On a recommendation I borrowed out Riemann’s Zeta Function by Edwards. It’s been suggested as bed time reading… Heh. Not the first maths book recommended as such, I’ve yet to do so with any of them. One day.
Edwards suggests to “read the classics”. Meaning the most famous works of the most famous mathematicians. In particular he means Riemann’s original paper Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse, obviously he means a translation (for mono lingual English speakers).
As insane as reading Riemann sounds, it’s not nearly as insane as reading Grassmann (which made no sense to mathematicians). I think I agree with him. There isn’t any other way to really get a taste for where the passion comes from. So many maths texts provide very minimal context for the development of the ideas. They might provide things in a chronological order of development and think that suffices, but it doesn’t.
To get a real taste for a subject you have to dig around and stumble down the same dead ends. It isn’t enough to know the topic if you don’t know why it’s interesting. This doesn’t mean you have to understand the original papers completely. I mean, Riemann? Good luck me.
I probably would have run to the hills at this idea two years ago, but last year I had to research Hilbert’s 10th Problem. I went on long tangents, reading all sort of ancient papers by people that have theorems named after them. I actually wrote a pretty crappy paper by the end of it. I got so side tracked by logic, I took too long get around to doing any number theory. It was a number theory course. At the time I regretted that, but in hindsight I’m glad. Who gives a fuck about marks anyway eh?
Also all the ancient logic got me confused when I came to write the paper. They had odd conventions that are very different to the way they’d be written now.
I started with Hilbert’s address and Hilbert himself. Then I read Gödel’s paper where he first proved his more famous incompleteness theorem. I read papers by Kleene, Church, Turing, Post etc, each one subtly changing the course of mathematical history. Then I read all the papers by Davis, Putnam, Robinson and Matiyasevich which led to the completion of the solution of Hilbert’s tenth problem (vast tracks of these got me lost). It was a true mathematical odyssey that far more fascinating by reading the source, rather then via popular science novels or even retrospective maths papers. All of the papers would be available semi publicly in almost any University library.
I wish I could find a similar hook for my thesis. Then I’d be set, I’m having so much trouble looking for a place to dig my fingers in. Grassmann seems too far removed from my thesis. I guess I should find out who really came up with the definition I’m looking at, since it’s supposedly been know for a while. Or at least I could find out which century it came into the mathematical consciousness.
So yeah I should read the classics, but time is always a factor. In our results orientated education system it also requires an assessment reason.
I’m not promising anything to myself.
