's work] would amount to praising myself. For the entire content of the work ... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years.

while privately writing to a friend to say:

I regard this young geometer Bolyai as a genius of the first order.

Of course, by invoking the former I meant to imply the latter. Perhaps a more suitable quote might be that of Kelvin, having first read George Green's Essay on electricity and magnetism:

I have just met with Green's memoir, which renders a separate treatise on electricity less necessary... I have, most unwittingly, trodden almost exactly in his steps as far as regards electricity.

I'd say playing around with tricks and working out how they work is a very Maths Jam activity so anyone considering attending one should regard this as very much the sort of thing that happens at a Maths Jam. Find your local one, or set one up!

300 posts later, who is Peter Rowlett?

2012-01-02T11:45:00.002Z

This is the 300th post to this blog. At 100 posts and 200 posts I paused for a recap of my current circumstances. This 300th post coincides with the change of calendar year, which seems to bring out a great deal of reflection from people. Nevertheless, I will try not to get too mushy on you!

When I started this blog in February 2008, I had recently begun work as University Liaison Officer for the Institute of Mathematics and its Applications, and decided to blog about my travels around the UK talking to university student groups about why they should join the IMA. After 100 posts, in March 2009, I had recently started working alongside the IMA job in e-learning for the School of Mathematical Sciences at the University of Nottingham.

By my 200th post, in June 2010, I had reduced my hours with the IMA to continue to work for Nottingham. My role title at Nottingham had changed from e-learning to Technology Enhanced Learning and a change of emphasis, as I saw it, from being a teaching support person acting through technology to a tech support person who dealt with teaching meant that I was feeling much less well placed. Shortly afterwards, in August 2010, I finished at Nottingham and, extremely sadly, with the IMA to move full-time to the University of Birmingham. There I work on the Mathematical Sciences HE Curriculum Innovation Project for the Maths, Stats and OR (MSOR) Network as part of the National HE STEM Programme.

The National HE STEM Programme is a major higher education intervention seeking to enable HE to engage with schools, enhance curricula, support graduates and develop the workforce. My part is focused around curriculum development in the mathematical sciences. A major part of this work had us running the HE Mathematics Curriculum Summit, an event this time last year that brought together those with an interest in mathematics teaching at university whose priority recommendations we are acting on in a series of curriculum innovation projects this academic year.

What of the future? The National HE STEM Programme is a three-year initiative which finishes on 31st July 2012 and the Higher Education Academy has withdrawn funding for Subject Centres like the MSOR Network, so my job will end with no chance of follow on work. Of course this means I am quite preoccupied with worries about income in the latter half of 2012. I have a strong interest in teaching and would love it if someone would employ me as a mathematics lecturer. I think my CV is strong for curriculum development aspects and schools outreach but many lecturing posts are really about serious mathematics research, while my research is in the curriculum development aspects of teaching, learning, assessment and support. Even for those few that aren't, the number of candidates applying for jobs now means that, while I have some relevant teaching experience, my lack of mathematics PhD means I am not at the top of the pile. I believe I would make a good lecturer, strongly interested in pedagogy (as it could improve student learning and the student experience, rather than as a philosophical pursuit), and that I would enjoy such a role. I just need to convince someone else of this, or stop barking up this tree and find something else to aspire to do.

Outside of work, I remain registered for a PhD in e-assessment in mathematics, which I must complete by July 2013. I think this is on track as it moves into a final experimental phase.

At 200 posts, I had recently started a weekly mathematics-based conversation with Samuel Hansen of ACME Science. Well, we've just published the 79th almost-weekly episode of the Math/Maths Podcast, which was a review of the year 1811 (not wanting to merely rehash 2011). Samuel and I have started a shared blog for writing practice over at Second-Rate Minds. My write-up of my 2010 Maths Jam Conference talk about a simple puzzle and what I think it can reveal about student thinking got a lot of attention and I am pleased with a piece I wrote reflecting on Hardy's Apology. I have also been editing posts written by Samuel, which has been an illuminating experience.

I no longer work for the IMA but I remain a member (MIMA) and have a volunteer role on the committees for the East Midlands Branch and the Early Career Mathematicians Group. Having been co-opted to Council of the British Society for the History of Mathematics at my 200th post, I have since been elected to Council and continue to serve in this voluntary role. I remain a STEM Ambassador and contributed a mathematics stall to the East Midlands Big Bang STEM Festival.

Nobel prize for mathematics

2011-12-28T08:45:00.000Z

There's no Nobel Prize for Mathematics

This is a common statement. I've certainly used it myself. Recently it occurred to me to be annoyed with this.

Nobel Prizes are awarded in physics, chemistry, medicine, literature, peace and economics, but not mathematics.

On the other hand, mathematics is widely applicable and I think I could convince you it is certainly used in physics (career), chemistry (career), biology (career), medicine (career) and economics (career). (Links to the excellent Plus Magazine and Maths Careers.) The case for literature and peace might be a bit harder to sell. But even without these two we still have a majority.

So perhaps from now on I will try to remember to say:

Most of the Nobel Prizes are for Mathematics¹

[1. there is a fallacy here: for example, saying that some mathematics can be applied to economics does not mean that all economics involves mathematics. But, shh!]

Christmas presents

2011-12-26T10:58:00.000Z

What did I get for Christmas (mathematically, at least)? My big present was an Acme Klein Bottle, whose website claims it to be one of "the finest closed, non-orientable, boundary-free manifolds sold anywhere in our three spatial dimensions". This is a 3D representation of a 4D Klein bottle; a pale shadow, of course, although the cheerful and entertaining information leaflet that came with the bottle claims this an advantage: "You can actually hold an Acme Klein Bottle in your hand. Those highfalutin' 4-dimensional ones can only be held in your mind". Here is a photo of mine:

I also got a set of physical puzzles which are nice to have a supply of. I find I am sometimes laying puzzles on a table for students to play with and solid, physical puzzles, while perhaps not the most mathematically interesting, are certainly an attractive draw. People can't resist picking up and playing with wooden blocks, it seems!

I got a copy of The Great Mathematicians by Raymond Flood and Robin Wilson, a past and present President of BSHM, which claims to present "mathematics with a human face, celebrating the achievements of the great mathematicians in their historical context". You can watch a lecture given by Raymond and Robin at the launch of the book at Gresham College.

As a bit of Christmas day craft, inspired by the escapades of the Manchester Maths Jam, we made dodecahedron star lanterns. Unlit, these are like this:

And lit they come alive like this:

Merry Christmas everyone! What mathematical presents did you receive and what mathematical activities did you do this year?

Pictorial proofs

2011-12-20T15:59:00.001Z

I received this message from Alan Stevens, Nottingham Maths Jam attendee. I am putting it here so readers of this blog and the other Maths Jams might consider the topic as well.

Although I won't be able to make the next MathsJam at Nottingham I've thought of a theme you might like to consider. I don't know if you have themes, but, if you do, how about "Pictorial proofs and derivations"?

Probably the most obvious pictorial proof is of Pythagoras's theorem (in fact there are probably several such). Do your mathsjammers know of any more?

I thought of this while viewing James Tanton's YouTube channel, where he has a very pictorial way of looking at maths, including a very nice pictorially based derivation of the geometric series 1/3 + 1/3^2 +1/3^3 + ... = 1/2.

If you haven't seen someone in a t-shirt displaying a pictorial proof of Pythagoras, you haven't been going to the right sort of conferences! The James Tanton video reminds me of a pictorial demonstration of summing 1/2 + 1/4 + 1/8 + ... which I used in a lecture, after Zeno's paradox of Achilles and the tortoise, when I was trying to get across the idea of an infinite series summing to a finite amount. Shading half a square, then a quarter, then an eighth, and so on it looks like you will eventually shade the whole square and nothing more, a useful illustration that the series converges to one. In fact, I repeated this in the micro-teaching session of my Postgraduate Certificate in Higher Education course and a screenshot of the slide after I drew on it using the interactive whiteboard is below. I'm not sure if this constitutes a proof, though.

Why I like some bad maths stories

2011-12-19T10:11:00.000Z

My two most recent posts here have been about a story reporting a coincidence as more exceptional that it is and 'bad maths' reported in the media. Both are examples of mathematical stories being reported in a way that is not desirable. Somehow, though, I like the whist story and dislike the PR equations. I have been thinking about why this might be the case.

The PR-driven, media-friendly but meaningless equations from the first article are annoying because they present an incorrect view of mathematics and how mathematics can be applied to the real world. Applications of mathematics are everywhere and compelling, yet the equations in these sorts of equations seem to present little more than vague algebra. The commissioned research with seemingly trivial aims I find more difficult because, as commenters on that article pointed out, it is really difficult to decide what is trivial. Still, reporting that a biscuit company has commissioned research into biscuit dunking is either meaningless PR or else a matter of internal interest, and certainly nothing like what I expect mathematicians do for a living.

Coming back to our Warwickshire whist drive: what do I like about this story? It too presents incorrect information about mathematics and the real world, claiming that the event, four perfect hands of cards dealt, is so unlikely that it is only likely to happen once in human history (and it happened in this village hall!).

I think the difference is that the mathematics used, combinatorics and probability, appear to be correctly applied. The odds quoted, 2,235,197,406,895,366,368,301,559,999 to 1, are widely reported and I see no reason to doubt them.

The problem, then, is one of modelling assumptions. Applying a piece of mathematics to the real world involves describing the scenario, or a simplified version of it, in mathematics, solving that mathematical model and translating the solution back to the real world scenario. In this case, the description of the scenario in mathematics assumes that the cards are randomly distributed in the pack. This modelling assumption, rather than the mathematics, is where the error lies.

The result is still a bad maths news story, presenting a mathematical story as something other than what it is, but while the PR formulae are of little consequence, this incorrect application of a correct combinatorial analysis is something we can learn from.

'Bad maths' news stories

2011-12-13T10:29:00.000Z

On the Math/Maths Podcast, we frequently cover 'bad maths' stories. A recent example was the bobbing apples story we spoke about in episode 71: Halloween Fruit Special. This proposed a "mind-bogglingly complicated equation", provided by a supermarket, for finding the perfect bobbing apple:

D = 3 x (2 + T^2) x M / (10 x T), where D is diameter, T is typical texture of an apple, and M is average mouth size.

Along with another formula from a rival supermarket (I reproduce this as reported; I imagine the second equals is supposed to be a plus):

B = (BU + S) x (C = BI), where B is bobability, BU is buoyancy, S is size, C is colour and BI is biteability.

A headline like "Mathematician finds formula for the perfect bobbing apple" is a tell-tale sign of bad maths in the news. Or is it? Actually there are several types of story that all appear under this same style of headline.

A couple of years ago Simon Singh launched a mini-campaign against 'phoney formulae' being reported in the news. Simon describes being asked by a PR company for an equation to say that the perfect shopping day coincided with the launch of a shopping exhibition, saying to the PR company,

I would engineer the equation so that the graph peaked on the day you require. There would be no real science behind the equation, but it would look sensible and convincing.

and getting the response,

Your ideas and formulas are perfect and exactly what we are looking for and it would be great to confirm you working with us.

As well as calling them "absurd PR equations", Simon also gave a more serious warning, saying this,

demeans mathematics and science by giving the impression that academics waste their time on frivolous topics and are willing to come up with the appropriate answer if someone is prepared to pay them enough money.

A 2004 BBC article, "Formula for the perfect formula", claims the origin of this media fascination with formulae was a piece of work by Len Fisher on how to dunk biscuits, sponsored by a biscuit company. What is described in that article is, I think, something subtly different from what Simon is railing against.

Len seems to be taking corporate sponsorship to do real experiments (the original article describes a "two-month investigation"), just that they are experiments with fairly trivial goals. The article describes a scientist who is aware that newspapers just want "to make a story look scientific" but motivated by a desire to communicate science to the public through any means available. In the case of the biscuit dunking, Len is quoted describing the physical processes and saying: "As with most things in physics, we can write equations which govern this".

I doubt the biscuit manufacturer cared in advance how long a biscuit should be dunked for (though they are presumably interested in getting their brand in the news) and Len claims to be doing real science to answer the question. I have also heard people describe being approached by PR companies with ready-made meaningless formulae to which the approachee is asked to put their name, on behalf of some brand. This seems similar to but slightly different from Simon’s case, where he is apparently asked to manufacture a realistic-looking piece of pseudo-mathematics to back up a pre-determined conclusion, or Len’s, where a brand name is associated with some trivial piece of research.

Simon also speaks about the danger of confusing real research with these PR equations. In Math/Maths 52: World's Smallest Klein Bottle we covered side-by-side the formula for the perfect cup of tea and that for the perfect golf putt. The former appears to be just PR for a milk company but the latter, although you could imagine a headline like "Mathematicians discover the formula for the perfect putt" being dumb PR for a golf equipment company, appears to be based on genuine research. Using mathematics to improve the performance of sports people and manufacturing of sports equipment is big business. The author, a physics professor at Yale, filed a patent in 2005 through the university for a golf training aid, marketed through a spin-off company. This was described by the Dean of the Engineering Faculty at Yale as "a great example of the joy in practical application of basic science and engineering". Over in the UK, I expect this would be an example of 'knowledge-transfer' and much sought-after evidence of the positive impact university research has on wider society.

There is another interesting case, when a real piece of research is explained using a metaphor which then gets reported as its real purpose. This may be what happened in a 2010 story in the Guardian, which is about a paper on Recursive Binary Sequences of Differences published in Complex Systems that we spoke about on Math/Maths 7. Attempting to explain potential applications to blending problems, the researcher seems to have given the trivial example of pouring coffee. The work is reported under the headline "How to pour the perfect cup of coffee" with explanation: "Years of research have resulted in the definitive way to pour the best second cup of coffee". I don't know what happened here but it looks to me like some number theory with potential applications to chemistry is being presented in a way that might lead you to believe it is one of Simon's "absurd PR equations".

So what have we learned? Rail against bad maths in the media when you see it, but be careful to check you've found what you think you've found and be aware there are levels of severity.

Four perfect hands: An event never seen before (right?)

2011-12-06T18:26:00.000Z

A couple of weeks ago there appeared several reports of an astonishing coincidence. Reports in the Daily Express, The Sun and the Daily Mail tell of a game of whist at the village hall at Kineton, Warwickshire. In whist, one deals 52 cards equally between four players. During this particular game, all four players were dealt one entire suit each.

All three reports refer to an analysis by Dr Alexander Mijatovic of Warwick University. It is always difficult to know how much of what is reported is faithful, but the fullest account of his words was given in The Sun:

The chances of this happening are so humongous that it is almost impossible.
The event can only be compared to natural occurrences.
It would be the same as a person having a tiny drop of water and then finding that same drop of water in the Pacific Ocean.
I would question whether the cards were shuffled the correct number of times but if they were, and the people involved are sure they were, then it is probably safe to say this is the first time this hand has ever been dealt in the history of the game.

It is this last sentence, in particular, that caught my eye: "it is probably safe to say this is the first time this hand has ever been dealt in the history of the game". I took a quick look on Google News, which indexes old newspapers. I obeyed the following rules: I ignored results when only one perfect hand was dealt (hardly remarkable at all!); I didn't pick a second result from the same decade (although there were plenty, particularly in the 1920s and 30s) and I didn't spend very long at all on this. Here are a set of articles I found:

I was particularly taken with an account by Catherine Ford in The Calgary Herald of 29th November 1983, which contains,

Every bridge player fantasizes about the perfect hand - being dealt the 13 cards of one suit - and the perfect game, in which each of the four players receives all 13 cards of one suit. The odds of this happening are 2,235,197,406,895,366,368,301,559,999 to 1, which explains why a plain brown envelope, sealed in 1946, is among my mother's prized possessions. It contains the cards which dealt one perfect suit to each player.

William Hartson, commenting in The Independent on one such incident in 1998, said:

There are about six billion people in the world. If they all played one hand of cards every five minutes, 12 hours a day, such a coincidence would happen about once every ten trillion years. On the other hand, there are a good few practical jokers around who would love to sneak a doctored pack of cards to four unsuspecting players to create the perfect whist hands when dealt. I know which possibility my money is on.

It is tempting to suggest that someone made these stories up, or stacked the deck as a joke. However, it turns out these assumptions aren't needed to explain what is happening.

Essentially, Dr Mijatovic was right to question whether the cards were shuffled correctly (so I wonder if this was actually the main thrust of what he said). Basically, whist is a game in which the objective is to stack the deck. A card is played and the other players must follow suit if they can, meaning the cards at the end of the game are particularly well ordered into suits. If the shuffling does not completely randomise the deck (and it often doesn't) then the probability of a perfect game occurring is increased greatly. There is a good summary of this on the MAA website at Ivars Peterson's MathTrek.

Samuel Hansen pointed out on the Math/Maths Podcast when we spoke about this that this is still very unlikely and may even be worthy of note in a local newspaper, so we should let people have their fun. He's right, of course - I am mostly just amused by the claims of just how unlikely this is and the way an event that happens every few years is set up as unlikely to happen during the lifetime of the human race.

Shifting decline of mathematical preparedness?

2011-12-04T11:48:00.000Z

Last year I wrote On the Decline of Mathematical Studies, and ever was it so, which looked at several examples of people complaining that the new generation of mathematics students were not as well prepared as the current one, with quotes from the late 20th C, mid 20th C. and even from the early 19th C. I wondered whether the problem was one of perception, or whether mathematics teaching could really be in constant (or, as Tony Mann pointed out, cyclical) decline.

I have just read 'Mathematics at the Transition to University: A Multi-Stage Problem?', an essay by Michael Grove (of the National HE STEM Programme, which supports my project) which offers an interesting view on this question. Though the complaint, that students are not prepared for university courses, sounds the same, Michael suggests the root cause and manner in which this problem manifests itself has changed. He backs up his argument with findings from several recent reports. His essay is worth a read if you are interested in this issue.

Having identified a possible root cause for the current situation, Michael also makes recommendations for what can be done to address this and points to relevant work the Programme is doing.

My Erdős number?

2011-11-24T09:22:00.001Z

People ask, from time to time, what is your Erdős number? For a long time I've said I haven't got one because I haven't published a mathematical research paper. When I gave this answer to Samuel Hansen last year he told me that any research paper counts, not just those in mathematics. This left me idly wondering and today, having listened to Samuel discussing social network theory on the Big Science FM podcast, I finally decided to have a go. There are a few possibilities, none of which seem, to me, entirely satisfactory.

Short answer: At most 4. Probably.

Long answer:

My list of publications is on my website. I do not appear on MathSciNet.

MathSciNet tells me Edmund Harriss wrote 'Flattening functions on flowers' with Oliver Jenkinson, who wrote 'Zero temperature limits of Gibbs-equilibrium states for countable alphabet subshifts of finite type' with R. Daniel Mauldin , who wrote 'The nonexistence of certain invariant measures' with Paul Erdős. This gives Edmund an Erdős number of 3. Edmund and I are both authors on the paper 'The unplanned impact of mathematics' in Nature, which would make my number at most 4. However, this was a strange piece and although it is listed as one paper on the Nature website it was actually a series of seven short pieces under a common title and introduction. It is difficult to say whether this counts as a collaboration.

From the same root article, MathSciNet tells me Mark McCartney has an Erdős number of 5, Graham Hoare has 4 (although this is via a biography 'Stefan Banach (1892–1945). A commemoration of his life and work' in Mathematics Today which may not count (see below)), Juan Parrondo has 5, Julia Collins has 5 and Chris Linton has 4. These all have the same problem as Edmund above and are all greater numbers than Edmund's anyway.

For another route, MathSciNet tells me Joel Feinstein wrote 'A fixed-point theorem for holomorphic maps' with Richard Timoney, who wrote 'An extremal property of the Bloch space' with Lee Rubel, who wrote 'Tauberian theorems for sum sets' with Paul Erdős. This makes Joel's Erdős number 3. Joel and I have a paper 'Media Enhanced Teaching and Learning', in the new issue of MSOR Connections. This would make my number 4. MSOR Connections is a mathematics education practitioner journal and I am not sure if this counts.

Stephen Hibberd and Cliff Litton, with whom I collaborated on some of my first articles, including 'MELEES - Managing Mayhem?' (Proc. Mathematical Education of Engineers IV), both have an Erdős number of 4. Going this route, mine would be 5. Being a paper in conference proceedings, this seems the most 'real' route.

So what are the rules? The Erdős Number Project says:

Our criterion for inclusion of an edge between vertices u and v is some research collaboration between them resulting in a published work. Any number of additional coauthors is permitted. Not normally included are joint editorships, introductions to books written by others, technical reports, problem sessions, problems posed or solved in problem sections of journals, seminars, very elementary textbooks, books on history, memorial or other tributes, biography, translations, bibliographies, or popular works.

The Nature article perhaps doesn't count then, even if it counts as a collaboration, as it is a history or perhaps even popular article (exposition rather than original research). By this definition, the article with Joel Feinstein does seem to count. We've collaborated for a couple of years on using tablet PCs to deliver mathematics lectures, both while I was at Nottingham and since then, and have run several workshops on this topic. This collaboration led to this paper on Joel's use of this technology in his lectures. So I suppose that would make my Erdős number 4.

Of course, like any social network analysis, the members of a network may not be able to find the shortest path through it. For example, I co-authored with Claire Chambers who has a healthy number of co-authors but as her work now is in education around geography they are not included in MathSciNet. I have other co-authors on my list of publications that don't appear in MathSciNet but may, as I appear to, have a number. Indeed, any of the authors listed above could have a shorter route found by leaving MathSciNet's database. So I should say my Erdős number is "at most 4".

I find you can only go so far down this rabbit hole before it all seems far too preposterous to go on, so I will stop.

Oh, email

2011-10-30T11:31:00.001Z

I feel, increasingly, that I am not coping well with my email. I just found some data to illuminate this. So here is what has happened to the raw number of emails sent and received over the past eight years.

This year so far (up to yesterday, the 29th October) I have 19357 emails, more than a thousand emails more than I did in 2010 or 2009. The mean is 65 per day, which seems about right. I get fewer than this at weekends and during some parts of the year, but I have noticed before that many workdays I send and receive about 90. These numbers seem terrifyingly large.

Even more annoying about this is that at the end of 2010 I signed off a load of email discussion lists, removed myself from some quasi-spam circulars sent by companies I'd bought things from and turned off a lot of email alerts from Twitter, Facebook, etc., in order to reduce the volume of email I was processing. The 2011 data includes this reduction.

Oh, and none of this is spam - these numbers exclude both the spam box and any spam emails that I manually removed from my inbox.

Looking at the 2011 data: Let's assume each email takes me a minute to deal with (read or write; some are just discarded in a few seconds, others might take a few minutes; it's a crude average). Then 19357 minutes is a little over 322 hours. Assuming a 7.5 hour working day (haha), this is 43 days. There have been 215 weekdays so far this year. Allowing for holiday and sick leave (I've had a bad year for the latter), this means I'm spending something like a quarter of my time processing email.

Some questions that arise from this analysis:

Does this help me cope with my email? (No, but I feel less like I'm doing something wrong when I'm overwhelmed.)
Is this normal?
Is there anything I can do about it?
Should I have taken the time used to write this post to clear some of my backlog?
Should I have written a post about something less navel-gazing?
What did I do with all my free time in 2004-6 when I had 10,000 fewer emails per year to deal with?

How many barleycorn in a giant slipper?

2011-10-23T10:03:00.000+01:00

On Thursday this week you, as I, may have awoken to giant slipper news. The story, that Tom Boddingham ordered a size 14.5 slipper but was sent a size 1,450 after manufacturers failed to spot a decimal point in his order, was widely reported. I first saw it on the Telegraph site but they've done their Ministry of Truth Records Department thing and now the link leads to a story telling you about the hoax so here's a link to the same story at the Mirror: "Gigantic XXXXXXXXXXXXXXXXL slipper delivered to man who ordered a size 14.5 but got a size 1,450". The Mirror story also guesses a number of X's but I don't recall this from the original so will ignore it as the Mirror's addition. This tells us, in a 'quote' from Mr. Boddingham, that the slipper "measures 210 x 130 x 65cms".

The original story said that the factory in China thought the shoe was for a shop display, so thought nothing of the strange order. It does not explain why a shop display would order a 7ft slipper using shoe size terminology or how the extra materials or shipping costs were met.

There's a proper bit of journalism over at the Guardian, "Was the 7 foot 'monster slipper' really a PR stunt?", which covers much of what is wrong with the article. The PR company say the story was from the retailer and they assume it was true. The retailer said it's definitely true. This also has some discussion of Joseph Jennings, who apparently works for the company, and his visual similarity to Mr. Boddingham, pictured with the giant slipper article.

I feel slightly strange about the idea that missing the decimal point out of 14.5 would naturally lead to 1450. I suppose it might be that the ordering system always takes two decimal places and it was really 14.50 that was ordered. I don't know why failing to spot a decimal point has to be a "translation error" by the Chinese, and not just an overlooking. This might be reasonable as a translation error if we remember that different cultures use decimal and thousands markers differently, with some using comma for the decimal mark and dot for the thousands separator (not China, though). Even so, the dot isn't three places from the end. In China, according to Wikipedia (so it must be true) the dot is sometimes placed every four digits, but no mention of two.

Anyway, happy this is a hoax and ready to leave it I idly decided to check the numbers. According to Wikipedia, UK shoe size is based on the length of the "last", the foot-shaped template over which the shoe is manufactured, measured in barleycorn, a basic Anglo-Saxon unit used as the legal definition of the inch in many medieval laws in England and Wales. There is no precise relation between the last and the eventual shoe size (this is why two styles of shoe claiming to be the same size can be so different and why I can't tell if I'm a 14 or 15; a real pain because shops don't generally stock those sizes but I don't know which to order online) but we can safely assume the size is similar to that of the eventual shoe.

Wikipedia gives UK adult shoe size as 3 x the length of the last in inches - 25. A barleycorn is about one third of an inch, which is where the 3 comes from, and the -25 takes out the child sizes. Adult size one is then based on a last measuring 26 barleycorn or a bit under 9 inches.

Size 14.5, then, would be based on a last measuring about 13 inches:
3 x n - 25 = 14.5
39.5/3 = n = about 13

Using the same formula, size 1450 would be based on a last of 1475 barleycorn, which is about 492 inches, or 41ft:
3 x n - 25 = 1450
1475/3 = n = about 492

The article claims the giant slipper is 210cm long, which is a little under 7ft. The funny thing is that the 14.5->145 error (which seems, to me, more natural) would give a last of almost 5ft, a more reasonable size for a man-sized slipper.
3 x n - 25 = 145
170/3 = n = about 57

Of course, the reason I find this sort of thing interesting is the willingness newspapers have to report stories like this without fact-checking or, seemingly, common sense-applying. I'm also annoyed that they don't bother to check even the most checkable facts - the arithmetic. That the arithmetic doesn't add up, given all else that is wrong with the story, shouldn't really surprise me, but still I can't help feel that if you're going to write this up then two minutes with a calculator would give you a flaw, even if no other alarms were raised.

Experimental checking

2011-10-21T17:03:00.000+01:00

Yesterday I mentioned the importance of experimentally checking mathematical results in a piece over at Second Rate Minds. You may know that Second Rate Minds is the writing exercise blog on which Samuel Hansen and I take turns writing and editing each others pieces while we enjoy playing with different styles. This time I decided to try to find a press release in the morning and have it written up into a piece within the day (the transatlantic time difference and working hours of my editor notwithstanding). From my experience covering mathematics in the news on the Math/Maths Podcast, I am aware that time and again we see the same story almost word-for-word on different websites, all sourced from the same press release. I didn't just want to repeat the press release, but tried to give it my own spin. The result I found confirmed an assumption behind diffusion and I wrote of the importance of work that relates the assumptions behind computations to the scenario being modelled.

Also this week, I arrived home from the IMA East Midlands Branch talk and wrote an account of this over on the IMA Blog "IMA Maths Blogger". In this talk Prof Chris Linton at Loughborough gave an engaging account of the discovery of Neptune, which was found following a mathematical prediction based on irregularities in the orbit of Uranus. At the end, Chris also mentioned a prediction of an extra planet, Vulcan, used to attempt to explain a discrepancy in the orbit of Mercury. In fact Mercury's orbit was different from the predictions made by Newton's Laws because of a limitation of those laws in describing physical reality and one of the first tests of Einstein's relativity was that it predicted the orbit of Mercury correctly. Given the recent Nobel Prize awarded to Saul Perlmutter, Brian Schmidt and Adam Riess "for the discovery of the accelerating expansion of the Universe through observations of distant supernovae", observations that led to the theory of dark energy, Chris left us with the thought: is dark energy a Neptune situation (something out there we can't yet see) or a Vulcan situation (a limitation of current theory)?

This morning I listened to an interview with Brian Schmidt on the Pod Delusion in which he described the process of discovering the unexpected result. Attempting to check whether data on supernovae showed the universe expanding at a constant rate or slowing down, Schmidt explained they found something altogether more unexpected:

That data showed, jeez, the universe wasn't slowing down at all, it was speeding up. And so that was a real crazy thing to be confronted with. It didn't make a lot of sense. It seemed just impossible so that was a pretty scary time when we first saw that result ... Initially you just start looking for problems and checking and rechecking everything but after a while you've done everything you can and nothing's obviously wrong so we opened it up to the team and said 'okay guys, we've got this crazy result. Any test you want to us to do we'll test. We think we've tested them all at this point but anything you want to do'. And the group came up with all sorts of things to think about so we went through and worked more but at some point it slowly sunk in that the universal acceleration that we were seeing just wasn't going to go away. So it took a few months but we did everything we can several times, had several people do it, and everyone just got the same answer.

Imagine my surprise later on today when I heard the same story again, this time from Marcus du Sautoy on his BBC documentary on the recent 'faster than light' neutrino discovery. Talking about research which appears to show neutrinos travelling fractionally faster than the speed of light, Marcus said:

Under our current understanding of the universe, this just isn't possible. The researchers themselves were pretty shocked by the results. They spent many months looking for mistakes. They brought in outside experts. They pored over the figures hundreds of times, searching for an error ... but they couldn't find any mistakes, so they decided to publish.

Of course, the first result has led to major developments in astrophysics over the last decade, while the later remains to be verified. Still, when you hear about teams rushing to be the first to publish some result, and when people seemed so quick to dismiss the neutrino result, it's quite striking to hear how long the original researchers spent privately checking their results.

I think this checking of observations against theory - confirming a theory, rejecting one or finding its limits - and the process behind doing so is interesting and points to the importance of relating your theory back to the real world context it is modelling. You might justify the theory or you might not. Either way, who knows, you may discover something remarkable.

Least world records

2011-10-18T09:00:00.000+01:00

This morning I saw a tweet from Tony Mann about Berry's Paradox, formulated by Tony as "The smallest integer not identifiable in a tweet". (A paradox, of course, because that phrase identifies a specific integer.)

This reminds me that I have noticed a few times recently people online reciting the joke that goes like: "I hold the world record (jointly) for least world records (this one)". (Here's an arbitrary example found through Twitter search.)

Accept for the moment that such a record exists. Then someone who held one world record for something else (most socks being worn by people spinning plates in a leisure centre, or something) would also jointly hold one world record, so would share the world record for least, so would hold two, so wouldn't share the record...

Second-Rate Minds: my second post

2011-10-09T15:03:00.000+01:00

I just published my second post over at Second-Rate Minds, the mathematical writing blog launched by Samuel Hansen and I back in August. This is a comment/review piece about my reading of G.H. Hardy's influential 1940 essay A Mathematicians Apology. You may remember we took the name of the blog Second-Rate Minds from a quote from the Apology. As an attempt to be provocative, the piece is entitled: 'Hardy’s Apology: what’s to dislike?'

Sarah

2011-10-03T09:33:00.000+01:00

It has been nearly a month since I posted here. Sorry about that. My friend Sarah Shepherd died last month. I expect many people reading this blog will know Sarah for her work on iSquared Magazine or perhaps you'll have heard Sarah as my guest on the maths news episodes of the Travels in a Mathematical World Podcast.

A fund is open in Sarah's memory in aid of Rethink. Please consider donating to this.

Twitter 'worse at counting than hyenas'

2011-09-09T14:34:00.000+01:00

On twitter.com a tweet will have listed under it a statement like: "Retweeted by Jim and n others".
I've noticed for a while now that the value of n seems incorrect. Idly, I asked on Twitter if people have noticed this.

@IgorCarron said that "Jim plus n others" means there should be n+1 people in total. This is what I would expect, given my fragile grasp of the English language, but I suspect this is not what is happening. I think n is actually the number of retweeters including Jim, not excluding him as the wording would suggest. Then the correct form should be "Retweeted by Jim and (n-1) others" or "Retweeted by n people including Jim".

My cynical brain says people would object to and complain about a lower number being displayed so Twitter would put the higher number, but then why not use the "n including" language, which has the virtue of being correct?

@christianp has seen "and others" when only one person has retweeted a message! @AlexHymers reported having seen inconsistencies when only two people have retweeted a message. If the problem is at the n=1 end of the scale only, that is interesting. If this were a poorly coded student project I might suggest the error is in the part of the code that decides whether to pluralise the "other(s)". (Of course, this is a major international company and not some poorly tested bit of code...)

With an sensible practical mindset, @relinde suggested an experiment: "Ask two people to retweet your message, and see if it says 'by Jim & 1 other' or 'by Jim & 2 others'. I think the first."

I sent a message (Tweet 1) to @relinde and @christianp asking them to ReTweet (RT) my message. @christianp did so. Impatient, I tweeted out generally for one person to RT the message (Tweet 2) giving a link to Tweet 1. @AlexHymers retweeted Tweet 1. Then @relinde did as well. My impatience had got me three RTs. The result? Tweet 1 was "Retweeted by relinde and 3 others". The wording suggests four, when only three had retweeted it.

However, at the same time two users, @OnThisDayinMath and @englishblonde had, misunderstanding the instruction, retweeted Tweet 2. This now displayed "Retweeted by englishblonde and 1 other". The wording here was correct: 2 retweets.

Remembering hyenas and monkeys can count to 3, is it the case that Twitter can count reliably only as far as 2?

One final note: @timtfj says "n in 'retweeted by A and n others' seems to vary between meaning n and n-1, but always to be an integer". Does anyone have a counterexample?

Nottingham Maths Jam on BBC Radio Nottingham

2011-09-07T17:59:00.000+01:00

At the August Maths Jam, we in Nottingham were joined by a reporter from BBC Radio Nottingham's breakfast show, who wanted to know what we were all about. A feature was broadcast last Friday. You can listen to this for a very limited time at: Andy Whittaker, Friday 2nd September. The Maths Jam section starts at 1 hour 56 minutes and lasts for about 3 minutes.

A brisk trade in souvenir mugs

2011-09-01T16:03:00.000+01:00

Readers of this blog may be aware that my local maths history comes much in the form of George Green, a local miller and mathematician (indeed it is a George Green mug I am drinking from in the Math/Maths Podcast album art). I noticed the following passage in the introduction to the Proceedings of the 1990 Undergraduate Mathematics Teaching Conference written by Ken Houston:

George Green (1793-1841) who discovered "Green's Theorem" was a miller in the village of Sneinton (now part of the City of Nottingham). Recently the windmill has been restored to working order and a visitor's centre has been built beside it. Our conference trip was a visit to Green's windmill and the mill centre. After our tour of the windmill and the centre there was a brisk trade in souvenir mugs and no doubt many undergraduate students of vector analysis will hear about Green's mill next session.

Unexpected GCSE Success at Your Local School

2011-08-27T11:48:00.000+01:00

There were jubilant scenes yesterday (Thursday) with the long wait finally over for students across Your Town who received their GCSE results. Students at Your Local School are basking in glory after achieving set of eye-catching results.

Boys bucked the national trend, performing better than girls by 5 per cent.

Top performer at Your Local School was teenager Top Pupil (16), who acheived a clean-sweep of A* grades, including Maths and English. She said "It's hard to describe the feeling really. It's fantastic."

Now Top, who hopes to become a vet, will go to Your Local College to study for A Levels. She also plays the clarinet, and has recently been on tour with the Country Youth Orchestra.

At Your Local School, a stunning 92 per cent of students picked up five or more A* to C marks, hot on the heels of last week’s 96 per cent A-level pass rate.

These results are among the best in the country.

Head teacher Robert Teacher, due to retire after today’s results and 18 years in charge, was buoyed by the students’ success, saying: “I’m very pleased. The pressure on them now is far greater than it ever used to be since they are under pressure all the time, but these are the best results we’ve ever had."

The national A*-C pass rate rose for the 23rd year in a row, figures show.

Related stories:
'Record numbers' of A* grades across County
Toddler gets A* in GCSE Maths

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Second-Rate Minds

2011-08-24T12:09:00.000+01:00

For writing practice, Samuel Hansen and I are collaborating on a new blog, Second-Rate Minds. We take the name from a quote from the beginning of A Mathematician's Apology by G.H. Hardy (1940):

There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.

We plan to alternately write short pieces on and around mathematics and edit each others writing. I wrote the first post, "Moving on a strange diagonal", a write-up of my 2010 Maths Jam Conference talk about a puzzle and my thoughts on its use in education. Expect future posts at roughly two a month. If you want to keep up with future posts there is an RSS feed and a Twitter account.

From Our Own Mathematics Correspondent

2011-08-19T11:00:00.001+01:00

You may remember I contributed a piece last month to the Pod Delusion Podcast on the unplanned impact initiative. Well, this week I've done it a second piece. This is becoming a habit.

The Pod Delusion describes itself as

a weekly news magazine podcast about interesting things. From politics, to science to culture and philosophy, it's commentary from a secular, rationalist, skeptical, somewhat lefty-liberal, sort of perspective. A bit like From Our Own Correspondent but with more jokes.

This time my item is about the recent report of the Vorderman taskforce into mathematics education. You may remember I wrote a recent blog post on this topic, 'People may not like Vorderman, but her report?' This piece covers similar ground but in audio and with a couple of days more experience. Plus you can hear me make the "spelling/grammar/literature, arithmetic/algebra/mathematics" argument.

What about the rest of episode 98 (19th August 2011)?

We speak to Craig Reucassel from The Chasers about why satirists should be allowed to use Parliamentary footage, find out about our care footprints, and find out why the arms trade is like slavery (and other cheerful stuff like that).

In the introduction to my piece (starts at 08:45), host James O'Malley describes me as the Pod Delusion's "mathematics correspondent". Does that mean there'll be further contributions (and that I've been type-cast)? We'll see.

Hot research question: Do mathematicians like pizza?

2011-08-17T18:45:00.002+01:00

I took part in a fun exchange on Twitter this afternoon. I'm preserving it here because Twitter tends to lose these things.

Anyway, go and fill in Alison's survey! It really is only two questions and is just a bit of fun.

(By the way, do you remember the 2010 Pizza Hut ad campaign "People love pizza - they don't love math!"? I wonder if this is what Alison is really researching...)

ajk_44 Alison Kiddle
Thought I'd collect some data. Fill it in, feel free to share it, and I'll blog the findings if there are any. bit.ly/nuXt2i

ajk_44 Alison Kiddle
I should point out that it's a very quick survey and will probably take you less than 15 seconds to fill in. bit.ly/nuXt2i

ColinTheMathmo Colin Wright
I've filled in @ajk_44's survey - it took less than 15 seconds. bit.ly/nuXt2i

Tony_Mann Tony Mann
Took me longer - Q1 is complicated. RT @ColinTheMathmo I've filled in @ajk_44's survey - it took less than 15 seconds. bit.ly/nuXt2i

peterrowlett Peter Rowlett
.@Tony_Mann @ColinTheMathmo @ajk_44 I agree with Tony. Probably took me 20 seconds.

ajk_44 Alison Kiddle
@peterrowlett @Tony_Mann I owe you each 5 seconds then, I'm sorry for the false advertising. And thanks for filling it in!

plusmathsorg Plus Magazine
@ajk_44 I think the results will be ground-breaking!

ajk_44 Alison Kiddle
@plusmathsorg early indications are that almost everyone likes pizza, and that the vast majority of people are mathematicians.

peterrowlett Peter Rowlett
2 question, 15 sec survey. Please fill in bit.ly/nuXt2i RT @ajk_44: early indications: vast majority of people are mathematicians.

Tony_Mann Tony Mann
@peterrowlett @ajk44 Majority of respondents may be mathematicians but survey doesn't ask if they are people rather than, say, hyenas

ajk_44 Alison Kiddle
@Tony_Mann drat. It's too late for me to add a "What species are you" question. I don't think I'll be able to get any meaningful results.

peterrowlett Peter Rowlett
"Academic questions @ajk_44's research findings" RT @Tony_Mann: Majority of respondents may be ... but survey doesn't ask if they are people

plusmathsorg Plus Magazine
Ground breaking study finds that most people are mathematicians (and like pizza) bit.ly/nuXt2i

peterrowlett Peter Rowlett
Now the media present @ajk_44's initial result as final before all data collected! Terrible! RT @plusmathsorg Ground breaking study finds...

ajk_44 Alison Kiddle
I'd intended to use Twitter for data gathering for my Masters thesis next year. This afternoon may have damaged my academic credibility :-)

plusmathsorg Plus Magazine
@peterrowlett @ajk_44 We are acting in the public interest.

Tony_Mann Tony Mann
@PeterRowlett Unfair! You put out press release tweet reporting hearsay @ajk_44's results and then blame media @plusmathsorg for reporting

peterrowlett Peter Rowlett
@Tony_Mann I don't think it's for @ajk_44 & I to communicate findings clearly. It's up to the media @plusmathsorg to understand researchers.

Update (19/08/11):

plusmathsorg Plus Magazine
@peterrowlett @Tony_Mann @ajk_44 If public are all mathematicians they must know before it's too late. Waiting for end of study is unethical

Tony_Mann Tony Mann
.@plusmathsorg @peterrowlett Since when did press care about ethics? Obviously study has Research Ethics Committee approval so up to @ajk_44

ajk_44 Alison Kiddle
@Tony_Mann @plusmathsorg @peterrowlett what are ethics?

peterrowlett Peter Rowlett
@ajk_44 wait, what ARE you doing with all this sensitive, lucrative pizza/mathematician data?

ajk_44 Alison Kiddle
@peterrowlett creating a business plan to open a multi-million pound mathematical pizza shop :-)

peterrowlett Peter Rowlett
Thought I was supporting science but @ajk_44 is collecting data for a multi-million £ maths pizza shop! Don't fill in bit.ly/nuXt2i !

Tony_Mann Tony Mann
@ajk_44 @peterrowlett since your data are public everyone else will be doing business plans too so better rush

People may not like Vorderman, but her report?

2011-08-14T09:30:00.000+01:00

The Conservative Party have published a report, "A world-class mathematics education for ALL our young people". The initial reaction I saw on Twitter was very negative, entirely directed to Carol Vorderman's personality characteristics and her qualification to chair such a study. On Monday when I tweeted a link to the report @slewth asked, "I mis-read that as the Voldermort report. Did I do wrong?" My reply: "Indistinguishable, from the Twitter reaction I've seen". But what about what is actually in the report?

There are positive responses to this report from representatives of the Advisory Committee on Mathematics Education (ACME), Mathematics in Education and Industry (MEI), Confederation of British Industry (CBI) & the Wellcome Trust given in the Conservative website news story announcing the publication.

There is also a positive response from the Royal Society on its website, "Royal Society response to the Vorderman report on mathematics education". The Institute of Mathematics and its Applications (IMA) published a press release, "The Vorderman report recognising mathematics is critically important", responding positively. The IMA Twitter feed (to which I contribute but not this post) said the report "highlights importance of @IMAmaths CMath and CMathTeach qualifications (pg. 84)". The Royal Statistical Society published a statement, "Britain will benefit from moves to boost young people's ability with numbers, says Royal Statistical Society", again "warmly welcoming" the report.

There are certainly others, and I don't propose a complete collection, the point is I haven't been able to find an organisation saying negative things. I spoke to Martin Smith, who works for the Advisory Committee for Mathematics Education (ACME), via Twitter and he agreed, "Nope! Messages are very similar to ACME". Although the name at the top of the report is Carol Vorderman, there are four group members and two research assistants listed. The two group members and one research assistant that I know I respect very well.

Still, a lot of the chatter I've seen on Twitter has been negative.

A lot is made of the qualifications of Carol Vorderman to carry out the investigation. The Times Higher Education refers to the taskforce "led by TV presenter Carol Vorderman" and the Sun, with characteristic charm, refers to "TV sums whiz Carol Vorderman". Both seem to be denigrating (or perhaps I'm just reading that into it).

I don't like when people say she's "a brilliant mathematician". I don't know what she's like at mathematics (is there some evidence of this I'm missing?). I know she's said to be very quick at mental arithmetic (accidentally confessing to not watching Countdown, oops) and I think people saying she's a mathematician are misunderstanding what mathematics is.

Much is made of her third class engineering degree. I don't think it's fair to say that what qualification a person did over 30 years ago should have any effect on what they do now. People are also critical of products she endorses.

Still, not much of this has anything to do with the report or its recommendations. I'm not interested in Carol Vorderman as a person. I'm interested in content of the report and its recommendations, and more particularly, what Government will do about them. (There's an ambiguity there: the report was commissioned for the Conservative Party when in opposition, so it isn't a report of this coalition government.)

Put up as key headlines by the Conservatives in their news release about this:
- report argues: "A child's mathematical 'career' is effectively determined by the age of 11";
- recommends compulsory maths in some form until the age of 18, replacing the present GCSE maths system with one offering two GCSEs and improving the mathematics subject knowledge and confidence of primary school teachers and new trainees.

Notes from the executive summary (incl. probable omissions and errors):

Policy and regulation:
- define maths as 'subject of critical importance status' & exempt it from statutory blanket regulations which are applied across all subjects;
- involve higher & further education and employers in school-level education;
- greater attention paid to students who "are deemed to 'fail'", system should account for different needs of these students;
- relax regulation to allow for innovative practice;
- some form of mathematics education for all students to 18, "merely to bring us into line with the rest of the developed world (with whom we compete economically)";
- "major changes" in the working methods of Ofqual and Ofsted;
- exam boards to act collectively.

Curriculum and assessment:
- as well as daily maths lessons, primary school children should practice number work in other areas of their daily routine;
- financial numeracy within the curriculum;
- end Key Stage 2 National Test (SAT) in its current form as it is a bureaucratic system of accountability which is detrimental to children’s mathematical education;
- the new National Curriculum should not predetermine teaching methods or the chronology of learning;
- the present system of one GCSE is not suitable for such a diverse cohort, offer two (as exists for English Language and English Literature);
- reward students who achieve a higher standard in a smaller area of the curriculum, rather than a low standard across a much wider curriculum;
- no changes to present AS and A levels, it is not intended that all students take AS and A level mathematics;
- support FMSP.

Teachers:
- improve subject knowledge and confidence of primary school teachers and new trainees (including requiring B at GCSE for new primary school initial teacher training);
- status of secondary specialist mathematics teacher better defined, ring-fence funding for CPD of these teachers;
- review teacher CPD to ensure it is cost-effective.

Parents:
- help offered to parents with their maths skills.

Universities:
- cap on undergraduate numbers in mathematics is in conflict with need for more specialist mathematics teachers so Government inter-departmental cooperation is needed, calls for university mathematics departments to "be allowed to take on all suitably qualified school leavers";
- many other university departments (incl. STEM, economics, social sciences, nursing, computer science "and many more") should return to requiring A level mathematics or increase their mathematics requirement.

Even if you don't read the report there's an interesting diagram on page 11 (page 19 of the electronic document) which might be worth looking at.

So what do people think? I've seen a few newspaper articles that basically report the key recommendations as the Conservative website does. I've seen a few blog posts agreeing with the recommendations, for example this post "Numeracy" by Athene Donald is being passed around Twitter. Anthony Seldon, Master of Wellington College, writes an opinion piece in the Independent: "A maths challenge we must answer".

What about dissenting voices? These are few and far between, as far as I can see. Kevin Houston blogs to say the main problem with the two headline recommendations about compulsory maths to 18 and two types of GCSE: shortage of teachers. He sees the latter of these as more likely, as these students are already being taught mathematics but wonders where the extra teachers will come from to teach the extra students from 16-18. However, the report says both must go together, and blames in part the lack of these for the shortage of teachers and lower skills of primary teachers that are causing many of the problems highlighted. Kevin's post has an interesting analogy starting "What would I have recommended?" that is worth reading.

A blog post at fullfact.org questions the reports use of the OECD data on international comparisons of mathematics education. The blog Political Scrapbook points out that the report praises private tuition in other countries and is concerned about the conflict of interest because Carol runs an online private tuition company.

I asked for views on Twitter or Google+ on the actual report content, rather than Carol's credentials. Not many were forthcoming. Sharon Evans would like to see the report recommendations "work out okay" but is concerned that governments tend to change policy too often. Sharon says, "What is needed is sustainment of policy so that things have a chance to settle down as change cannot happen or be measurable overnight and we shouldn't expect it to be." Peter Price, writing as an outsider (he's lived in Australia since he was 13), points out that many similar issues are faced in Australia and agrees with the recommendations "almost 100%". He highlights recommendations around maths education for would-be Primary school teachers, bureaucratic monitoring of the system and resultant so-called 'teaching to the test' and he regards "idea that all school leavers should have completed mathematics study to 18 years" as "pretty essential".

So what will Government do to act on the report and its recommendations? Only time will tell.

Relatively Prime is funded

2011-08-03T21:59:00.000+01:00

Well, incredibly, Samuel Hansen has done it - Relatively Prime will be funded in six hours, having now crossed the minimum funding limit. (If you want your name on the list of funders you can still donate $5 by 11:13pm EDT and every little extra will help.)

Anyway, moments after the bid came in that pushed Relatively Prime over the magic $8,000 I spoke to Samuel, who broke through his shock to give a hearty thanks to everyone who had supported him. You can listen to this recording at acmescience.com as "Relatively Prime is Funded":

So after a rather long wait everyone came through at the death and the ACMEScience Kickstarter project Relatively Prime got funded. I want to thank all of you who helped make this dream of mine a reality. Right after the pledge that knocked us over the edge happened I talked with my Math/Maths co-host Peter Rowlett to talk about how it felt. Listen to how happy I sound.

Next time you wake up, Relatively Prime will be a missed opportunity... unless you act! 5 key facts

2011-08-03T09:25:00.001+01:00

This is the last opportunity you have to support Relatively Prime. Five key facts:

Relatively Prime will be worth listening to.
Relatively Prime will be a series of eight hour long podcasts to tell stories from the world of mathematics by Samuel Hansen. Read Hints about Relatively Prime, where I have collected the hints Samuel has given about the stories he would like to tell.
Relatively Prime is different from all the mathematics podcasts you have ever heard.
Samuel's ambition for this project goes beyond any amateur endeavour you are used to (I say this as an amateur podcaster). Listen to five minutes of me quizzing Samuel about the project.
If Relatively Prime doesn't raise $8,000 it won't happen.
As I write, 125 wonderful people and me have donated $5,448, which is really amazing but falls short of the target.
The way Kickstarter works, if Relatively Prime fails to achieve the $8,000 target IT GETS NOTHING. This isn't a pledge-drive with a vague target - if Relatively Prime doesn't reach its target it will fail.
As I write, Relatively Prime needs $2552 in the next 18 hours. Just looking at people who've clicked the bit.ly link (not those who've visited the link directly) there are currently 2,838 clicks. If they had all left a dollar Relatively Prime would be funded by now!
Supporting Relatively Prime is quick and easy.
Payment is through Amazon, so if you've used Amazon you don't need to worry about giving another site your credit card details, and Amazon takes care of the currency exchange.
Relatively Prime is good for mathematics communication.
Samuel Hansen is a budding mathematics communicator. During his masters degree he has been engaged with such activities as the Strongly Connected Components mathematics interview show, the Combinations and Permutations comedic mathematics chat show, the Math/Maths Podcast news/current affairs show, the Math/Maths Week 2010 public lecture tour of the UK and the Math/Maths History Tour of Nottingham series of videos. Now he has graduated he is looking for his place in the world and Relatively Prime will give the world the opportunity to capture his enthusiasm and talent for the cause of mathematics communication.
You know how the Fields medal is awarded "in recognition of distinguished research but also to encourage further effort"? Well Relatively Prime is our opportunity to do the same for Samuel - to recognise his work and to encourage further effort from someone with potential.
It will also be good to think that we live in a world where good quality mathematics communication is valued.

Reading list:

Peter Rowlett: Why I supported Relatively Prime and you should too;
Katie Steckles: Stories worth telling are... worth a few dollars, surely? ;
Plus Magazine: Relatively Prime: stories from the mathematical domain;
Dave Gale: I'm supporting Relatively Prime;
Who've I missed? Oh, that must be enough to be going on with!
Look at some of the things people have been saying on Twitter about this (no login required).

Here's an indicator of progress:

On communication and Google+

2011-07-30T12:20:00.000+01:00

I am bad at communication. Here is what I have observed:

I reply well when messages are short, informal and don't require much structure or thought. Emails with some people are easy, if I feel like we are on the same wavelength, can speak briefly and to the point, use shorthand we both understand etc. I reply quickly to Sam, my podcast collaborator, with whom I have email exchanges like: "Saturday?" "Yep." "7pm my time?" "Sure." Twitter also fits into this category. Short, informal messages with an interface that works well on my phone are easy to reply to.

I don't reply well to more in depth messages. It's not that I have a problem with writing in sentences and thinking complex thoughts, it's mostly a question of immediacy. I can knock out a quick email easily on my phone on the bus, or as a quick aside to the piece of work I am really doing on my computer. If I have to think about a reply, it goes on my to do pile, which is a strange and disturbing realm from which nothing returns. Emails sink down my inbox screen with alarming speed. Following recent unavailability, I have fallen far behind. Work days at the moment are a struggle with the most urgent work while my undealt-with email pile is fast approaching 1000. (Will it self destruct when it reaches four digits?) Having such a large, looming unknown in my life is quite disconcerting. I hope the quiet summer will give me time to catch up.

Of course, when an issue is too big for a tweet and a twitterer changes to email, they discover the forgotten realm of my inbox. If it was too big for a tweet, it is too big for a short, quick email and I've added it to the pile. (This isn't deliberate, and I'm annoyed with myself about it. But, you see, if I don't sort out this thing by tomorrow I'm going to miss that deadline...)

Where does Facebook fit? I find Facebook annoying. People send private messages which are basically like long emails but appear in a different place so I can't reply so easily. I don't find it as easy to quickly dip in and read something interesting, or engage with someone's quick message because the web interface has more junk going on and the service doesn't work so nicely on my phone. I'm fed up of meeting people and having conversations like: "You know my ?" "Really, wow, congratulations!" "What? But surely you knew? I did post it on my Facebook wall." (Yes, really.) Originally I refused to sign up to Facebook and only did so once I started working for the IMA and we were starting a group. Now I no longer work in that sort of area, should I get off Facebook? I'm really tempted.

Into this picture steps Google+. Again I resisted the first attempts to get me on it but I've been using it for three weeks now. I sort of like it. I don't have to worry about abbreviating myself to 140 characters like on Twitter but there is still an expectation of short, quick updates. I'm not constantly asked to play games and other stuff. And people can reply in a way that keeps the conversation together better than Twitter. Still, there's something about it that isn't quite clicking with me. It may be the lack of people on there, which will be fixed in time. I'm still not quite sure.

Looking for a place for Google+ in this mess of my online communications feels a bit like having a problem at one end and having a solution at the other and trying to fit the one to the other even though they don't go together. Still, Christian Perfect suggested Google+ was a better place for conversations around the Math/Maths Podcast. I regularly ask on Twitter 'What's happened in your mathematical world this week?' Christian is suggesting I could collect the replies more sensibly on Google+. Further than this, I wondered if I might put up one or two stories and see if anyone had any comments on them that I could collect that way.

So I'm going to give it a try. Take a look at this week's messages on my Google+ page - one about The Code and maths communication, the other asking for news from your mathematical week. Now, I'm off to tweet that I put up a new blog post...

Hints about Relatively Prime

2011-07-27T09:09:00.004+01:00

Although we all know Samuel Hansen will do a fantastic job telling stories behind mathematics, provided you donate some money to help him do so, we don't entirely know what those stories will be. Here are a list of tweets I've seen on Samuel's Twitter stream about this, giving hints.

help me tell people how crickets led to a better understanding of Kevin Bacon through math

Why does it seems that 20% of your friends get you 80% of your news?

Can slime molds make Steiner trees?

Networks are the basis of our social lives & what I'm trying to leverage to support my Kickstarter Relatively Prime

True story: It take 362 pages to prove 1+1=2. Find out more by Supporting the Relatively Prime Kickstarter.

Can a war over a math discovery make a country to fall years behind in science?

Ever wonder what how a river and logic could both lead to the same mathematical discovery?

Wondering if you can musically represent a function? Support Relatively Prime and I will have the chance to answer

Parallel lines intersect at exactly two points! Find out why this is true by supporting Relatively Prime.

The shape of the Internet is hyperbolic. And if you want to know why support my kickstarter Relatively Prime

Plus there's the original hint on the Kickstarter page:

is it true that you are only 7 seven handshakes from the President, what exactly is a micromort, and how did 39 people commenting on a blog manage to prove a deep theorem ... With each episode structured around topics such as: The Shape of Things, Risk, and Calculus Wars, Relatively Prime will illuminate each area by delving into the history, applications, and people that underlie the subject that is the foundation of all science

So if you haven't got the message yet, find out about these stories by supporting Relatively Prime. My previous post focused on ways you can help as well as donating, including a ready-written blog post for you to put on your blog.

Relatively Prime is failing; what you can do to help

2011-07-26T08:58:00.010+01:00

Trying to study mathematics without the human stories is like reading a typed transcript of a Rolling Stones concert. The Relatively Prime project will throw the mathematics television out of the hotel window.

On Friday as I was going to bed I sent a message to Samuel Hansen, try to think of anything we could do to promote Relatively Prime on the Math/Maths podcast this week. By Saturday he had five people who had sent him audio recordings of their reasons for supporting, which he had edited into a 1 min advert for the Kickstarter fundraising project (the quote at the top of this article is from one of those funders). We then had a chat in which I asked Samuel about the project, what sorts of stories he was going to tell, what made it different from other podcasts he does. The result is in the latest Math/Maths Podcast 57 and has been released as an 8 minute audio piece through the acmescience podcasts. Listen to the funders' reasons and our conversation here.

I've become quite vexed with the process of promoting this. If you look at Samuel's twitter stream you can see him tweeting intriguing questions that will be answered by Relatively Prime. A sample of three:

Can a war over a math discovery make a country to fall years behind in science?...Can slime molds make Steiner trees? I'll tell you if you support my Kickstarter Relatively Prime...help me tell people how crickets led to a better understanding of Kevin Bacon through math

I thought this was a neat idea and ReTweeted these when I saw them. This, and other marketing Samuel is doing, is attracting interest and, as the graph of donations, cumulative amount and time shows, there is a steady increase but it simply isn't increasing quickly enough (click to enlarge).

It amazes me that 93 people have so far donated $3,793, but we have a problem. If the whole amount isn't raised, all donations are cancelled. That's the way Kickstarter works. So it's a question of reaching new audiences. Samuel can keep tweeting, and I can keep tweeting on his behalf, but the message isn't getting further out. I already posted on this blog about the project - "Why I supported Relatively Prime and you should too" - and according to Blogger some 250 people have viewed that post. So I'm running out of new audiences to reach.

This is where you come in. If you haven't donated to Relatively Prime, please consider chipping in some money. Small amounts sum to larger amounts, so even a small amount will help. There are only eight days to go.

If you have donated, please have a think - is there anything you can do to help promote the project. Post a message on whichever social networks you use. Put a message on your blog. It doesn't have to be as elaborate as this one! Here's some text you could use for a quick blog post:

Relatively Prime: Stories from the Mathematical Domain

Relatively Prime will be an 8 episode audio podcast featuring stories from the world of mathematics. Tackling questions like: is it true that you are only 7 seven handshakes from the President, what exactly is a micromort, and how did 39 people commenting on a blog manage to prove a deep theorem. Relatively Prime will feature interviews with leaders of mathematics, as well as the unsung foot soldiers that push the mathematical machine forward. With each episode structured around topics such as: The Shape of Things, Risk, and Calculus Wars, Relatively Prime will illuminate each area by delving into the history, applications, and people that underlie the subject that is the foundation of all science.

I think this could really be an amazing project, but it can only happen with your support. So please, if you can, support it financially, or please twitter, tumblr, reddit, blog, or any other thing about it - you can use the nice link http://bit.ly/relprime

Please just take that block of text - title and 2 paragraphs - and paste it on your own blog. It should only take you seconds and by doing so you will help break the message out of the same circles and reach new, interested people.

Plus, if you have any ability to get something written or an audio interview released though any sort of outlet in the next week please contact Samuel Hansen and give him the opportunity to talk about his project. You get some interesting content for your podcast/radio show/magazine/whatever and you'll be helping Relatively Prime.

The unplanned impact of mathematics

2011-07-13T18:01:00.033+01:00

Time and again, pure mathematics displays an astonishing quality. A piece of mathematics is developed (or discovered) by a mathematician who is, often, following his or her curiosity without a plan for meeting some identified need or application. Then, later, perhaps decades or centuries later, this mathematics fits perfectly into some need or application.

I have recently been interested in this idea, particularly as research funding bodies have been increasingly asking researchers to predict the impact of their research before it is funded, and research quality is being measured partly by its short term impact. On this issue I spoke to more and more research mathematicians and a pattern started to emerge: mathematicians tend to think of this aspect of mathematics as axiomatic, and generally come up with one of the same three examples to justify this position - number theory in cryptography, logic in computing and complex numbers in fluid mechanics.

This made me a little concerned. If every research mathematician you speak to comes up with the same few examples, is the story going to be sufficiently convincing?

I decided there must be mathematicians out there who have less well known examples of mathematics having impact that could not have been planned by the original discoverer - unplanned impact of mathematics. This might be mathematics pursued for curiosities sake, or that had a direct application and was later found to have a different, unexpected one.

Acting in my position as a member of the Council of the British Society for the History of Mathematics (BSHM), I put out a call for further examples. The BSHM has charitable aims around promoting awareness, knowledge and study of the history of mathematics. I spotted a win-win: BSHM could raise awareness of the history of our subject and, in turn, provide researchers with a greater range of examples to call on.

This began a slightly unreal process, particularly when one of my contributors, Edmund Harriss, was able to put me in touch with Nature, who were interested in taking a set of seven contributions.

The field of topology provides an illustrative example. This was started by Euler and studied for 250 years as a purely theoretical discipline before, in the last two decades, finding applications as diverse – and alien to Euler – as DNA, galaxy formation and robotics. These applications rely on the 250 years of pure research, but those advances would not have been made if the researchers had to justify the planned impact before studying their mathematics.

In technology, quaternions, a 19th century discovery which seemed to have no practical value, have turned out to be invaluable to the 21st century computer games industry, while work on the best way to stack oranges started by Kepler in 1611 is essential to modern telecommunications.

Einstein’s theory of relativity, which seemed to come as a spark of genius from nowhere, nevertheless drew on abstract geometry developed half a century earlier. Fourier’s theory of vibrating strings, via very abstract mathematics in the 20th century, has now yielded new insights into quantum physics.

Gambling on 16th century dice games led to a discovery in mathematical probability that is crucial to the insurance industry, while a recent insight into a quantum theory thought experiment has unexpectedly found applications in the outbreak of viral disease and the risks associated with stock market volatility.

These seven examples, contributed by Julia Collins (topology), Mark McCartney and Tony Mann (quarternions), Edmund Harriss (stacking oranges), Graham Hoare (Einstein's geometry), Chris Linton (Fourier analysis), Juan Parrondo and Noel-Ann Bradshaw (Parrondo's paradox) and me (dice games), appear in the 14th July 2011 issue of Nature. Go and get a copy and see for yourself!

I'd still like to hear more examples of mathematics displaying this astonishing quality, and I am exploring options to distribute these. You can send me yours - the details are on the BSHM website.

Update 22:15: Link to the article in Nature. Hear me talking about this on the Nature Podcast - you can access the podcast using the following player. The unplanned impact bit starts at 08:44 (though listen to the rest, of course!).

Update 15/07/11 08:20: I recorded a segment for podcast the Pod Delusion, 15th July 2011. Listen to it all, of course, but my bit starts at 19:10.

Update 18/07/11 08:36: Edmund Harriss joined Samuel Hansen and I and we spoke about The unplanned impact of mathematics for Math/Maths Podcast 56: The unplanned impact of mathematics.

Update 25/01/12: Tim Harford wrote a column in the FT on this on 24th September: New ways with old numbers (also on FT.com).

Maths at the East Midlands Big Bang Fair

2011-06-29T11:18:00.001+01:00

Recently I was invited to take a mathematical puzzles stall to the East Midlands Big Bang science fair. This took place in Nottingham yesterday. I gathered a few friends from the Nottingham MathsJam group, which I run, and we planned what we could do with a stall. We agreed a list of puzzles we could put together and run. We felt it was important to have solid, physical puzzles and games that would attract people to the stall, including making use of the floor area, as well as more advanced and intriguing items and a takeaway sheet. I wanted the takeaway sheet to provide some advice on problem solving techniques as well as some puzzles to try. There were various extra constraints as well as what we could physically make with no budget, including the difficulty of catering to the wide age range of those attending: 9 to 19!

We met a couple of weekends ago and agreed a set of puzzles, tried them on fellow MathsJammers at the monthly meeting last week and have spent the last week or so making bits and pieces ready for the fair yesterday (particular thanks in that regard are due to John Read and Kathryn Taylor). We called the stall "Solving it like a mathematician". For big, attractive, fun we had Latin squares with giant playing cards, a puzzle involving arranging tokens inside a giant circle (a hula hoop) and matchstick puzzles with giant matchsticks (bamboo canes). For hands on activity we were making Möbius strips. The more in depth tabletop exercises included: Buffon's needle for estimating pi (we got 3.78 from 141 throws); a 'wisdom of crowds' guessing how much rice is in the jar and rice on the chessboard exponential growth combo; and, the fifteen puzzle and how to tell if an arbitrary position can be solved. Each puzzle had an advice sheet and these as well as the handout are available on a page on my website.

I have been unwell recently so I took a lighter load than I might have for the day. I helped set up the stall and stayed for the first hour, in which not much was happening, then left until the afternoon. Here is a picture of the stall, ready to go but sans visitors.

After the first hour, I left the stall in the capable hands of John Read and Ian Peatfield for the morning. We had agreed a kind of shift system - I didn't want everyone arriving first thing and us all getting tired mid-afternoon. I went and found a cafe for a quiet read. When I returned after lunch Ian had finished his stint, Alex Corner and Noel France had joined John, and the stall was abuzz! Here is a photo.

Apart from the combination of bamboo cane 'matches' and plastic plate 'coins' for some of the oversized puzzles leading to a plate spinning class, everything was going as planned. Soon we were joined by Kathryn Taylor and the five of us spent the afternoon rushing around after wave-upon-wave of pupils. That every few minutes another pupil was dragged away from the stall, "put that down now, we've got to leave", by their teachers was, I think, a sign of success. Here's one more picture from the afternoon.

Overall, I am very pleased with the stall we made and the team who ran it. My first science fair and a very pleasing experience indeed. I hope some of our visitors saw some interest in mathematics and the couple of hundred who took the advice sheet might learn something about approaching problems. Now, to find somewhere to store my new 'puzzles stall kit' for next time!

Congratulations should go to David Ault and his team for organising the fair which, as far as I can tell, went very smoothly.

Developing mathematical thinking - a generational problem?

2011-06-18T10:21:00.001+01:00

We were sent a link to a blog post by Katie Steckles for the Math/Maths Podcast a couple of weeks ago. I'm preparing for the recording of episode 52 in a few hours and I thought I would share my thoughts on the topic here.

The blog post quotes another, 'The Mathematics Generation Gap'. This starts with "Profs do not know how their students were taught mathematics, what their students know, what their students don't know - and have no idea how to help their students bridge those gaps." This makes me think of the document written by MEI and published by my employer with others, "Understanding the UK Mathematics Curriculum Pre-Higher Education – a guide for Academic Members of Staff". The problem this looks to address is that "it is not always clear what mathematics content, methods and processes students will have studied (or indeed can be expected to know and understand) as they commence their university-level programmes".

However, the main thrust of the article is on what is called "The arithmetic gap": "profs over a certain age (and some immigrant profs) were drilled in mental math;... students under a certain age haven't been. Some implications of the arithmetic gap are familiar: profs who can't understand why students insist on using calculators; students who can't understand why their profs are so unreasonable. ..." The article goes on to talk about analogue clocks and even Google Maps as forming a difference in understanding and approach between students and their professors.

The blog post Katie sent a link to, titled '"The Mathematics Generation Gap"', talks about "mental arithmetic tricks". I don't want to quote the whole thing here and stop you going to read the other post so I'll take out a lot of the detail (...), but it gives an example: "to multiply any single digit number by nine, just add a zero to the end and subtract the number... Then, it's easy to generalize, 9 times any two digit number is the number with a zero attached minus the number... Then extend further ... This can be generalized further... This also leads directly to the proof..." Then we come to the main argument:

How do you discover this rule, and learn how to take it to a proof, without rote exercises that force you to search for shortcuts? I understand that the response to all of the above is to use a calculator instead, these tricks aren't needed if you have a calculator at hand, but that isn't the point. The point is that these exercises lead to additional insights, proofs, etc. and those insights are critical for more advanced insights and more complex proofs.
The inductive type reasoning that emerges from these exercises is valuable in many settings -- I'd guess learning to find patterns is a skill that is useful beyond pure mathematics -- and I worry that an over reliance on calculators will erode the development of these skills. I am absolutely convinced, for example, that forcing people to do econometric and statistical exercises by hand develops intuition that you cannot get any other way, and this is a key to moving on to doing proofs.

A related area is whether to allow use of computers for solving advanced mathematics. At work in January we ran the HE Mathematics Curriculum Summit, the report of which is now available. This included a debate on, basically, whether students should be expected to use memory, acquire subject knowledge and demonstrate technical fluency, or whether the computation part of mathematics could be left to computers, leaving the students to worry about when and why a particular calculation is used. However, the compelling arguments for me of students performing mathematics by hand there lay in understanding what a computer would be doing and what its limitations would be, whereas the arguments in the blog post seem to be that performing mental arithmetic develops other skills that a mathematical thinker ought to have.

What is my view? Certainly the point isn't finding the numbers; if it were a calculator or computer can be used for certainty. Having said that, there are other areas of mathematics that are well suited to developing this mathematical thinking. I appreciate the desire to encourage pattern searching, logical reasoning, abstraction and extension, but I'm not sure forcing students who haven't been brought up on mental arithmetic to do such tricks is a productive way of doing so. If everybody has a phone or calculator in their pocket that can solve the question in a millisecond, then forcing them to not use that device and do it by some mental trick instead is just going to put people off, I would say. Beyond this, a lot of people have a genuine anxiety, or some even a disability that can produce a panicked reaction when faced with numbers. Doing something in a non-numerical area might be much more effective. Tilings seem to be a good option, and at work we are running a workshop at Greenwich in a couple of weeks, led by Noel-Ann Bradshaw and at which Katie is a presenter, on using problems, puzzles and games to develop mathematical thinking. Areas such as these can be used to develop the same skills but don't have the hangups of mental arithmetic. In fact, I have a group of people coming round this afternoon to plan our stall at a local science fair in a couple of weeks. I intend our stall to be themed around using puzzles for developing problem solving skills. Beyond this, mental arithmetic forms part of a number of magic tricks for which a calculator would give the game away, so perhaps encouraging students to play around with this sort of thing may give a motivation to learn some mental arithmetic tricks. (Of course, this all depends what topic you are trying to teach.)

Overall, I think the battle is lost - the distinction between profs and students is not as clear as this article would have it because plenty of (and increasingly many) lecturers will have been brought up on calculators as well. I agree there are differences between how lecturers and students approach mathematics, some of which will be generational due to the increasing availability of technology; some will be due to the lecturers being unusual (perhaps more capable and motivated than average) students in their day. Still, if the aim is to develop a mathematical topic, using modern tools to make this more efficient is a good thing; if the aim is develop mathematical thinking I think there are more interesting approaches for developing the kinds of skills the blog post author would like to develop.

The blog post ends: "But what is your view on all of this?" Katie has sent me her view for the podcast and she may choose to repeat it in the comments but because I have been sent it for one purpose I don't feel I should copy it out here. Perhaps you will share your views in the comments.

Why I supported Relatively Prime and you should too

2011-06-14T10:44:00.002+01:00

Samuel Hansen is asking for people to support his crowd-sourced podcasting project Relatively Prime: Stories from the Mathematical Domain, ideally by donating some money but also by blogging, tweeting, etc. about this.

As far as I can see, Samuel is at a crossroads. He passed his Masters degree in mathematics and is about to graduate, so he is thinking about the next steps. One way lies Samuel the math communicator, the other way is Samuel who has some job in some office somewhere. Now, don't get me wrong, Samuel might make a very good 'some office worker', but I feel sure he could make a very good mathematics communicator and we need more of those.

Samuel is an enthusiastic communicator of mathematics and has the technical skills to make an excellent producer of content. You may have enjoyed what he does as my co-host on the Math/Maths Podcast, or his interview show Strongly Connected Components, or his irreverent maths chat show Combinations and Permutations. Much as these are good outputs, they all have an element of being as good as they be in spare time. I don't know about you, but of the two options on his crossroads I would like to live in a world where Samuel can take his enthusiasm and technical expertise and spend some serious time concerning himself with mathematics communication. One way that you and I can make this happen is by pitching in a few quid (or dollars, or whatever, Kickstarter seems to deal with the whole currency thing) and pushing him down the math communication fork in the road. This project, surely, can only be the start. Sure, you can also get some goodies, like your name on a list of funders or even a producer credit, depending how much you donate, but really the prize is knowing you had a hand in arranging the world so that Samuel is a math communicator.

The way Kickstarter works is that if Samuel doesn't reach his target you won't be charged and the project won't go ahead. So there's no risk in that sense. Donations start from just $1 so get over to Samuel's Kickstarter page and get pledging! If you really can't afford to, please consider putting a message about Samuel's project on your blog, on any website you have access to, on your social network accounts. If you're the type of person who's impressed by 'celeb endorsements', Samuel has had messages of support so far from Rob Eastaway, Dave Richeson, James Grime, David Bradley & Edmund Harriss. To find out more about the project you can view the video below.

Topics from the first year of the Math/Maths Podcast

2011-06-01T14:26:00.001+01:00

Here is a list of some of the topics we've covered on the first year of the Math/Maths Podcast. The 50th episode this weekend will be live streamed (find out more).

Ahead of our 50th episode we'd love to hear your memories of the podcast's first year or anything relevant you'd like to tell us. You can tweet @peterrowlett, @Samuel_Hansen or email.

Episode 1: Martin Gardner; 3D imagining a bee hive; Logicomix; Abel Prize collected; CBI predicts skilled worker gap as recovery takes hold; Mental Calculation World Cup 2010; & more.
Episode 2: Sharks use fractals to hunt; Reclusive Russian math genius is a no-show to pick up $1M prize money; Fibonacci Knives; Lincoln's math exercise book; arXiv vs snarXiv; Rock Paper Scissors; World Cup; Professor Risk; Edinburgh Your days are numbered: the maths of death; Talking Maths in Public;
Episode 3: World Cup; What makes the sound of vuvuzelas so annoying?; Math Deficiencies Increase Foreclosure Risk; Multiplication makes things bigger; If sports got reported like science...; Chatroulette Genital Blocking Algorithm; First self-replicating creating spawned in Game of Life; 13 Stripes and 51 Stars; Bletchley Archives; UK universities deliver ¬£2.97 billion in services to business and industry; Michael Gove speech: 'mathematics is the foundation on which our civilization rests' etc.; Maths Busking; A Brief History of Mathematics; & more.
Episode 4: Decline of mathematical studies; How chicks count; Academic work ethic; Boxer Nathan Cleverly earns maths degree; Letter: Feynman to Wolfram; 'Theorem' generator; Unpublishable Mathematics; The Royal Society's Summer Science Exhibition; Robert Boyle: wishlist of a Restoration visionary; & more.
Episode 5: Perelman officially declines $1 million for Poincare proof; GOALIE; Teaching applications 'up by a third'; Mathematician deciphers hidden 'Hello Code'; Apple uses formula that is 'totally wrong'; Alex doesn't win Samuel Johnson Prize; Alan Turing Named Top Pioneer; & more.
Episode 6: Paul the Psychic Octopus; World Cup visualisation; National STEM Centre elibrary; Women in Maths; campaign on twitter for a podcast for Brief History of Maths; The algebra of music; #mathchat; Antoni Gaudi cathedral; & more.
Episode 7: fighting terrorism; "cool" science stories; space dinosaurs; pouring coffee; 4-time lottery win; Wolfram on maths curriculum; Mandelbrot on fractals; dance; International Mathematical Olympiad; whether data are or data is; Abel Prize nominations; and more.
Episode 8: Pi day; Godel Prize and Kyoto Prize winners; 'Buckyballs' in interstellar space; Bridges Conference; asciiTeX; Formula for the perfect handshake; Algebra as a Faustian bargain; Maths at British Science Festival; maths puzzles outreach; MathFest; James Grime's RSA challenge; & more.
Episode 9: The attention received by the Tuesday Boy problem; A-level reforms; Women's International Math Congress; rowing; data sorting; sperm movement mystery; The Mandelbrot Monk; swarms of locusts; quantum cryptography; atomic clocks on International Space Station; elections; heart disease; moss spores; MathFest Tweetup; & more.
Episode 10: left-handed boys; the Mathematical Side of M. C. Escher; nested water, land and nations; the number of books in the world; Seventh graders describing scientists; pi to 5 trillion decimal places; Scientopia; drug-resistant malaria; careers in bioinformatics; Kickstarting Punk Mathematics; Sci Foo; improved invisibility cloaks; non-transitive dice; MathJax; and more.
Episode 11: Your Days Are Numbered: The Maths of Death; Simplest Solution to Rubik's Cube; Professor Matt Parks; 2010 China Girls Math Olympiad; Students’ Understanding Of The Equal Sign; A relatively serious proof that P does not equal NP and the after effects thereof; International Congress of Mathematicians 2010; Superconductors and fractals; Pi-hunting; iSquared Magazine; the house where Einstein stayed & more.
Episode 12: International Congress of Mathematicians 2010; Fields and Chern Medals, Nevanlinna and Gauss Prizes; Maths A-level numbers; A*; Are exams getting easier?; computer vs. pen-and-paper tests; Futurama; vintage calculators; Euclid's Elements In Colour; wikimath; a conversation with Matt Parker live in Edinburgh; and more.
Episode 13: Plus Magazine, live from the International Congress of Mathematicians; Roberto Carlos' free kick; A New Kind of Baseball Math; More on P !=NP; The #mathgeek experiment; Clustered Networks; measuring physical constants; testing string theory; Twitter Venn; Mangahigh; and more.
Episode 14: Prime birthdays; gravity defying coffee cup; maths education & innovation; why parents can't do maths today; students get iPads; child-killing maths quiz; cult of youth; Danica McKellar books; chaos following the big bang; the two quadrillionth slice of pi; the National Cipher Challenge; hyperbolic Internets; British Science Festival; Pi-Hunting; constrained writing; recommended reading for new maths & stats lecturers; bed bugs; postgrads who teach; projectile dynamics in sport; and more.
Episode 15: Math Prizes; Google 10^100; Ed Milband's maths geek credentials; maths lesson world record; Joseph Kruskal; Kavli Education Medal; Recursive Pizza; quantum dice; Wolfram blog; Standing on a stepladder makes you age faster; bacterial growth; maths graduates in IT; Fibonacci pigeons; special guest James Grime's Enigma Project in Finland; Bletchley Park; more bed bugs; and more.
Episode 16: special guest Colin Wright on MathsJam and to each other about: the first truly habitable exoplanet; Ed Miliband again; breast cancer statistics; the uncanny accuracy of polling averages; chemometrics and tea; polymath 3; the origin of altruism; Mom and Dad taking math classes; Singapore Math in the USA; UK schools enlisting Indian maths tutors online; the Carnival of Mathematics; the magic square on the Sagrada Familia; and more.
Episode 17: Rubicks Cube Robot; Winning with mathematics; Pizza Hut is Anti-Math; Vedic Maths rejected; Musicians with Ph.D.'s; the mathematical secrets of verse; Klein Bottles; nanoscale Mobius strip; Calculator Plots onto Images; Irish Maths Week; Numerologists; 10/10/10; Science is Vital; World Statistics Day 2010; getstats; USA Science & Engineering Festival; G4G Celebration of Mind; Teaching Math as narrative Drama; Who are your important living mathematicians? & more.
Episode 18: Benoit Madelbrot; STEM; Mathematics is vital!; Great Mathematicians on Math Competitions & School Mathematics; Curious mathematical law is rife in nature; Augusta School Board Approves Single Sex Math Classes; Study: It's Hard to Bring Down the Electric Grid; Mathematika Goes Online; Ray and Charles Eames Powers of Ten Video Response Design Competition; Calling all maths artists; And the Nobel Prize in Mathematics goes to...; Maths in a Box; Solving a Rubik's Cube blindfolded; Math/Maths Podcast Live Recording at Greenwich; & more.
Episode 19: World Statistics Day; Barack Obama on MythBusters; Change the Equation; UK Spending Review; Marathon Math: How Not to Hit the Wall; the physics of the wet dog shake; Gathering for Gardner Celebration of Mind; Ridiculous-Sounding Math Classes; Pumpkin Pi; and more.
Episode 20: Can bees do maths?; How much math do we really need?; Paul the Octopus, how psychic was he and what does Mahmoud Ahmadinejad think?; Roller Coaster Math; Happy Birthday SI Units; Math Happiness in Korea; Pumpkin Math; Topswops; Bo Burnham Math Song; Complex Power Towers; Mathematics Genealogy Project; Samuel's Facebook Network; Math/Maths Live & more.
Episode 21: UK graduate destinations; Jihadist Economics; Electric current to the brain 'boosts maths ability'; US House Network Analysis; New Statistical Model Moves Human Evolution Back Three Million Years; Geometric Death Frequency; Flexible metamaterial springs to life; Matt Parker Millennium Problems Guide; £10,000 bill for £21.60 theft case that turned out to be maths error; important living mathematicians; Women’s choices, not abilities, keep them out of math-intensive fields; MathML 3; preparations for Math/Maths Week; & more.
Episode 22 - LIVE from MathsJam!: A special episode with no news but views from the floor at MathsJam. Special guests this week (who gave their names): Colin Wright, Rob Eastaway, Bubblz the Mathematical Clown, Hugh Hunt, Dan Hagon, Jeff Morley, Timandra Harkness, Alex Bellos, James Grime, Phil Ramsden, Andrew Jeffery, Colin Graham and Sara Santos.
Episode 23 - LIVE from Greenwich: Android phone solves Rubik’s cube in 12.5 seconds; Edmonton Eulers; Relativistic trading; American math achievement; Russian maths problem teaches students who's really in power; NASA's Metric Failure; quantum error threshold; Top Five Utterly Incomprehensible Mathematics Titles; Your own maths theorem for £15; and news & stories (including stories from MathsJam) from the floor at Greenwich. Special guests this week: Mitch Keller, Tony Mann, David Singmaster, Nic Mortimer and Noel-Ann Bradshaw.
Episode 24: Linking geometric problems to physics; Card Tricks and Data Compression; Racial profiling; The aftershocks of crime; Mumford Receives the National Medal of Science; Improve your maths to get rich & boost the economy; Anti-Complexitism; The Meaning of Maths; Vi Hart Math Doodles; various competitions; and more.
Episode 25: Innumeracy Behind Airline Security; Poker at high school; Incredible Edible Foam; Dear Santa: Please Send Owl Puke; 20th C.'s Most Boring Day; Secret of Big Caves Revealed by Math; Non-Transitivity; The kilogram; The Mismeasurement of Science; SAT vs A levels; TDA beats recruitment targets in science and maths; Country rankings in math and science; advent calendars; Math/Maths LIVE from Greenwich: Now on video; Combinations and Permutations Episode 57; and more.
Episode 26: the invention of calculus (again); Providing Incentives to Cooperate Can Turn Swords Into Ploughshares; Google Chrome OS advert Math; WikiLeaks founder was ‘no star’ mathematician; Singapore's Math Priority & US Parents overconfident in children's mathematics; PISA World education rankings; ant algorithms; time before Big Bang; celebrating 12/12; interest on your credit card; Skyscraper Equation; Oxfam formula for a happy Christmas; Best Mathematical Writing of 2010; Math Article Shows Collaboration Is Not Limited by Geography—or Age; The World's Social Networks; Lego Antikythera Mechanism; Single Digits; Christmas tree designed in GeoGebra; Royal Institution Christmas Lectures; and more.
Episode 27: Finding order in chaos; Modeling Snowflakes in Wintry Wisconsin; Mobile phone radiation linked to people jumping to conclusions; IBM supercomputer set for Jeopardy quiz show showdown; Primary School Students Conduct and Publish a Study on Bees; Students taking maths post-16; BREAKTHROUGH in algorithms: Improved algorithm for Metric TSP!!!!!!!!; Human networking theory gives picture of infectious disease spread; Pythagoras, a math genius? Not by Babylonian standards; 3D printed icosidodecahedron; Possible New European Heritage Label for Bletchley Park; NCETM Special Award for STEM - Does maths count?; Math/Maths in Google Books Ngrams; and more.
Episode 28 - Review of the Year: 1910: In a traditional move for the start of January we attempt a review of the year. In an untraditional move, we choose the year 1910. Topics covered: the death of Florence Nightingale gives a good reason to look at the development of modern statistics; the publication of Principia Mathematica volume 1 by Russell and Whitehead brings up axiomatisation and inconsistency; the publication of Einstein's special relativity leaves some questions about freefall and gravity; Geiger & Marsden firing alpha particles at gold foil has Rutherford questioning the structure of the atom; ten years on from Hilbert's Problems we ask how many have been solved; plus we look at the work of new LMS President and 1910 Royal Society Sylvester Medal winner Henry Baker and new Fellow of the Royal Society G H Hardy.
Episode 29: Rapture Math; 2011 numerology; 2011 Joint Mathematics Meetings and Exhibition of Mathematical Art; Batman Probability; 'The worst info graphic of 2011'; NASA's? best and worst science fiction movies; Pedantry on Euler and masts; mathematical matter; 100 Years of the Principia; Ten News Stories of 2010 - and the Statistics that Made Them; Celia Hoyles awarded the first Kavli Education Medal; Why a Cloned Cat Isn't Exactly Like the Original: New Statistical Law for Cell Differentiation; Math Monday is the best of 2010; The 12 Math Carnivals of 2010 and the 73rd Carnival of Mathematics; LMS Membership survey; 2nd Tomorrow's Mathematicians Today Conference; Robot solves Rubik's cube in 15 seconds & more.
Episode 30: special guest Katie Steckles on Maths Busking and MathsJam; unlucky house numbers; Mathematics-Inspired Dance Work; Perfecting Animation, via Science; The Mathematics Of Beauty; Geomagic Squares; Irving Kaplansky's "A Song about Pi"; Edsac computer to be rebuilt at Bletchley Park (by Boffins); An App for Every Course; Oxford and A*s; Maths Inspiration Photo Competition 2010 winner and runners up; and more.
Episode 31: Putting reality back into the equation; Weak gravitational lensing and weak arguments; Me and My Algorithm; Mass Animal Deaths; Counting Animals; Yes, bonuses do work – but for fruit-pickers, not City bankers; Finite formula found for partition numbers; Prime numbers in the House of Lords; Rhonda Hughes Honored with AWM's First M. Gweneth Humphreys Award; National Curriculum Review - Call for Evidence; How much will the budget cuts affect your studies?; Vi Hart; Straight Statistics; and more.
Episode 32: Edmund Harriss' job search; Museum of Mathematics; Watson 'wins' Jeopardy!?; Few Students Show Proficiency in Science, Tests Show; Seattle's 'Discovering' math curriculum; Cal State Northridge professor charged with allegedly urinating on colleague's office door; Coincidence odds are wrong yet again; Mathematical Model Could Help Predict and Prevent Future Extinctions; Long-standing conjecture on Plane Partitions proved; Researchers use cell 'profiling' to detect abnormalities -- including cancer; Atom counting helps kilogram watch its weight; Math Monsters; Google donates 1 million euros to IMO; Japanese man gains world record for pi calculation; & more.
Episode 33: Dr Ian Porteous; President Honors Outstanding Mathematics, Science, and Engineering Mentors; Macroscopic invisibility cloaking of visible light; Tau Manifesto; Cracking the Scratch Lottery Code; Penny Bias; Informed Choices; Teacher training places and goodbye to the golden hellos; As 3,500 meteorologists meet, one man's forecast: Chance of pirates; Bringing the Census into the internet age; Mathematicians design bone implants for the future; New Mathematical Model of Information Processing in the Brain Accurately Predicts Some of the Peculiarities of Human Vision; Snowdecahedrons; Crime maps: how useful?; What's Andy Carrol really worth?; Ed Miliband admits being 'a bit square'; Why nerds rule the world; The Art of Computer Programming, Volume 4A released; Record numbers apply for university places; Marcus du Sautoy to be MA President; & more.
Episode 34: The Best Questions For A First Date; The Science of Soccer Substitutions; Role of statistics regulator; Math may help calculate way to find new drugs for diseases; Proposing math models to enhance two-way wireless network communication; Without language, numbers make no sense; Unique math program helps students; Aloha Math; Overweight Kids Who Exercise Improve Thinking, Math Skills: Study; Mathematics teachers learn to inspire students by encouraging pattern hunting; The pointy end of pineapple numbers; Giant Leaps; Researchers produce world's first programmable nanoprocessor; 2011: Ranking 200 Jobs From Best to Worst; 1942 adding machines: a marvel of non-essential zero elimination!; The blackboard - a modern classic; Carnival of Mathematics #74; Bite-sized History of Mathematics; Valentine's day mathematics; & more.
Episode 35 - Why Maths? Special: a special episode in which Samuel and Peter spoke to Ruby Childs about her investigations into why some people like maths and choose to study it further, when others don't and whether we should be saying "maths is fun".
Episode 36: Watson, Jeopardy and beyond; mathematician credited with solving one of combinatorial geometry's most challenging problems; Ants build cheapest networks; 'Periodic Table of Shapes'; Pride in poor maths culture 'must be tackled'; Alan Turing's Patterns in Nature, and Beyond; Alan Turing Papers bought by Bletchley Park Trust; It's a young numbers game; World Education Rankings (episode 26 call-back); Fastest-Declining Academic Fields; Maths and Sport: Countdown to the Games; 20 Top Math Teacher Tweeters; Radical Statistics essay competition; Math Raps; special guest Julia Collins joins Samuel to discuss Engaging with Engagement; and more.
Episode 37: Math/Maths History Tour of Nottingham; U.K. Powerless to Stop ‘Jedis, Witches’ Spoiling 2011 Census; Apportionment in the European Parliament; the world’s most difficult maths problem; The Hodge Conjecture; pi birthday; Polisticians, Demographics and Destiny; All it took to beat Watson, the "Jeopardy"-winning computer, was a rocket scientist-congressman; The End of Algebra?; Compulsory Maths; Dyscalculia Day; The Way You Learned Math Is So Old School; Learning Math with a Video Game; I predict a riot: Where the next dictator will fall; getstats Stats Buskers; and more.
Episode 38: A short one this week because Peter wasn't able to talk to Samuel. Peter apologised and spoke briefly about: Earthquakes and tsunamis, and prediction; Celebrating mathematical women; Pi Day; and your correspondence.
Episode 39: nuclear radiation; the Worst Statistics in the World; SOCCER SKILLS DOWN TO MATHS AND SCIENCE SAY SPORT BOFFS; Mathematicians invent a new way to pour stout; Can bees color maps better than ants?; Is mathematics discovered or created?; Bressoud Testifies Before House in Support of STEM Funding; Les Valiant Wins ACM Turing Award; ABEL PRIZE 2011; Romanian Masters in Math & Science; Riemann hypothesis; Using cams to solve math problems; Mathematics of Web Design & the Golden Section; The maths of 007 Top Trumps; calculus-based CAPTCHA; What Pi sounds like; & more.
Episode 40: RSS urges people to fill out Census; The Abel Prize 2011: John Milnor; A Schock Prize for an enormous theorem; Organized religion 'will be driven toward extinction' in 9 countries, experts predict; Deciphering hidden code reveals brain activity; James Gleick's Information; Banking cheats will always prosper; Public School Math Doesn’t Teach Students How to Reason; Mathematics in Movies; 14 Holidays Every Math Major Must Know; Education bosses shamed as recruitment advert for MATHS teachers shows equation... with the WRONG answer; How to make a Slinky look like a Klein bottle; and more.
Episode 41 - What makes a mathematician? And who should communicate mathematics? Also: Math Awareness Month; MathFest 2011; Peabody Awards; GCHQ Code Cracking Challenge; & more.
Episode 42 - Maths in the City: special guest Rachel Thomas on Maths in the City; Pioneer Anomaly Solved; 3D Knight's Tour; Antikythera Mechanism; Google grants for math; FBI cryptography - Help Solve an Open Murder Case; Requiring Algebra II in high school gains momentum nationwide; Mangahigh Launches 100% Free Games-Based Math Resource for US Schools; Gauss Facts; and more.
Episode 43: Did Samuel pass his thesis defence?: Letting There Be More Mosquitoes May Lead to Fewer Malaria Deaths; Australian mathematicians say some endangered species “not worth saving”; Are Ants Smarter Than Fifth-Graders at Math?; the Duckworth-Lewis Method; 2 reviews of Alex's Adventures in Numberland; Ethnomathematics; How do routefinders find their routes?; New Symmetries; Open University to get US funding; The On-Line Blog of Integer Sequences; The Big Risk Test; MathsJam 2011; whether Samuel passed his thesis defence; and more.
Episode 44: Prehistoric Sat-nav is back: Museum of Math has a Home; Prehistoric Sat-nav is back; Snow Alogrithms; Amazon’s $23,698,655.93 book; Flu Math; Professor who "makes maths fun' gets top award; A Better Way to Teach Math; Child calls 911 for maths help; 10 Charts About Sex; Olympic sports; Predictive Health Prize; Gambling with Secrets; Otomata; Glee is Wrong; and more.
Episode 45: Will Grigori ever speak to the press again?: White Blood Cells Solve Traveling-Salesman Problem; Grigori Perelman Interview ("Grigori Perelman claims he can control Universe"); UK Voting - AV referendum; Push to define year sparks time war; What do you want on your tombstone?; Early math skills predict later academic success; STEM Education DATA; Strange Places to Prove Theorems; Ravi Kannan Wins Knuth Prize; Mathematical Guggenheim Fellows; Why we’re all far too sure of ourselves; In a Data-Heavy Society, Being Defined by the Numbers; and more.
Episode 46: Early Mathematics Day: a report from special guest Dan Hagon live from the BSHM/Gresham College Early Mathematics Day; Grigori Perelman; the Maths of AV; The Greatest Mathematicians of All Time; Could Han Shoot Second?; Paul The Psychic Octopus - The Movie; 40 Years of P vs. NP; TakeAIM: Articulating the Influence of Mathematics; Good maths journalism example: Tackling the big unaswered problems; Journal of Humanistic Mathematics; High School students offer flood of ideas; Why Bayes Rules; 13-Year Periodic Cicadas Emerge; Mangahigh now 100% Free also for UK & Republic of Ireland Schools; 14th Early Career Mathematicians Conference; The Calculus I Student; Numbas; and more.
Episode 47: Listener questions: This week Samuel and Peter were joined by special guest James Grime to answer listener questions. What use are graphics calculators? What is your favourite number? How do you solve 6/2(2+1) (and do you care)? Is maths rapidly developing or finished and polished? Why is most taught maths pre-1950? Is maths discovered or created? When did you first consider yourself a mathematician? What do you think of the arts? What do you think about the stereotypical mathematician? Can a short proof of Fermat's Last Theorem exist? What's the best maths communication conference? How do people use Twitter for networking and publicity?
Episode 48: Apocalypse, post-apocalypse & extinction: Judgment Day Mathematics, and what happens next; You're Living in a Computer Simulation, and math proves it; Calculations may have overestimated extinction rates; Teeth Clenching Mathematics; The Danger of Praise; Supercomputers crack sixty-trillionth binary digit of Pi-squared; S. Korea US to Exchange Math Teachers; Teenagers must stick at English and maths; 71st Putnam; Olympiads; World Measurement Day; Arabic-Indic numerals; Calculus Rhapsody; and much more.
Episode 49: MathsJam Explosion: K3,3 is planar; Hardwired Geometry; Italian Seismologists Charged With Manslaughter for Not Predicting 2009 Quake; Highest paying majors; Code-cracking machine returned to life; Scenes de ballet; How maths can help with (almost) everything; 144 BC Chinese War Game Theory; dyscalculia and math anxiety; jargon; 75 Years of Computer Science; MathsJam explosion; and more.

Math/Maths Podcast - 1 year and 50 episodes later

2011-05-29T14:44:00.005+01:00

Samuel Hansen and I have been doing the Math/Maths Podcast (#MathMaths to those on Twitter) for almost a year. In fact, our 50th episode next weekend will coincide with the one year anniversary of our first recording.

To celebrate, we plan to stream the podcast recording live as we record it. We will record at 4pm British Summer Time, that's 8am Pacific or 11am Eastern Time, on Saturday 4th June 2011. We have some technical bits to sort out (we can definitely do audio and we may be able to do video too) but check back here on this blog for details of where to join in. We'll be looking for your input on the day!

UPDATE: We did a technical test and it all seems to work. The link on the day will be the Math/Maths Podcast channel on ustream.

Too old for such silly toys

2011-05-22T12:15:00.000+01:00

Recently I had a birthday. My family kindly bought me a set of mathematical presents, including a Tippe Top, a Rattleback and a Gaussian gun. I show these and my other presents in action (the mathematical ones, at least) in the following video.

HE Mathematics HE Curriculum Summit in THE

2011-05-13T23:11:00.000+01:00

There is an article on the website of Times Higher Education (THE) 'Maths teaching seeks the formula for good graduates', which is about the report of the HE Mathematics Curriculum Summit, which I edited. I recording some thoughts about this hours before the deadline for the related funding call as episode 8 of the Maths HE Curriculum Innovation Project Podcast and wrote them as a blog post on my work blog.

Smart Phone Apps for University Mathematics

2011-05-11T14:58:00.001+01:00

You may remember I work on curriculum innovation as part of the Mathematical Sciences Strand of the National HE STEM Programme. Hazel Kendrick, who works on outreach, has been collecting a list of smart phone and tablet apps for mathematics undergraduates and lecturers. Her original request to the Maths-Prom mailing list said:

We are interested in compiling a list of free or low cost apps for smart phones which undergraduate maths students are currently using to help them in their studies or lecturers are using in their teaching.

Here are the suggestions Hazel has received so far (in no particular order), with a note about the app, the price and where to get it. These suggestions are from users of the Maths-Prom mailing list. Please contribute your suggestions in the comments!

Mathscard
A-level maths formulae from Loughborough University
FREE
www.mathscard.co.uk/apps/
List of maths apps for the ipad at Mike Croucher’s blog Walking randomly
Mike is also developing a list of Android maths apps in the near future
www.walkingrandomly.com/?p=2692
www.walkingrandomly.com/?p=2947
www.walkingrandomly.com/?p=3512
Wolfram Alpha
Wolfram Alpha introduces a new way to get knowledge and answers—not by searching the web, but by doing dynamic computations based on a vast collection of built-in data, algorithms, and methods. Type in a question and it will attempt to provide an answer.
£1.19
http://products.wolframalpha.com/iphone/
Apollonius
Apollonius is the first (and so far the only) Interactive Geometry Software (IGS) for the iPhone and iPod Touch. It allows you to make geometric constructions (such as those made using a compass and straightedge/ruler) and move their parts smoothly using the device's touchscreen.
£2.39
Available at the Apple App Store
Appcyclon
Graphic Calculator (there are many other alternatives).
£1.19
Available at the Apple App Store
iMathematics
A maths reference guide with formulae and theorems.
FREE
Available at the Apple App Store
Differential Calculus Study Guide
A reference Guide
59p
Available at the Apple App Store
iMatrixLab
Calculates with Matrices
59p
Available at the Apple App Store
Learn Statistics
Statistical Tool - includes dynamic graphs etc
£2.39
Available at the Apple App Store
Math Ref
A maths reference guide (free for lite version)
59p
Available at the Apple App Store
Fractal Apps
There are lots of fractal Apps around, many of which are free.
Various prices
Available at both the Apple App Store and as an Android Market App
A+ timetable
Useful for students to put their timetable into
FREE
Available as an Android Market App
ES file explorer
Students can keep all their notes and coursework online and view them like a PC.
FREE
Available as an Android Market App
Apps for changing handwriting to text –e.g. the WritePad App
Useful for taking notes.
£2.39 for WritePad App
Available at the Apple App Store
Astronomy Course Assistant
Interactive reference and computational tool for students studying introductory astronomy. The app can reference information on constellations, planets, and other astronomical objects.
£2.99
http://products.wolframalpha.com/courseassistants/astronomy.html

Please contribute your additional suggestions in the comments!

Maths of AV: a reading list

2011-05-03T11:59:00.002+01:00

On the recent Math/Maths Podcast, among other things, we discussed the upcoming referendum on the UK voting system. Since then, I've become aware of a few more articles and blog posts that may be of interest. The referendum asks for a "Yes" to change the method of running the election of MPs to Westminster to the Alternative Vote (AV) system, or "No" to keep the existing "First-Past-The-Post (FPTP) system. The BBC have a Q&A that covers the basics. The referendum is this Thursday, 5th May. If you are undecided, or interested in the issues, here is a reading list. I am focusing on those articles which deal with the topic from a mathematical point of view. (Alright, a few of them are more 'economics', but we all enjoy a bit of subject-line-blurring, don't we?) There is much writing purely on the politics of the debate, but you can find that elsewhere (although be warned: the campaign has been called "a new low in the quality of British political argument").

A piece by Jacob Aron in the New Scientist, 'Mathematicians weigh in on UK voting debate', looks at, and provides some commentary over, two blog posts: 'Two cheers for AV' by economist Dennis Leech and 'Is AV better than FPTP?' by mathematician Tim Gowers. Both look at some misconceptions of the whole debate and, while giving a fairly impassioned and to some extent balanced look, both are nevertheless pro-AV. In particular, Gowers' list of claims made by the "No" campaign is well worth a read.

A typically mathematician approach is to reach for proven results and several articles highlight theorems in voting theory, most notably Arrow's theorem, which gives conditions in which no voting system can produce a fair result. David Broomhead, writing in the Guardian under the heading 'A formula for fair voting' and sub-heading "The AV debate so far has been riddled with false assertions. Here's the mathematics to prove it", touches on Arrow's work and also explains the Gibbard-Satterthwaite theorem, on tactical voting. Tony Crilly goes into Arrow's work in some depth in Plus under the title 'Which voting system is best?' and also gives an entertaining voting scenario in which twenty people are voting to elect one of three candidates and, depending how votes are counted, any of the three candidates can win.

This morning, Tony Crilly has a piece in the Independent, 'The maths of AV: A small step towards a fairer vote', in which he explains a few quirks of the two systems and gives a little history.

Tim Harford wrote on Twitter today to highlight two blog posts he wrote: 'Vital, yet unrepresentative. That’s democracy for you' in the run up to the 2010 General Election, on the proportion of the vote needed by each party to win a majority and, yes, Arrow's theorem; and, 'Why small parties can punch above their weight' on the morning after that election, about the game theory of forming coalitions.

There is also some interest in the claim by the "No" campaign that AV is too complicated for people to understand. This is covered by Gowers in his piece and also by Johann Hari in his pro-AV piece: 'If you get the X-Factor, you can get AV', which contains provocative talk about "a campaign that thinks you are too thick to count to three".

A fan of a good visual representation, I note the "Yes to AV (and beer)" graphic posted by Adam Ramsay in a piece entitled '11 reasons to vote Yes on Thursday'.

There has been a lot of "Yes"-leaning writing listed here. I haven't seen anyone arguing strongly that FPTP is mathematically a better system than AV. Most arguments against seem to be those listed by Gowers - or, as I have seen it called, "scaremongering and peddling untruths". The closest I've heard is something like 'vote no because AV doesn't go far enough'. I'm happy to be corrected.

Further contributions are most welcome in the comments or via Twitter.

Mathematical podcasting

2011-04-20T10:13:00.001+01:00

Samuel Hansen and I appear in the report from the 13th IMA Early Career Mathematicians Conference in the latest Mathematics Today, which we spoke at on 'Mathematical Podcasting', during "Math/Maths Week" last November.

Next up were two of our more tech-savvy colleagues Samuel Hansen (University of Nevada, Las Vegas) and Peter Rowlett (University of Birmingham), who introduced us to the world of Mathematical podcasting. Samuel and Peter performed a great double act, sharing their experiences of Mathematical podcasting with us in a very entertaining style. They also divulged some of the tricks of the trade, and encouraged us all to try it out.

There's also a photo taken by Tony Mann of Samuel and I recording the Math/Maths Podcast live at the MathsJam 2010 conference.

'Technology in mathematics HE teaching & learning'

2011-04-16T07:56:00.001+01:00

On the second day of Young Researchers in Mathematics 2011 at the University of Warwick I gave my second of two talks, this time on 'Technology in mathematics HE teaching & learning'. This is a demo of some ways people are including technology in their teaching, learning and assessment. This follows the talk on the first day, 'Innovation in mathematics HE teaching & learning', which was a lively discussion about university teaching.

A recording is below:

There are many ways in which technology can be used to benefit students in mathematical sciences HE teaching and learning that you may wish to explore during your academic career. However, there are also ways in which technology can be misused, or a lot of effort can be undertaken to little or no benefit. This talk discusses developments in HE curriculum particularly relating to technology in teaching, drawing on examples from work funded by the Mathematical Sciences HE Curriculum Innovation Project, and discusses the process of determining when innovations are needed and whether they are effective.
Recorded at Young Researchers in Mathematics 2011, 15th March 2011, University of Warwick.
The Mathematical Sciences HE Curriculum Innovation Project is operated by Peter Rowlett, MSOR Network as part of the National HE STEM Programme.

'Innovation in mathematics HE teaching & learning'

2011-04-15T08:20:00.002+01:00

I am at the conference Young Researchers in Mathematics 2011 at the University of Warwick and last night I gave the pre-dinner talk on 'Innovation in mathematics HE teaching & learning'. I recorded this and it is available below.

Here is the abstract:

There are many issues in mathematical sciences HE teaching and learning that, if you are just setting out on an academic career or hoping to, you will need to address during your time as a lecturer. A lively discussion considered mathematics HE teaching and what might be expected from graduates of mathematics degrees. The talk gave developments - recently undertaken or that may be needed - in HE curriculum, drawing on examples from work funded by the Mathematical Sciences HE Curriculum Innovation Project, including from a high level Summit convened in January 2011 to discuss priorities in curriculum development in HE mathematical sciences. Details are given of a £150,000 funding call for curriculum innovation projects in mathematical sciences which is currently open to bids.
Recorded at Young Researchers in Mathematics 2011, 14th March 2011, University of Warwick.
The Mathematical Sciences HE Curriculum Innovation Project is operated by Peter Rowlett, MSOR Network as part of the National HE STEM Programme.

Hidden Science Map

2011-04-08T10:51:00.001+01:00

I have added myself to the Hidden Science Map and written a profile. This asked about my education and route into mathematics, a week in my life, what attracted me to what I do, & more. Here is its description of itself:

The Hidden Science Map has been created to show how much science goes on all around us.

The best way of understanding how the map works is to have a play with it. (If you haven't already.)

The more science, technology, engineering and maths people, and organisations, who put a profile on using our profile questionnaires, the more pins there are to explore, and the more interesting the searches will be.

It's for school students, parents, and anyone who's curious about science and its applications to be able to see that 'science' goes on all over the place. It's not just in university laboratories, and it's being done by all sorts of people, not just ones wearing white coats. (You should be on the map too though, white coated university science people.)

In case you're wondering, that's why it's called 'Hidden' Science Map. A lot of science, engineering, technology and maths jobs frankly don't get the profile they deserve. If someone has trained as a science person but uses the skills in other sorts of jobs, that's even harder to visualise. The map should serve to bring all this out into the open to inspire the next generation of science people.

It will be around for at least six months from March 2011. This is the pilot phase to see if this type of application is popular both with the science people of the UK, and the map's visitors.

Types of scientist (or mathematician)

2011-04-06T09:06:00.000+01:00

I am interested in a recent paper from the Science Council. This discusses the different roles scientists have in society beyond actually researching cutting edge science. For example, I would feel strange about describing myself as a 'scientist' (perhaps in the news media sense of: "Scientists have discovered...") but when I see the Science Council descriptions of "The Communicator Scientist" and "The Teacher Scientist", I would happily be described as a "Teacher/Communicator Scientist". This would mean I am involved in enthusing and training "the next generation" of scientists.

I believe a lot of people graduate mathematics thinking that if what they are doing isn't at least as hard as third year undergraduate maths then it isn't 'real' maths and, by extension, while they did maths at university, they aren't now a mathematician. Even when what they are doing for a living is mathematical, it's just not cutting edge research.

The categories are listed below and full descriptions are given in the Science Council paper "10 types of scientist – science jobs are not all the same":

Explorer
Investigator
Developer/Translational
Service provider/operational
Monitor/regulator
Entrepreneur
Communicator
Teacher
Business/Marketing
Policy maker

Audio and video content produced during Math/Maths Week 2010

2011-04-03T09:39:00.001+01:00

Here is a record of everything with Samuel Hansen and I from the week Samuel came to visit me in the UK in November 2010. Chronological order of recording. Ish.

1. Math/Maths Podcast Episode 22 - LIVE from MathsJam! (13/11/10; Stone, Staffs.; audio, 41:44).

Math/Maths Live recording at MathsJam on Saturday 13th November 2010. A special episode with no news but views from the floor at MathsJam. Special guests this week (who gave their names): Colin Wright, Rob Eastaway, Bubblz the Mathematical Clown, Hugh Hunt, Dan Hagon, Jeff Morley, Timandra Harkness, Alex Bellos, James Grime, Phil Ramsden, Andrew Jeffery, Colin Graham and Sara Santos.

2. Combinations and Permutations Episode 57: LIVE, with audium! (13-14/11/10; Stone, Staffs.; audio, 36:23).

Samuel hosted and Peter appeared as a guest with Matt Parker and James Grime in this episode of Samuel's (doesn't mind its language) podcast, Combinations and Permutations.

3. James Grime's The Mathematics of Bell Ringing (14/11/10; Stone, Staffs.; video, 3:59).

Peter appeared in this video by James Grime recorded in a quiet corner at the end of MathsJam.

4. The Math/Maths Computing History Tour of Nottingham - Burroughs and Ada Lovelace (16/11/10; Nottingham; video, 6:49).

Nottingham is the burial place of the Byron family and particularly Ada Lovelace, regarded as the world's first computer programmer, who worked with Charles Babbage on his Difference and Analytical Engines. Nottingham was also the overseas manufacturing plant for Burroughs Adding Machine Company, a precursor of modern computers, which became one of the eight major United States computer companies and ultimately joined a merger to form worldwide IT brand Unisys.

When Samuel Hansen visited Peter Rowlett in Nottingham, Peter took Samuel on a mathematics and computing history tour of the city. In this video, Peter shows Samuel some of the sites related to this story in Nottingham, following a clue from David Singmaster's Mathematical Gazetteer of the British Isles, and Samuel tells Peter some of the relevant history of computing.

5. Math/Maths History Tour of Nottingham - George Green: Miller, Mathematician, and Physicist (16/11/10; Nottingham; video, 12:03).

George Green (1793-1841) was a miller in Sneinton, Nottingham who worked in his spare time to develop mathematics that, although unrecognised in his own lifetime, has been very useful to mathematics since. His work was rediscovered by Lord Kelvin and applied first to electromagnetism, later even to Nobel Prize-winning work in quantum theory, and continues to be useful to physicists and mathematicians today.

When Samuel Hansen visited Peter Rowlett in Nottingham, Peter took Samuel on a mathematics and computing history tour of the city. In this video, Peter takes Samuel to visit some of the sites from Green's life in Nottingham, including Green's windmill, Nottingham's mathematical playground, Nottingham High School and the Bromley House Library.

6. Math/Maths History Tour of Nottingham - When Einstein came to town (16/11/10; Nottingham; video; 4:14).

Albert Einstein visited Nottingham in 1930 to give a lecture on his new theories of relativity at University College, Nottingham. The blackboard he used was varnished over and preserved, and a scrapbook of newspaper clippings is full of stories.

When Samuel Hansen visited Peter Rowlett in Nottingham, Peter took Samuel on a mathematics and computing history tour of the city. In this video, Peter takes Samuel to the School of Physics and Astronomy at the University of Nottingham to see Einstein's blackboard and find out what happened when Einstein came to town.

7. Math/Maths History Tour of Nottingham - George Green's Slide (16/11/10; Nottingham; video; 0:10).

Just a silly video in which Samuel and Peter take a trip down the pi slide in the Mathematical Playground at George Green's Mill.

8. Math/Maths Podcast Episode 23 - LIVE from Greenwich (17/11/10; Greenwich; audio, 41:28).

This episode recorded live at the University of Greenwich. This week Samuel and Peter spoke about: Android phone solves Rubik’s cube in 12.5 seconds; Edmonton Eulers; Relativistic trading; American math achievement; Russian maths problem teaches students who's really in power; NASA's Metric Failure; quantum error threshold; Top Five Utterly Incomprehensible Mathematics Titles; Your own maths theorem for £15; and news & stories (including stories from MathsJam) from the floor at Greenwich. Special guests this week: Mitch Keller, Tony Mann, David Singmaster, Nic Mortimer and Noel-Ann Bradshaw.

9. Math/Maths Live at Greenwich bootleg recording by James Clare (17/11/10; Greenwich; video: 08:21).

Video recording made by audience member James Clare of first 8 minutes of the Math/Maths Podcast recording at Greenwich.

Samuel Hansen's visit to the UK and associated activities were supported by: University of Nevada, Las Vegas, University of Greenwich, University of Leicester Mathsoc, Nottingham Trent University, MathsJam, Nottingham High School, Bromley House Library and the Institute of Mathematics and its Applications. We are grateful also to the School of Physics and Astronomy at the University of Nottingham for letting us film there.

(Not that it's any way to judge anything, but I make that 1:59:58 of audio and 35:36 of video for you to listen to and watch.)

Math/Maths History Tour of Nottingham 3/3 - When Einstein came to town

2011-04-02T09:19:00.000+01:00

When Samuel Hansen visited me in Nottingham I took him on a maths and computing tour of the city and we filmed content for three videos. Here is the third, on a visit to Nottingham in 1930 by Albert Einstein.

There is a YouTube playlist with all the Math/Maths History videos and a Google map of all the locations we used.

Albert Einstein visited Nottingham in 1930 to give a lecture on his new theories of relativity at University College, Nottingham. The blackboard he used was varnished over and preserved, and a scrapbook of newspaper clippings is full of stories.

When Samuel Hansen visited Peter Rowlett in Nottingham, Peter took Samuel on a mathematics and computing history tour of the city. In this video, Peter takes Samuel to the School of Physics and Astronomy at the University of Nottingham to see Einstein's blackboard and find out what happened when Einstein came to town.

Listen to Samuel and Peter on the Math/Maths Podcast, a weekly maths news roundup from Pulse-Project.org.

Samuel Hansen's visit to the UK and associated activities were supported by: University of Nevada, Las Vegas, University of Greenwich, University of Leicester Mathsoc, Nottingham Trent University, MathsJam, Nottingham High School, Bromley House Library and the Institute of Mathematics and its Applications.

Reflections on a short puzzle in Elluminate

2011-03-31T08:38:00.001+01:00

Stephen Lee (MEI) approached me regarding a 'Virtual IMA Branch talk' which would be delivered by Elluminate. The advantage is that anyone can access this, even those who cannot access a standard Branch talk. We agreed I would give a puzzles talk.

Last week we did a short practice run, with a couple of volunteers, @christianp and @SundayTeaTime (Thanks!). I did a couple of river crossing puzzles. Here it is, followed by some reflection:

I found it strange to know how to pace the talk with no real audience feedback. When we allowed multiple microphones to be active the system had an enormous lag, so we set it to what I'm thinking of as walkie-talkie mode, where I had control of the mic until I released it to Stephen. This was strange, partly because you might say something and expect a laugh or a murmur from the audience (perhaps at the start when I blame Stephen in advance for it all going wrong) and you don't get that, and also because I am used to recording a two-way conversation via Skype for the Math/Maths Podcast, where Samuel Hansen and I tend to interrupt each other.

I found it strange having no visual clues to how well the audience was understanding what I was saying. I have given this puzzle before a live audience seven times from years 11-13 (what's that? 15-19?) to undergraduate and university staff. Then, it is relatively straightforward to get an idea of whether people are following or not but here it wasn't so easy. I think this caused me to under-explain a few things, like the precise definition of the puzzle while we were trying to solve it, and I think it caused me to rush a bit.

Specific feedback given at the end that I need to address for the real thing:

The window wasn't all on screen for one person, so a smaller window would be helpful.

To keep the puzzle definition on screen while trying to solve it would be an advantage.

Watching the puzzle back seems to me a little slow, but then I know what's coming and I'm not playing along at home. When I've asked a question it is hard to know how long to leave it to wait for a response. Again, when I'm talking to Samuel dead air is to fill, but here you need to give people some time to think about the problems. I would be very interested to hear in the comments how you found watching it back.

Invasion of privacy

2011-03-28T15:00:00.000+01:00

Q: What is your name?
A: Peter Rowlett

Q: What is your sex?
A: Male

Q: What is your date of birth?
Yes, okay, I'm not going to put that here (but I don't doubt you could find out if you tried).

Q: On 27 March 2011, what is your legal marital or same-sex civil partnership status?
A: Married

Q: Do you stay at another address for more than 30 days a year?
A: No

Q: Are you a schoolchild or student in full-time education?
A: No

Q: What is your country of birth?
A: England

Q: How is your health in general?
A: Good

Q: Do you look after, or give any help or support to family members,
friends, neighbours or others because of either:
- long-term physical or mental ill-health / disability?
- problems related to old age?
A: Yes, 1-19 hours a week

Q: How would you describe your national identity?
A:
English
British

Q: What is your ethnic group?
A: English / Welsh / Scottish / Northern Irish / British

Q: What is your main language?
A: English

Q: What is your religion? (This question is voluntary)
A: No religion

Q: One year ago, what was your usual address?
A: The address on the front of this questionnaire

Q: What passports do you hold?
A: None

Q: Are your day-to-day activities limited because of a health problem or disability which has lasted, or is expected to last, at least 12 months?
A: No

Q: Which of these qualifications do you have?
A:
1 - 4 O levels / CSEs / GCSEs (any grades), Entry Level, Foundation Diploma
5+ O levels (passes) / CSEs (grade 1) / GCSEs (grades A*- C), School Certificate, 1 A level / 2 - 3 AS levels / VCEs, Higher Diploma
2+ A levels / VCEs, 4+ AS levels, Higher School Certificate, Progression / Advanced Diploma
Degree (for example BA, BSc), Higher degree (for example MA, PhD, PGCE)

Q: Last week, were you:
A: working as an employee

Q: In your main job, are (were) you:
A: an employee

Q: What is (was) your full and specific job title?
A: Educational advisor

Q: Briefly describe what you do (did) in your main job.
A: HE funding and staff development

Q: Do (did) you supervise any employees?
A: No

Q: At your workplace, what is (was) the main activity of your employer or business?
A: Higher Education

Q: In your main job, what is (was) the name of the organisation you work (worked) for?
A: University of Birmingham

Q: In your main job, what is the address of your workplace?
A: University of Birmingham, Edgbaston, Birmingham, B15 2TT

Q: How do you usually travel to work?
A: Train

Q: In your main job, how many hours a week (including paid and unpaid overtime) do you usually work?
A: 31 - 48

Census 2011: What did I do?

2011-03-27T13:13:00.000+01:00

Recently I wrote Census 2011: What do I do? about the "occupation" questions on the UK 2011 Census form. The issue was to summarise what I do in a way that would be as understandable as "School teacher" or "Car mechanic" and I tried to list everything I do in my earlier post. Particularly because the question asks about your main employment, following a helpful suggestion from commenter Liz, I put "Educational Advisor". I feel like I've been sold short by being pigeonholed, but it's better than everything else I thought of. The second part was to describe what I do in only 34 characters (including spaces). "Higher education funding and staff development" was too long, so I put "HE funding and staff development", which isn't really right in any case.

And the Census failed to capture that I am a student part time alongside work, which I think is a missed opportunity. And it didn't find out I take the bus to the railway station on the way to work, so my local Council's pleas about allocating funds to local areas won't be helped. There are some other issues (BSc or PhD? What's the difference?) but let's stop there.

Sigh.

Math/Maths History Tour of Nottingham 2/3 - George Green: Miller, Mathematician, and Physicist

2011-03-27T12:27:00.000+01:00

When Samuel Hansen visited me in Nottingham I took him on a maths and computing tour of the city and we filmed content for three videos. Here is the second, on Nottingham's most famous mathematical story, George Green.

There is a YouTube playlist with all the Math/Maths History videos and a map of the locations used in the videos.

George Green (1793-1841) was a miller in Sneinton, Nottingham who worked in his spare time to develop mathematics that, although unrecognised in his own lifetime, has been very useful to mathematics since. His work was rediscovered by Lord Kelvin and applied first to electromagnetism, later even to Nobel Prize-winning work in quantum theory, and continues to be useful to physicists and mathematicians today.

When Samuel Hansen visited Peter Rowlett in Nottingham, Peter took Samuel on a mathematics and computing history tour of the city. In this video, Peter takes Samuel to visit some of the sites from Green's life in Nottingham, including Green's windmill, Nottingham's mathematical playground, Nottingham High School and the Bromley House Library.

Listen to Samuel and Peter on the Math/Maths Podcast, a weekly maths news roundup from Pulse-Project.org.

Samuel Hansen's visit to the UK and associated activities were supported by: University of Nevada, Las Vegas, University of Greenwich, University of Leicester Mathsoc, Nottingham Trent University, MathsJam, Nottingham High School, Bromley House Library and the Institute of Mathematics and its Applications.

Census 2011: What do I do?

2011-03-17T09:48:00.003Z

I notice people on Twitter filling in the Census 2011 form already. (This is strange to me, because it is a record of who was in your house on the 27th March 2011. What happens if you get hit by a bus tomorrow? What if you're called away for work or a family emergency? What if you meet a nice boy/girl tomorrow and he/she is staying at yours, or you at his/hers, on the night of the 27th?) So I'm looking at the form.

Putting aside the question of whether I am English or British, and the difficult modesty-inducing issue of whether I can speak English "Well", or "Very well", and the concern that if I work I am asked to skip the question "Last week, were you: a student?" (a real missed opportunity to get some useful information and, it seems to me, indicative of a misunderstanding about part time education), or the fact that my journey to work (about 70 miles each way) must be either by train, by bus or on foot but not more than one of these, we come to the tricky issue of occupation. Along with employer details, the specific questions are:

"What is (was) your full and specific job title?"

This seems easy. My job title is "HE Curriculum Innovation Advisor". However, the prompts are "For example, PRIMARY SCHOOL TEACHER, CAR MECHANIC, DISTRICT NURSE, STRUCTURAL ENGINEER", so the question really seems to want a generic version of what I do. James Grime put "mathematician". As I said to him: if I taught I'd be a lecturer; if I did maths I'd be a mathematician. I'd like to be a lecturer, but I'm not. So what am I?

"Briefly describe what you do (did) in your main job".

This question allows 34 characters (including spaces) on the paper form. Oh dear!

So what do I do? Professionally, I do the following:

The main day job is HE Curriculum Innovation Advisor for the Maths, Stats and OR Network, a Higher Education Academy Subject Centre at the University of Birmingham, where I work on the Mathematical Sciences HE Curriculum Innovation Project, funded by the National HE STEM Programme.
I suppose my employer is properly the University of Birmingham. The work is split, I think, into four parts: HE Curriculum Innovation Fund (distributing funding and supporting funded projects); Research into current mathematics HE curriculum (read: course delivery and design), particularly "sector priorities" to inform distribution of the Fund; Dissemination of funded project and research outcomes and staff development; and, admin related to the other parts (although I am greatly supported in this latter by the MSOR Network).
PhD, Nottingham Trent University
Alongside this I am doing a part-time, self-funded PhD on, broadly, e-assessment in mathematics at higher education level. If you work in HE mathematics I have a questionnaire on advantages and disadvantages of e-assessment open until 25th March 2011 that it would be great if you could fill in.
Council Member, British Society for the History of Mathematics (BSHM).
Voluntary. Here I am a member of Council, a director of the company and trustee of the charity BSHM. This involves various specific voluntary activities, such as my 'unplanned impact' initiative and the upcoming talk on the Golden Section which I initiated and had a hand in organising. This also means I have an advisory and decision making role with the rest of Council on BSHM affairs.
Senior Vice Chair, Institute of Mathematics and its Applications East Midlands Branch.
Voluntary. This mostly involves helping to organise talks in the region.
Chartership Leader, Institute of Mathematics and its Applications Early Career Mathematicians Group Committee.
Voluntary. I am on the committee for the group and involved in collective decision making. Specific activities I am involved with are organising a pilot of a mentoring scheme for IMA membership and chartership applications and I will be attending the IMA Council Strategy Weekend in March which will make a strategic review of IMA activities, mission, etc.
Co-Host, Math/Maths Podcast for Pulse-Project.org.
Voluntary (in the sense that no one wants to pay me to do this, rather than this being necessarily a voluntary or charitable activity). A mathematics news/current affairs sort of podcast for Oxford science communication project Pulse-Project.org. I have a weekly chat with Samuel Hansen, upload the recording and add some text to a webpage on pulse-project.org. Recently this also involved a short lecture tour and recording some videos on mathematics history in Nottingham.
Organiser, MathsJam Nottingham.
Voluntary. I organise the Nottingham branch of this 'puzzles in the pub' monthly event.
STEM Ambassador.
Voluntary. I volunteered to be a STEM Ambassador in Nottinghamshire and have been CRB checked for this purpose. Working out of town a lot means I'm often not available to help with events but recently I attended an event to get teachers interested in using STEM Ambassadors and I am talking with the Big Bang East Midlands about running a stall and/or giving a talk.
Paid maths speaking engagements.
This year I had my first paid speaking gig. I gave a lot of talks in universities when I worked for the IMA but now my current job doesn't involve this and I don't have a lot of spare time, so when I was asked to give a talk I asked for a small payment for my time.
Other bits of writing.
I write this blog and I've been known to host a Carnival of Mathematics or write a popular maths article. So far I haven't been paid for this sort of writing.

On my website I describe myself using: "I work in maths promotion and maths education". On Twitter I say in my bio: "Mathematics incl. popular, recreational, education, history".

So, really, what do I do? Advice welcome!

Links to enthuse about mathematics

2011-03-09T17:04:00.000Z

A while ago an email was posted to a mailing list I am on. The IMA, my former employer and the professional body of which I am a member (and I hope you are too), are redeveloping their website and the redeveloped site will have a section "I Love Maths". The email asks for suggestions of content to link to and explains this will contain:

interesting articles on the history of mathematics;
biographies of mathematicians;
mathematical problems;
mathematical podcasts.

I sent an email back with a couple of suggestions. Then yesterday, on a sort of whim, I asked on Twitter for "Suggestions please: What websites, blogs, video, audio & online written resources could I link to to enthuse people about maths?" Here are the replies I have received so far. More welcome in the comments or on Twitter.

@CloudoidLtd and @joshgiesbrecht recommend the charming Vi Hart and her doodlings. Here's an example:

@jennycaddick recommended Plus Magazine. When I would give my careers talk for the IMA I would point out the Plus Careers Library and I'd always ask: "Do you read Plus?" and comment: "If you don't, you should. It's good!"

Plus magazine opens a door to the world of maths, with all its beauty and applications, by providing articles from the top mathematicians and science writers on topics as diverse as art, medicine, cosmology and sport. You can read the latest mathematical news on the site every week, browse our blog, listen to our podcasts and keep up-to-date by subscribing to Plus (on email, RSS, Facebook, iTunes or Twitter).

@acmescience pointed out the YouTube channels singingbanana by James Grime and TDAmathsmoneysavers by Matt Parker. Here are samples:

As well as his blog, reflectivemathsteacher, @reflectivemaths recommended Murderous Maths.

The books, the extra bits, games, hints, tricks, puzzles... they're all here !

You can watch a video here:

@dendari recommended Math Playground:

Welcome to Math Playground, an action-packed site for elementary and middle school students. Practice your math skills, play a logic game and have some fun!

@dansmath pointed me to his site dansmath.com, "for free lessons and link to my math(s) podcasts!"

@numberprose pointed me to the NumberProse Blog:

Welcome to my blog. I will share my thoughts on a variety of math-related topics. Sometimes when I go to a Spanish tapas restaurant after sampling some tapas, my taste buds are tantalized but I am left hungry for more. I need an entrée! Similarly if you are hungry for more information after reading a particular blog entry then click on the links for more in-depth reading.

@pkauppila recommended Math-Blog.com.

Math-Blog.com is dedicated to promoting the beauty of Mathematics at every level. It was started in 2007 by Antonio Cangiano, a Software Engineer and Technical Evangelist employed by IBM, who is very passionate about math. It began as a personal blog, but following its early success the site is now accepting external submissions and contributions by guest writers, with the long-term goal of making it a hub for those who intend to publish high quality, interesting and easy to follow mathematical articles on the Web.

Last but not least, @AbdelRSS pointed out the magazine published by his employer the RSS, Significance Magazine.

Statistics are key to understanding news, developments, and decisions. Updated daily, Significance brings you a statistical view of what's going on in the world.

Okay, I'm off to send in these suggestions. What did I recommend in my first reply? Well the IMA already know about the Travels in a Mathematical World Podcast but I recommended Strongly Connected Components and of course gave a nod to the Math/Maths Podcast. For history I sent in the MacTutor history of mathematics archive, the BSHM web resources section (although I've been asked to update this) and the new Bite-sized History of Mathematics written materials and podcast. I pointed out the first of three videos Samuel Hansen and I made on our History of Mathematics Tour of Nottingham and the two videos of lectures I gave for History of Maths and x, on cryptography and gravity. For blogs, I suggested the Big Two, Terence Tao's What's new and Tim Gowers Gowers's weblog, and also Greenwich Maths Time. For interesting reading I suggested Plus Magazine and Maths and Sport. For puzzles and problems I suggested Cut-the-Knot.org and recommended a link to MathsJam.

What would you recommend?

Math/Maths History Tour Locations

2011-03-05T13:41:00.000Z

I made a Google Map of the locations used in the Math/Maths History Tour of Nottingham. At present this includes the locations from video 1 - Computing: Burroughs Adding Machines and Ada Lovelace - but when the rest are released I will add those too.

I also made a YouTube playlist onto which I will add the new videos as they become available.

View Math/Maths History Tour of Nottingham Locations in a larger map

Math/Maths History Tour of Nottingham 1/3 - Computing: Burroughs Adding Machines & Ada Lovelace

2011-03-04T18:38:00.002Z

When Samuel Hansen visited me in Nottingham I took him on a maths and computing tour of the city and we filmed content for three videos. Here is the first. (Be sure to watch for the bit after the credits!)

Update (05/03/11): I made a YouTube playlist onto which I will add the new videos as they become available.

The Math/Maths Computing History Tour of Nottingham - Burroughs and Ada Lovelace

Nottingham is the burial place of the Byron family and particularly Ada Lovelace, regarded as the world's first computer programmer, who worked with Charles Babbage on his Difference and Analytical Engines. Nottingham was also the overseas manufacturing plant for Burroughs Adding Machine Company, a precursor of modern computers, which became one of the eight major United States computer companies and ultimately joined a merger to form worldwide IT brand Unisys.

When Samuel Hansen visited Peter Rowlett in Nottingham, Peter took Samuel on a mathematics and computing history tour of the city. In this video, Peter shows Samuel some of the sites related to this story in Nottingham, following a clue from David Singmaster's Mathematical Gazetteer of the British Isles, and Samuel tells Peter some of the relevant history of computing.

Listen to Samuel and Peter on the Math/Maths Podcast, a weekly maths news roundup from Pulse-Project.org.

Samuel Hansen's visit to the UK and associated activities were supported by: University of Nevada, Las Vegas, University of Greenwich, University of Leicester Mathsoc, Nottingham Trent University, MathsJam, Nottingham High School, Bromley House Library and the Institute of Mathematics and its Applications.

PhD questionnaire

2011-03-02T11:05:00.000Z

For my PhD I have written a questionnaire. I conducted interviews with UK higher education mathematics lecturers about their views of the advantages and disadvantages of e-assessment and traditional assessment (two users and two non-users of e-assessment). This questionnaire is based on the findings of those interviews and hopes to collect a wider range of views.

I would be very grateful if you could complete the questionnaire and pass this message on to anyone who you think might complete it. It is quite short; if it takes more than five minutes to complete I would be surprised.

If you are at all interested in this please consider completing the questionnaire but I am particularly interested to hear the views of those involved in teaching or supporting the teaching of mathematics at higher education level. I am not just interested in the views of those who use e-assessment; I would really like this survey to reach those who don't use e-assessment as well so they can offer their views on the advantages and disadvantages of different methods.

I will keep the questionnaire open until Friday 25th March 2011.

Thank you!

Samuel Hansen's Big Week of Podcasts

2011-02-28T15:42:00.001Z

Recently, Samuel Hansen blogged*:

I am an overly-active amateur podcast host. This has been a huge week for me as far as podcast releases have gone, with a total of four different, and new, podcasts available to download this week:
The ACMEScience Podcasts
Combinations and Permutations Episode 62: Jeff Goldblum on a Tilt-a-Whirl
4 mathematicians sitting around jawing over chaos theory.
Strongly Connected Components Episode 30: James Grime
YouTube phenomenon and professional Enigma Machine speaker joined me for an interview
Sam and Dan and Buckaroo Banzai
I am joined by Dan Sai for the 1st episode of a new podcast and we talk about the ins and outs of the best movie ever: Buckroo Banzai
Pulse-Project Podcast
Math/Maths Episode 35: Why Math?
My co-host Peter Rowlett and I are joined by Ruby Childs to talk about the reasons behind why people study mathematics.
I am well aware that most people probably do not care about any of this, but I would love if every single person who saw this just went and listened to one of these episodes. Oh, and if you already listen to one of these, or all of them, I would be really happy if you reblog this and help spread my podcasts through the internet.

(* alright, I may corrected a couple of spellings. And added a little punctuation. But go listen to his podcasts!)

400 words in 30 minutes on why I took maths further

2011-02-20T11:16:00.000Z

Goal: 400 words researched and written in half and hour. For me, for practice. Corrections welcome in the comments.

This time I try to answer a question from Ruby Childs: "why did you study mathematics?" Recently we recorded a Math/Maths Podcast with Ruby as a special guest and we discussed issues around this question. Why do some people like maths when others don't? Why do people take maths further?

This is a bit of a cheat for 400words, because it's a topic I didn't need to research. It's all personal. I could have just written this as a standard blog post but I've set myself up to try to do this piece of constrained writing and, hey, I'm busy this week so two birds with one stone is attractive!

Ruby would like more answers to this question. You can contact her via Twitter as @RubyChilds or send her a message via the Ask me anything feature on her tumblr blog.

∞

When I was nine, we moved house and school. I wasn’t particularly good at or keen on mathematics. Nine years later, I went to university to read mathematics. Recently I have been asked: Why did I choose to take maths further?
I recall moving into a small village primary school with the two boys in my year taking classes with the year above. The dozen or so girls in my year didn’t have this privilege. I was placed with the boys even though I would sit in the corner doing different work. However it sounds, I don’t remember this being a bad experience – it was simply that I hadn’t, at my previous school, covered the same material.
The headmistress, Miss Crabtree, was very keen on mathematics and though I don’t remember specific incidents I can only assume my enthusiasm for the subject from that age was from her. I seem have caught up well enough and, when we finished the primary school maths curriculum months before the end of school, Miss Crabtree brought out other “interesting material”. There was mathematics in these few months that we didn’t cover until the third year of secondary school.
At secondary school I found maths easy and enjoyed learning new topics. At GCSE I took three separate sciences. I was interested in science, too, but taking these as separate subjects unlocked a new mathematical GCSE: statistics. At A Level three of my choices were obvious – Maths, Further Maths and Physics. I chose Chemistry as my fourth.
Then came the careers questionnaires. I answered questions and the answer came back: Chemical Engineer. I did work experience in a local cement works and the university chemical engineering labs. Although it was interesting enough, I didn’t feel a proper enthusiasm for the subject. I decided to take physics instead, but still there was a bit too much messy lab work for my liking. I liked the logical structure and reasoning, which fit my way of thinking about the world. Eventually, and I don’t remember how, I came to understand mathematics was a valid option for university and signed up.
So why did I choose maths? I liked it, was good at it and the structure of it fit my way of thinking well. Did it fit my way of thinking because of early training from Miss Crabtree? Perhaps. In any case, this confused mixture of interest in physics and ability at logical thinking led me to prefer applied maths but do better at pure, and ultimately to excel at programming and go into a computing Masters degree. So that’s what led me to mathematics and what led me away again. Now, when something goes wrong or a problem needs solving, I can feel my brain starting a logical breakdown and I relax into mathematician mode, and I still like it.

∞

Time: 27 minutes. 473 words. Performance: too many words. I feel it would have been easy enough to take the last few minutes to shorten it by amalgamating paragraphs two and three to a new paragraph of half their overall length, but I decided not to because I am trying to give as full as possible an answer to Ruby's question. This doesn't quite fit the "400words" idea, but it's my game and I'll break the rules if I want to.

Explanation. More 400 words.

400 words in 30 minutes on sexy primes

2011-02-13T15:26:00.000Z

Goal: 400 words researched and written in half and hour. For me, for practice. Corrections welcome in the comments.

∞

With Valentine's Day upon us a seemingly appropriate mathematical topic is sexy primes. These numbers surely have some attraction to those in the mood for love.
In fact, the "sexy" in "sexy primes" is a reference to the Latin word for the number six: "sex".
Sexy primes are prime numbers separated by six places from another prime number. You may remember that a prime number is a number that can only be divided by 1 and itself. So 5 is prime because you can only divide it by 1 (to give 5) or 5 (to give 1). All other numbers divide into 5 to give answers which are not whole numbers. Try it: 5 divided by 2 gives 2.5 - not a whole number.
In fact, 5 is not just prime, it's sexy too. That's because 11 is also a prime and is six places from 5.
The next sexy prime pair? 7 and 13. Then, 11 and 17. Actually, that's the second time we've seen 11, isn't it? It's six places above 5 and six below 17, and all three are sexy primes. This means we've found our first sexy prime triplet: three primes with common difference six. The second of these is 7, 13 and 19. You can get sexy quadruplets too and one sexy quintuplet, but only that one.
A natural question to wonder at this point is: what is the largest sexy prime? The largest we know of has over 11 thousand digits, but is it the largest? Well, we know there are infinitely many prime numbers - Euclid proved this in ancient Greece - but the higher up the list of numbers you get, the rarer prime numbers are. The question of whether there are infinitely many sexy primes depends on the distribution of primes, and this is something we don't know. In fact, the question of the largest sexy prime leads us neatly to an unsolved problem called Polignac's conjecture. Alphonse de Polignac, a French mathematician in the 19th Century, made a conjecture in 1849 that, if true, would mean there are infinitely many sexy primes. However, 162 years later, this has neither been proved or refuted.
That mention of the year brings up another connection: 2011 is a sexy prime. That's because 2017 is also prime. Mathematics is an active field of research. Perhaps by 2017 we'll have our answer.

∞

Time: 31 minutes. 397 words. Performance: not bad. I discovered my text editor was counting words wrong, so that "we've" was counted as two words. Sigh.

N.B.: @stecks suggested that we cover 'Valentine's maths' for today's episode of the Math/Maths Podcast. @axiomsofchoice suggested sexy primes. So this piece owes a debt to them for the suggestion.

Explanation. More 400 words.

400 words in 30 minutes on chaos and the weather

2011-01-15T15:19:00.006Z

Goal: 400 words researched and written in half and hour. For me, for practice. Corrections welcome in the comments.

∞

Why does the weather forecast only go a few days into the future, and why are they so often wrong about what will happen in a couple of days time? If they know where the weather systems - clouds and so on - are right now, and they have a good computer model for how things change over time, why can't they predict the weather a fortnight from now, or a year?

The answer is that weather is a chaotic system. In everyday language, chaos means complete disorder without pattern but in mathematics the same word chaos refers to a particular phenomenon. Chaos theory studies the behaviour of systems that are very sensitive to small changes in initial conditions. This means slight differences in the starting point of a system can give very different results in the long term.

Because the system gives very different results when you run it twice with similar starting conditions, you might think that it involves some random elements that change each time you run the process. However, this mathematical chaos does not involve random elements. If you run the process twice with exactly the same starting conditions, it will give the same results. This is not like a random process - each time you run it you get a different outcome. We call such a process, in which running the system in the same way gives the same results every time, deterministic, because if we know everything about it we can determine in advance what will happen.

What makes chaotic systems interesting is that they are deterministic but so sensitive to initial conditions that they aren't predictable. A slight difference in the initial conditions can give massively different outcomes.

For the weather forecast, the computer model is fed by initial data from weather monitoring stations. If some of that data is slightly off, or if the computer model doesn't correctly guess what is happening between stations, the model can give radically different answers to what will actually happen. These differences mount up - if you got tomorrow's weather forecast slightly wrong and used it as the initial conditions to forecast the next day, then that could be very wrong indeed.

This is why weather forecasts are continually updated and why forecasts are only made reliably for a short period in the future.

∞

Time: 39 minutes. 388 words. Performance: took too long. I started without a clear idea and started writing as I was researching. At 25 minutes I gave up on one idea and started anew. Bad practice! I should try to remember to take some time to process before I start writing.

Explanation. More 400 words.

Pedantry on Euler and masts

2011-01-09T11:40:00.006Z

I listened to the second episode of A Brief History of Mathematics on Euler yesterday. I was quite taken with a quote from Euler which, to me, says something of the potential dangers of the application of mathematics to the real world. The relevant section of the programme is:

"In the year that Issac Newton died, Euler, then aged just 19, was awarded the most prestigious mathematical prize of the day, the first of many, many achievements and accolades he would receive during his lifetime. The annual mathematical challenge issued by the Paris Academy of Science in 1727 was this: "What is the best way to arrange masts on a ship?" At first sight it's a very practical problem, but the young Swiss mathematician Leonhard Euler attacked it as a purely mathematical puzzle. Despite having never set foot on a ship, he felt perfectly well qualified to calculate the optimal arrangement of masts. For him, it was a problem that could be solved by mathematics alone.
"'I did not find it necessary to confirm this theory of mine by experiment because it is derived from the surest and most secure principles of mathematics, so that no doubt whatsoever can be raised on whether or not it be true and takes place in practice.'
"Leonhard Euler had absolute faith in mathematics...."

Having copied this out and investigated a little, I have a couple of small factual problems with this passage.

Newton died in 1727 (on 20 or 31 March, depending on your calendar) and Euler was born 15 April 1707, so I'm happy Euler was 19 in the year Newton died. And Euler's report was submitted to the 1727 Grand Prize of the Paris Academy on the arrangement of masts on a ship. (Whether the Prize was awarded pre- or post-15 April I cannot find, but this seems almost irrelevant really; that, according to the Euler Archive, Euler wrote the paper in 1726 isn't really relevant since the claim made is of the award of the prize.) Euler didn't, however, win the prize. He came second. The first prize was shared between Pierre Bouguer and Charles-Étienne Camus. This is regarded as a substantial achievement in any case given Euler's age and the fact that Bouguer was an established expert on ships. The programme doesn't quite say he came first, but the wording "was awarded the most prestigious mathematical prize of the day" is strange when Euler was second to Bouguer and Camus.

My second factual issue is that I can't find the quote as quoted anywhere. I can only find it quoted online as:

"I did not find it necessary to confirm this theory of mine by experiment because it is derived from the surest and most secure principles of mechanics, so that no doubt whatsoever can be raised on whether or not it be true and takes place in practice." (emphasis added)

The quote is from Euler's submission to the Grand Prize, which was not written in English, so there are translation issues here. The Euler Archive at Dartmouth provides a scan of the original printed in Recueil des pièces qui ont remporté lex prix de l’académie royale des sciences (1732):

"Haud opus esse existimavi istam meam theoriam experientia confirmare, cum integra et ex certissimis et irrepugnabilibus principiis Mechanicis deducta, atque adeo de illa dubitari, an vera sit ac an in praxi locum habere queat, minime possit."

Ian Bruce provides an original translation where the relevant passage is given as:

I do not think that it is necessary to confirm my theory by experiment, since the whole has been deduced from both the surest and the most irrefutable principles of mechanics, and thus concerning that there cannot be the least doubt or the truth can be put to the test in practice.

In any case the latin "Mechanicis" or the Ian Bruce translation "mechanics" suggests "mechanics", not "mathematics".

This puts me in mind of another recent programme, The Beauty of Diagrams, in an episode on Newton and optics Marcus says "and, as Newton took up residence again at Trinity, over in Italy Galileo was busy working out the speed at which light reaches us from the Sun". The problem here is that Galileo died almost a year before Newton was born.

My feeling is that the Prize issue may have been a quick shorthand as this is a side point and the programme is very short overall. The essential point is "Euler made fantastic achievements from an early age and here's something of his view on the application of mathematics". Then the mathematics/mechanics mixup seems likely to me to have been a change to avoid having to explain the term mechanics.

I have a lot of sympathy with getting obscure facts wrong with this sort of thing, which I feel is an ever-present danger in everything I do and I'm sure I will sometimes land on the wrong side of correct. I also have a lot of sympathy with trying to get the core message across without getting distracted by details in a limited timeframe. This is something I haven't had a lot of experience with in my self-published podcast endeavours, in which if you need an extra 30 seconds to explain something you can just take it (although you perhaps shouldn't).

In any case, I would recommend any applied mathematicians hang a sign somewhere with the following wording, as a warning against arrogance:

"Haud opus esse existimavi istam meam theoriam experientia confirmare, cum integra et ex certissimis et irrepugnabilibus principiis Mechanicis deducta"
"I do not think that it is necessary to confirm my theory by experiment, since the whole has been deduced from both the surest and the most irrefutable principles of mechanics."
Leonhard Euler, c.1727.

Also, consider including the wording in your next grant application.

Cosmic-Ray Research Centre and Cold War Helter-Skelter in Secret Cave City

2011-01-06T12:03:00.005Z

Samuel Hansen directed me to this article: "The secret cave city under Nottingham". The article is highlighting The Nottingham Caves Survey, who offer:

The Nottingham Caves Survey is in the process of recording all of Nottingham’s 450+ sandstone caves. The project is now underway and we are surveying caves even as you read this. Keep checking the website for newly- surveyed caves! You can read more about the caves, see photographs, watch fly-through videos and take virtual tours.

The survey is producing some interesting images, such as the following (credit: Trent & Peak Archaeology / The University of Nottingham; click to enlarge):

Laser-scanned image of King David’s Dungeon, below Nottingham Castle. King David II of Scotland was reputedly held captive here in 1346.

Laser scanned orthographic plan of the Goose Gate caves, Nottingham. These caves include a medieval malt kiln, 18th-century brewery cellars and a 19th-century butchery.

And some very compelling videos:

I'm not sure about the use of the phrase "secret cave city" and the talk of the Survey using techniques to "reveal elaborate cave systems under the town of Nottingham" (in the post, not used by the Survey itself). I am pleased that the Survey is producing detailed scans of these caves, it's interesting business and nice to see them being made accessible through multimedia, but the caves were not previously secret. In my experience, the existence of widespread caves under Nottingham is fairly well known. The Survey knows this and is specifically scanning those caves that are physically accessible (although perhaps not all open to the public).

Nottingham is referred to by a biographer of Alfred the Great in 868 as "Tigguo Cobauc" which you see translated as "House of Caves," "Place of Caves" and "City of Caves". A book on the history of Nottingham I have has the following:

"Entering the town at the beginning of the seventeenth century, Bishop Corbett exclaimed: 'Why, the people live not in howses but are earthed in holes!' If a man was destitute, explained one writer in 1639, 'he has only to go to Nottingham with a mattock, a shovel, a crow or an iron, a chisel or a mallet, and with such instruments he may play the mole, the coney, and work himself a hole or burrow for his family where over their heads the grass and pastures grow, beasts do feed and cows are milked.' The caves in the area of the castle have been used as mushroom farms, cockpits, gambling dens, privies, drinking cellars and burial vaults. During World War II, some factories enlarged them as air raid shelters for their workers. Today the caves house social clubs, a rifle range, store-rooms and a cosmic-ray research centre. From time to time somebody gets even more exotic ideas for them - such as linking them together for a Tube railway or turning them into atomic shelters, to be reached quickly by people sliding down on mats as if on a helter-skelter. Builders, of course, regard them as a nuisance and a hazard, and refuse to give a firm quotation for work in the centre of Nottingham. But the tours of underground Nottingham run for the 1972 festival proved so popular that the city has woken up to its subterranean history as a tourist attraction. The thirteenth-century tannery (the only underground one in Britain) revealed in the multi-million pound Broad Marsh development, has been spared"
(Portrait of Nottingham by E. Bryson, 3rd ed. 1983, p. 26).

I reckon there's a good alternative history story in those imagined subterranean Thunderbirds-esk helter-skelter cold war bunkers.

The quote above is all interesting but the phrase "cosmic-ray research centre" in particular catches my eye. There is a paper 'The Absolute Intensity of Muons at 31.6 hg cm^-2 Below Sea-Level' by Crookes & Rastin (Nuclear Physics B 58 pp. 93-109, 1973) which describes an experiment in a cave under the Castle:

"A cave in bunter sandstone of uniform composition lies below Nottingham Castle, and this provides an experimental site at 43.0 hg cm^-2 from the top of the atmosphere. The apparatus used by Crookes and Rastin to measure the absolute intensity at sea-level in both the vertical and inclined directions was therefore used to provide similar data at this underground location" (p. 96).

The first picture above shows some of the caves under the Castle and it seems some of them provided an experimental site for detection of cosmic rays for physicists from the University of Nottingham in the 1970s.