Tuesday, November 04, 2014

Ancient mathematics

I was pointed to David Mumford, who reviewed a book about the history of mathematics in "India". They got pretty far along, though the paradigm was different and the exposition is tough to follow. By that I mean that they were much more strongly application-oriented (not proof-based) and a lot of the literature was written in terse verse to make it easier for students to memorize. Have a look. He also has a history of What's so Baffling About Negative Numbers--why did it take so long for the West to pick up on them when the Chinese and Indians had a handle on them long before.

I've said before that math isn't actually done in the abstract formal proofs you find in papers. A mathematician will noodle around with some models (often inspired by some application!) until some problem finally yields, and then he rewrites the result in a formal style that makes it sound like he was following a straight logical path to the answer all along. There's probably no help for that, but filling out papers with some more examples would help understanding. Certainly help me, anyway.

If his posts are any guide, Mumford seems to like examples. The most recent (as of today) is "An Easy Case of Feynman's Path Integrals." "Easy" is perhaps a bit relative, but I like the step-by-step way he evolved his model. Good writer.

1 comment:

Assistant Village Idiot said...

All my experimentation with mathematics was before age 20, over ground that others had trod. But I didn't know that the others had trod that ground, and at the end, it was at least ground that comparatively few had trod. But it was indeed just noodling, noticing, following up odd coincidences to see if they were nothing more or bespoke a deeper pattern. I have always thought of that as Pasteur's "chance favors the prepared mind." Many discoveries were made "by accident," but not really. They were made by people wandering around in an area where it looked like something was happening.