Thursday, 6 December 2012

Don't Give Up Mathematics

A long time ago when I was an impressionable young lad doing my first industrial work experience at Pembroke Power Station, I asked one of the engineers there if doing a degree in electrical engineering meant he could understand the huge circuit diagram he was unfolding. He said that it didn't, but it gave him the confidence to believe he could understand it.

That's one reason to do an undergraduate degree: the other is that, as Karl Popper suggested, it should give you the confidence and background knowledge to distinguish a fraud from the real thing.

You need to choose your subject to get either of these benefits. Any of the hard subjects - the ones where there are answers or clear standards of rigorous argument - will do, and outside the law and philosophy, that means it has to have some mathematics in it. (The presence of mathematics is necessary but not sufficient, as witness economics.) Also, philosophers tend to get a dose of formal logic thrown at them, and that's a branch of mathematics.

The real benefit of doing undergraduate mathematics is so you can study some post-graduate maths in your spare time when you enter into what's laughably known as the "real world". Remember the jolt you had moving from GCSE maths to A-level? That's what moving from undergraduate to post-graduate is like. All the abstract subjects you studied - especially topology, group theory and commutative algebra - become taken-as-read background knowledge.

The other casual remark I'll never forget in this regard was from John Bell at the LSE, at the start of his Boolean Algebras / Model Theory course. A light smattering of topology is required to understand the Stone Representation Theorem. If you didn't know any, he suggested, "just read the first three chapters of Kelly for next week". That's a one-term undergraduate course in point-set topology - in a week. Along with the day job.

Come on! Get with the program! Step up your game!

This doesn't work so well with the arts. People read Ulysses for an English Literature degree fer Gawd's Sake. And besides, reading Musil isn't hard because he writes badly, but because you need a lot of experience of the Worldly World before you can really grok it. Same goes for C P Snow's Strangers and Brothers. The more you get about in the world, the easier some of its great literature becomes to read - except Clarissa. 

The other great advantage of keeping up your maths is that lots of subjects are much easier for mathematicians to pick up than regular mortals - because they already have much of the background knowledge anyway. A mathematician reads an exposition of, say, cluster analysis in a very different way than someone who's still struggling with root-mean-square distances. 

No comments:

Post a Comment