Prime birthdays via Wolfram|Alpha

Recently on Twitter, Matt Parker (standupmaths) and James Grime (jamesgrime) were having a "nerd slamdown" working out next prime birthdays. This is the next date when the number of days since you were born is a prime. Here's how to work this out in Wolfram|Alpha.

For the purposes of this example, let's choose an arbitrary date in the past. Let's choose 15 April 1707 (Gregorian calendar). No prize but smugness for answering who's birthday that was (if you can't work it out, you can always ask Wolfram|Alpha "who was born on 15/04/1707?").

Go to www.wolframalpha.com and enter: "days since 15/04/1707". The result should look something like:

So our answer is 110805 days. Your birthday is probably somewhat more recent, so the number will be smaller (something like an order of magnitude smaller).

Next ask for "list of primes greater than or equal to 110805". This gives the start of an infinite list of primes. You can get more by clicking "More".

So we have an answer - 110807 days will be the next prime birthday. We know today is 110805 days since the date, so the next prime birthday is in two days. If you have trouble with working out a date you can ask Wolfram|Alpha that as well. Say you decide to take an interest in the prime 112111, you can ask for "112111 days after 15/04/1707" to discover the date you are looking for is Tuesday, 25 March 2014.

(N.B. If you grow weary of celebrating every prime birthday, why not celebrate just your palindromic prime birthdays. Here's a list within a reasonable range:

2 3 5 7 11 101 131 151 181 191 313 353 373 383 727 757 787 797 919 929
10301 10501 10601 11311 11411 12421 12721 12821 13331 13831 13931 14341 14741
15451 15551 16061 16361 16561 16661 17471 17971 18181 18481 19391 19891 19991
30103 30203 30403 30703 30803 31013 31513 32323 32423 33533 34543 34843
35053 35153 35353 35753 36263 36563 37273 37573 38083 38183 38783 39293

from World!Of Numbers).

On the Decline of Mathematical Studies, and ever was it so

When I started taking an interest in university mathematics teaching back in 2003/4, I quickly became aware of a report "Measuring the Mathematics Problem" (2000; also the 1995 Tackling the Mathematics Problem). This describes a decline in standards of students entering university and looks to serve as a call to arms to take action to prevent further decline. The preface of this reads:

Evidence is presented of a serious decline in students mastery of basic mathematical skills and level of preparation for mathematics-based degree courses. This decline is well established and affects students at all levels. As a result, acute problems now confront those teaching mathematics and mathematics-based modules across the full range of universities.
This report is aimed, therefore, at those in Higher Education who teach mathematics-based modules and those involved with admissions. There is a need for each department to become attuned to the full extent of the problem as it affects their students. The diagnostic testing of new undergraduates is recommended as an effective means of achieving this goal.
The report is also aimed at those charged with responsibility for setting the A-level Mathematics curriculum. Following the many changes introduced in the early 1990’s we would suggest that now is the time to take stock.

Now, I think it is important work and I mean in no way to belittle such worthwhile endeavour, but recently I have come across a couple of sources which set such despair in some context.

Firstly, see the following quote:

Today as never before mathematics is assuming an importance in the lives of everyone. Never has science, of which mathematics is the basis, played such a great role in the development of modern society and in the solution of both peacetime and wartime problems of organization and production. Even more, perhaps, in a time when everything depends on education toward reason is mathematics the unparalleled agent of mental discipline and the embodiment of constructive and inventive thinking.
Unfortunately, these aspects of mathematics have been greatly neglected in the recent past. Most of us have been subjected to a routine mathematical training in high school. Some of us acquire a certain degree of mathematical skill in liberal arts colleges or engineering schools. Few of us, however, have any real understanding of mathematics and what it is all about. What is Mathematics? was written to fill that gap.

This is from the cover blurb for What is Mathematics? by Richard Courant and Herbert Robbins. I can't tell if this was written in 1941, when the book was first published, or in 1960, when the edition I am holding was printed. (This book was revised in 1996 by Ian Stewart and is still available; it gets a review from Brian E. Blank in the Notices of the AMS in 2001.)

But we can do better than that. A few weeks ago, on the Math/Maths Podcast episode 4, Samuel Hansen read a little from a letter by Rev. John Toplis, written in Arnold, Nottinghamshire on October 13, 1804, entitled: "On the Decline of Mathematical Studies, and the Sciences dependent upon them" (as written up with commentary over at Skulls in the Stars). From this:

It is a subject of wonder and regret to many, that this island, after having astonished Europe by the most glorious display of talents in mathematics and the sciences dependent upon them, should suddenly suffer its ardour to cool, and almost entirely to neglect those studies in which it infinitely excelled all other nations ... It is a very great disgrace for a nation like this, which can proudly boast of a superiority over all others in arts, arms and commerce, to suffer the sublimest sciences, which once were its greatest pride and glory, to be neglected.

So it seems mathematics is often (or continually?) considered to be in serious decline. Does this mean contemporary concerns about mathematics teaching are misplaced? We can't say that, but it's interesting to consider that generational differences, rather than decline, may be at work.

I notice this week in his Bad Science column, Ben Goldacre talks about decline in A-Level standards: "Are exams getting easier? Nobody knows".

Teaching/research importance

Just looking out some stories for the Math/Maths Podcast and, from Tony Mann's Twitter stream, I came across a review in the New York Times of a facsimile of The First Six Books of the Elements of Euclid: In Which Coloured Diagrams and Symbols Are Used Instead of Letters for the Greater Ease of Learners, from which is quoted:

The arts and sciences have become so extensive, that to facilitate their acquirement is of as much importance as to extend their boundaries.

Oliver Byrne, 1847

What is the Math/Maths Podcast?

Just over a year ago, I wrote a post, "Echoes in an empty room", about how wonderful it was to hear someone who listens to Travels in a Mathematical World describe the podcast in their own words. It can be a strange and isolated experience recording podcasts and it is always encouraging to hear from someone who has listened and liked what I've done, but even more so when they articulate their own perceptions about what I have made (and when they differ from my own).

Now, Samuel Hansen and I are recording the Math/Maths Podcast. This differs from the "empty room" of my previous post because I am speaking to someone down the pipes of the Internet and we have an enjoyable time recording episodes (much more so, for me, than the stilted experience of recording intros to Travels in a Mathematical World), which reduces the need for such encouragement. Having said that, it is still pleasing to hear from people who are listening and liking, and we occasionally do hear from people in this way through Twitter, email or, for me, a couple of times in person. We don't have access to download stats but, even if we did, we know that just because someone is downloading doesn't mean they are listening, and knowing they are listening doesn't mean we know what they think about it.

We have been asked to write a description of the podcast for the Pulse-Project blog. We could easily write something, but we thought this was a good opportunity to encourage some listener feedback. Everyone's perceptions are different and it would be interesting to hear what you think of the podcast and what you get out of listening to it. It would be brilliant if you could write a description of the podcast and send it to us. We'll aggregate what we receive and write up a description of the podcast for the blog. We've already had one heart-warming comment from dansai, which reads:

I don't know much about Math...But I know I like this. Misters Hansen and Rowlett discuss interesting topics and in a way a dummy like me can understand. Listen, people, this thing is informative AND entertaining, so subscribe already!

This is fantastic to hear! I like to think the podcast will be accessible, of interest and entertaining to a general intelligent audience and not just to those versed in mathematics, but it's great to hear this is also the view of someone who listens. This can be a theme we draw out in our blog post.

If you subscribed through the iTunes Store, it would be especially great if you could leave your comment as an iTunes review (because this has other positive benefits). If you use another service, you could review it there (though you'll need to tell us where to look) or you can email your description directly to samuel@acmescience.com or leave it as a comment on this blog post.

No excuses! ;)