The Ideas Exchange provides an opportunity for each participant to put forward, in five minutes, an idea for subsequent discussion with sympathetic colleagues. It was suggested that this might be something which one had tried and wished to share, an idea that one was planning to implement and wanted advice on, or a mad suggestion that, with refinement and suggestions from others, might just turn into something workable. This was the second such Ideas Exchange weekend - my report on the first was published in

*MSOR Connections*(and one of the best pieces of news from the CETL-MSOR Conference is that

*Connections*will continue). That they work so well is due to the openness and friendliness of the participants: it's a delight to spend time with people so committed to teaching mathematics effectively.

There is a lot I could write about from both events (and much that I have still to digest). But this post will focus one of my "ideas" - not actually mine at all, in fact.

At my University's teaching and learning conference one speaker mentioned a proposal that every degree course should have a compulsory final year module on "how new technology will change this subject" or something similar. (I didn't catch the name of the person to whom this proposal was attributed.) Should maths degrees contain such a module?

My first reaction was that it would be hard to make a case to colleagues for dropping their favourite courses in Complex Analysis or the Analytical Algebraic Topology of Locally Euclidean Parametrization of Infinitely Differentiable Riemannian Manifolds or whatever. These courses obviously give students skills and techniques which are immediately valuable to a wide range of employers in a way which thinking about possibly applications of technology and mathematics could not possibly match.

But should our maths graduates be thinking more about how technology will change mathematics? I think there is a case. For one thing, new technology such as apps on mobile devices are making like better in many small (and some big) ways. I'd like our maths graduates to be among the leaders in this field, but I'm not sure that our teaching particularly promotes this kind of creative thinking. I'm also struck that, despite many university mathematicians' preference for chalk and blackboards, IT is changing maths in ways which we don't articulate to our students. At BMC last year Sir Timothy Gowers noted that Wikipedia is an invaluable tool for mathematicians, greatly facilitating the practice of our subject. In his recent LMS Popular Lecture Sir Timothy talked about the emergence of computers as research assistants. He, Terence Tao and many others use blogs as a tool for mathematical collaboration, and Gowers's Polymath project is perhaps shows how mathematics will be done by humans in the years before the field is taken over by creative computer research mathematicians.

It certainly seems to me that my childhood view of mathematics as an individual activity, which was perhaps only rarely a reality (Andrew Wiles?), is no longer tenable: technology is making mathematics an increasingly collaborative venture. And we should perhaps be making more of this in our undergraduate teaching.

Thank you for the kind comments Tony.

ReplyDeleteI'm not sure Wiles is a great example. My memory is fairly sketchy and I have lend out my copy of Singh's FLT but, although he famously locked himself away, I think he build on the work of many other mathematicians and didn't the solution really start to progress when he confided in another mathematician at his university? Furthermore, validation of his work came was via a conference presentation and peer review and further collaboration tightened up the non-proof into a proof.

Anyway, I was really commenting to point out something I said at the weekend: I feel that a mathematics education at university should prepare students for future challenges as the discipline develops and if our graduates are going to continue for 40 years or more, they will certainly experience more than can be imagined at present. This sort of course and the creative thinking and awareness of uncertainty it encourages would seem to be better preparation than most. I mentioned a 1960 advert I had seen for Burroughs Adding Machines. This reads: "The ever increasing demands for Burroughs equipment assures your students of going from graduation to good jobs fast when you train them on Burroughs machines!" (Business education world, 41, p. 6). I enjoy this as a warning against being too specific in your idea of what graduates need.

I am grateful to Peter Rowlett for pointing out a number of typos in the original post. The historical record now shows that these typos never existed.

ReplyDeleteMy view: No, they should not. Certainly make such a module optional, for the students who are finding formal mathematics courses a bit of a challenge, and want something nice and lightweight to ease their burden, but compulsory? Heck no.

ReplyDeleteAny mathematician worth his/her salt would be able to make their own way through the field of glorified science fiction which is futurology. Of course mathematicians should be thinking about how technology will change mathematics - but rather than be required to sit in pointless lectures and seminars, then write a vapid essay on the subject, they will (if they have any drive in that direction at all) be actively involved in *making those very changes themselves*.

My own contributions towards this drive - I hang out a lot at: www (dot) proofwiki (dot) org, which a few people here and there believe is worth taking a glance at.

donotwash - thanks for commenting. I appreciate your views (and will check out the wiki). I do feel the compulsory module idea is a provocation rather than a serious expectation. In the end it depends what one thinks a maths degree is for - if one thinks it's for learning as much maths as possible and cultivating rigorous mathematical thinking then one wouldn't want a module like this. If one thinks it's to give graduates skills that will make them employable in a wide range of professions most of which do not used advanced pure mathematics, then one might.

ReplyDelete@Tony: I appreciate your "provocation" technique! Provocative is good!

ReplyDeleteBut will a course in "how new technology will change this subject" be *able* to "give graduates skills that will make them employable"?

By all means offer courses on how to apply computer techniques to the various problems they will be expected to solve (whether this be offering practical courses on how to teach yourself a programming language in a day or two so as to be able to code up a widget to demonstrate something or other), but any such courses will necessarily not be "mathematics" courses as such, but plain-and-simple "technology" courses, and will of course be optional: maths graduates will generally (one hopes!) be savvy enough to have learned how to use technology independently of a university course.

However, suggesting that a course in futurology (which your suggestion seems to be) will make such a mathematician more employable (except perhaps as a journalist) does not ring true to me.