Barriers to teaching

Lecturer in Mathematics.
School of Mathematics, University of Excellence.
Competitive salary.

Applications are invited for the post of Lecturer in Mathematics.

The University of Excellence is ambitious for the future, priding itself on its commitment to world-leading research and investment in an outstanding research environment. The opportunity is available to join a dynamic, highly esteemed and international research programme. Candidates who can interact with one or more of the School's existing research strengths are particularly encouraged to apply.

As a successful candidate, you will have a PhD (or equivalent) in some branch of Mathematics and a track record of relevant research. You will have demonstrated the ability to publish consistently in leading research journals and be able to provide evidence of your experience attracting research funding. You will advance the School's research agenda by supervising a group of PhD researchers.

In the latest UK Research Assessment Exercise the School submitted research output from over 70 staff. 65% of this research was recognised as being either world-leading or internationally excellent in terms of originality, significance and rigour.

Underpinned by the quality of its research, the School offers a range of degrees from undergraduate to postgraduate level. The successful candidate will also be expected to contribute to the development and delivery of teaching in Mathematics.

Potential candidates are encouraged to check our website for full details.

Reading around the Alan Turing Pardon

I have a piece in this week's Pod Delusion episode 123 at 45:00 on the pardon for Alan Turing.

Here are links to some of the bits I talked about in this.

I spoke about concerns of overdoing the Turing celebrations, saying: what Turing did was brilliant, but we should celebrate what Turing actually did, not some imagined feats, and we should not forget others in doing so. You can read more about this and find out about the article which suggested that had Turing lived then Silicon Valley might have been started in the UK at 'Beware the Alan Turing fetish' by John Graham-Cumming.

Turing was convicted under Section 11 of the Criminal Law Amendment Act 1885. In 2009 Gordon Brown issued an official apology for the way Turing was treated. Read about the official Government apology in 'PM's apology to codebreaker Alan Turing: we were inhumane'. Read how the apology came about in 'How Alan Turing Finally Got a Posthumous Apology' by John Graham-Cumming.

Now there is a current e-petition calling for a pardon for Turing. John Leech MP issued an early day motion calling for this pardon. (I also mentioned the current e-petition calling for a pardon for Oscar Wilde.)

Asked a question in House of Lords, a Government Justice Minister said "a posthumous pardon was not considered appropriate". Read the text of Lord McNally's statement.

I've seen the refusal to pardon Turing described as "homophobic" and an "act of malice". Particularly, the complaint is that Turing is still seen as a criminal in the eyes of the law.

John Graham-Cumming on 'Why I'm not supporting the campaign for a pardon for Alan Turing', in which he writes about the Protection of Freedoms Bill, which "specifically allows for the disregarding of convictions under the old law that was used against Turing".

To honour Turing I suggested you might attend events under the Alan Turing Year banner, or donate to Bletchley Park's Action This Day! fundraising campaign.

This piece used audio from episodes 84 and 85 of the Pulse-Project Math/Maths Podcast.

A puzzle from James Grime about abcdef

Today James Grime tweeted this question/puzzle:

Is there a six digit number abcdef such that the following all hold?

1. a+b+c+d+e+f = y
2. ab+cd+ef=10y
3. abc+def=100y

If not, show why not.

A little tweeting back and forth verified that "ab" means 10a+b not a×b.

If you want to have a go at this, don't read any further until you have!

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First, rewrite the expressions so that both sides use standard arithmetic:

1. a+b+c+d+e+f = y
2. 10a+b+10c+d+10e+f=10y
3. 100a+10b+c+100d+10e+f=100y

I noticed that since a, b, c, d, e and f are all positive integers, so must y be. Then 10y must end in 0 and 100y must end in 00.

From 3, we see that in 100y only c and f contribute to the units, so c+f=0, or f=-c. See also that only b and e contribute to the 10s, so b+e=, or e=-b. 
Since a, b, c, d, e and f are positive digits 0-9, the only values that satisfy these equations are c=f=0 and b=e=0.

From 2, we see that in 10y only b, d and f contribute to the units. Therefore b+d+f=0, or d=b+f. Since b=f=0, we know that d=0.

So solutions to this problem have a being any digit 0-9, b=c=d=e=f=0, and so y=a.

The answer isn't no, nor is it quite yes. These multiples of 100000 are not exactly interesting!

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After I emailed Jim I was interested to see this solution, posted at The Wandering Monster, which took a substitution approach. On Twitter Dave Hughes gave his approach: "My solution was inelegant - I threw a C# program at it". How interesting to see how different people approach a problem!

Update (20 mins after posting!): Please check the comments for a caveat I've missed.

Things to do in London on a Tuesday

Next Tuesday I will spend a day off in London. I am asking people to offer suggestions for things I could do with my time by adding pins to this Google Map: PR's Day Off. A few people have already added their suggestions but it would be great to hear more.

View PR's Day Off in a larger map

Load the map, then you need to log in with your Google Account then a big red edit button should appear and you can add a pin. The description I put on the map:

Ground rules:
Date is Tuesday 21st Feb.
Free or low cost. It's expensive just to get to London.
I have a zone 1 & 2 tube card.
Train times are non-negotiable (fixed tickets).
I am going on the Maths in the City tour.
All else is up for grabs.
Make suggestions for places to go and things to see by putting pointers on the map. Explain why and give timings and a link if appropriate.
For timed events: Remember to allow enough time for travel (for someone who doesn't know where they are going).
Please don't delete other people's entries. If you disagree, by all means leave a comment to say so but don't delete something you haven't put there.

If you can't get the Google Map to work please leave your suggestion in the comments of this blog post.

George and Julian

Yesterday, the @mathshistory Twitter feed tells me, was the anniversary of the birth of Julian Schwinger (1918-1994), one of the great physicists of the 20th century. (Technically I queued this tweet up but there are a lot of days and a lot of mathematicians to remember...)

Schwinger is known to me particularly through his connection to the story of George Green. Green was a Nottingham mathematician who did work on electricity and magnetism (among other things) that, largely unrecognised in his lifetime, was discovered and brought after his death to further attention by William Thomson (later Lord Kelvin). The application of Green's work in 19th century science was impressive but it found a new legacy in the 20th century.

At the 1993 celebration in Nottingham of the bicentenary of Green's birth, Schwinger spoke about his use of Green's work (a talk written up as The Greening of Quantum Field Theory: George and I).

Schwinger's account is worth reading. He describes his use of Green's work first on microwave radar during World War II, then in the development of the microtron and synchrotron particle accelerators, and finally to solve a problem on quantum electrodynamics, work which earned him a share, with Sin-Itiro Tomonaga and Richard Feynman, of the 1965 Nobel Prize for Physics.

In the preface to his most famous work, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (1828), Green had written:

Should the present Essay tend in any way to facilitate the application of analysis to one of the most interesting of the physical sciences, the author will deem himself amply repaid for any labour he may have bestowed upon it.

Schwinger's account helps us to understand how Green not only impacted the physics of his age, but how it continued to have impact beyond anything Green could have imagined.

Mathematicians are people too

Last Saturday in the Telegraph there was a feature announcing the start of a numeracy campaign: Make Britain Count. This included an article by Rachel Riley about "the stigma around maths". She writes about the "image problem" of maths and numeracy:

I’m a blonde Essex girl, so I’m well used to being talked down to, but when I tell people I did a degree in mathematics at Oriel College, Oxford, I see their jaws hitting the floor. Mathematicians labour under a negative stereotype – older men in anoraks with beards and glasses. Maths isn’t sexy. 

She talks about problems of attitude and relevance to the real world, and the need for creative teaching to

teach children number skills from first principles. They have to know the underlying “why” of maths, not just memorise the formulas.

Let's talk a little about the issue of the image of mathematicians. Last night on Twitter I was approached by user @philhumpo, a teacher from Exeter, with this query: "I need a 'top 5 crazy mathematicians' (duelling Romans, drowning kittens etc)."

This sort of thing concerns me. I wondered in what sense he meant "crazy". Mathematics can seem to have an association with mental illness in popular culture and so I'm naturally concerned if "crazy" is being handled sensitively. Also, many of the interesting historical anecdotes turn out to be false or exaggerated, an issue touched on in my previous post.

Thankfully, it was just an issue of the brevity of messages on Twitter. Phil explained the heart of the problem. It's the last day of term today and Phil has his class of 15 year olds for a shortened lesson. He has discovered many of them think "all mathematicians are grey suit baldies with social problems" and hopes to disabuse them of this view.

With the reference to duelling mathematicians, Phil is clearly aware of Évariste Galois, who clearly has a romantic and stereotype-breaking story. Ramanujan is another good story. You can find online biographies of women mathematicians - Ada Lovelace, Mary Somerville and Sophie Germain are typical examples, though there are many more.

I also wondered about more contemporary sources. Recently I came across a photo blog "This is what a scientist looks like" via the @HESTEM Twitter feed. A quick search reveals just one mathematician featured so far. As Phil put it "hmmm… not a duelling Frenchman but not a grey suited baldy that's for sure".

I recommended Katie Steckles' video Playing Games with Squares. Katie certainly doesn't fit the stereotype and the video shows her having fun with mathematics.

There are a host of careers profiles from a range of different people in the Maths Careers Career profiles, where just scrolling down the page gives an idea of some of the stereotype-breaking people involved with mathematics, and a similar list is available with the Plus Careers Interviews.

I am sure there are countless more examples of mathematicians breaking the mold - mathematicians really are people too! - and I've only had a quick think about it. Perhaps you can suggest your favourites in the comments.

Why do we enjoy maths history misconceptions?

I don't think I have come to a conclusion from my previous blog post about historical accuracy and popularisation, though there were some interesting points in the comments (relating less to my comments about the 'errors which may be gently corrected' and more to the 'demands of the narrative').

George Jelliss and Thony C. both read the famously inaccurate Men of Mathematics by E.T. Bell in their youth and were inspired to mathematical lives as a result.

Will Daniels suggests I should hold different standards for different people, so those writing historical research are held to a higher level of accuracy than those writing for a popular audience. I'm not sure this feels right. Thony asks a really interesting question:

is it possible to achieve the inspiration generated by Bell's book and be historically accurate at the same time?

I think this is at the heart of the matter. If it is possible to inspire through popularisation while remaining completely accurate then I can safely hold everyone to this high standard. However, if inspiration requires a little showmanship, if telling a good tale means not getting lost in minor distractions and sub-clauses, then we have our double standard.

This brings me to a final, anonymous comment that includes the following statement:

I am a great believer in the wisdom of stories, regardless of their provenance. If some stories persist despite being disproven, there must be a reason.

My first reaction on reading this is that it is preposterous. If you start presenting stories you know to be disproven you are in the realm of historical fiction. Historical fiction is fine, but these are now just stories and have no place being presented as real accounts of historical mathematics and mathematicians. Then today I was struck by something relevant.

I was listening to Paul Dirac and the religion of mathematical beauty on the Royal Society Library podcast while wrangling with the washing machine. This recording, of a talk given in March 2011 by Graham Farmelo, covers the life of Paul Dirac. Farmelo talks about how Paul Dirac is considered to be the theoreticians' theoretical physicist, yet he had a very practical schooling and took a practically-focused engineering degree. Farmelo says (15:40):

Let's get one thing right, he was a very practically-minded person. Completely different from the image that he has among most theoretical physicists.

This is as so often the case; the established fact isn't just slightly wrong but completely wrong. This is the case in the story that Einstein did poorly at school, a misconception that Thony C. tells me is not as well known as I thought it was when I used it as an example in my previous post.

Do we really want to believe Dirac is a theoretician with no practical sense, that Einstein was a terrible student made good? Is there really some "wisdom" in these stories that causes them to "persist despite being disproven"?

Rather than necessarily being wise, I think we are drawn to certain types of story. The Dirac perception reinforces the view of a flawed genius; a theoretical physicist with no sense of the real world. The Einstein story perhaps speaks to a desire for the plucky underdog to win out in the end.

Aren't these classic Hollywood ideas? Do other common misconceptions fit into the Hollywood-style? (Galois' heroic struggle against the odds to invent Galois theory in a single night before the dual springs to mind. What others?) Do, in fact, stories that deviate from historical record and persist deviate when the story fails to fit a certain sort of narrative?

Perhaps more importantly, are there correct historical stories which fit a classic Hollywood narrative? (I'm thinking, for example, of George Green teaching himself advanced mathematics "in the hours stolen from [his] sleep".) Perhaps stories of this type are the key to achieving Bell-like inspiration while maintaining historical accuracy.