Be smart by being systematic?

I’ve just got this notice of tomorrow’s Trinity Maths Society meeting (details of when/where at that link, if you are in Cambridge). Sounds as if it should be fascinating …

Prof Tim Gowers FRS (DPMMS):

“Can interesting mathematics problems be solved systematically?”

Solving a mathematics problem that is not a routine exercise can often  feel more like an art than a science. Different people attack problems  in different ways, and ideas can appear to spring into one’s mind from  nowhere.

I shall argue that solving problems is a much more systematic

process than it appears, and shall also try to explain why, if that is  the case, it has the features that make us think that it isn’t. For the  bulk of the talk, I shall attempt, with help from the audience, to solve  an Olympiad-style problem that I have not seen before, and to do so  systematically rather than by waiting for a clever idea to appear out of  the blue. The attempt is not guaranteed to succeed, but I hope that it  will be informative whether or not it does.

Perhaps, in the spirit of the times, someone should try live-blogging as the clock ticks down through the meeting! I’m not sure I’ll be able to get there — but if I can, I’ll try to take notes good enough to report back, as Tim Gowers can be fascinating on this kind of topic.