Tuesday, December 30, 2008

Feynman Lectures for math

I need an equivalent Feynman's Lectures for mathematics.

I've had plenty of math and science courses as an undergraduate and now as a graduate student. I did well in math, but have always felt that this was due to superficial, short-term rule memorization, rather than to a deep and fundamental understanding. Basically, most courses were slow enough for strugglers, and those with an intuitive feel didn't have to work terribly hard. Courses were generally crowded, taught by overworked grad students with poor teaching skills and limited English, with textbooks long on pages and short on clarity. There was little deliberate carryover between courses, and each introduced new jargon, styles, and notation. The result was a handful of memorized facts and rules not forming any cohesive structure, and which slip away with disuse, which is a real shame for such a fascinating subject.

I think it boils down to textbooks being the worst possible way to actually learn something. I've had the opposite experience with science, not because the textbooks are better (they aren't), but because I know which authors to read. I've read much more widely from authors such as Asimov and Sagan who can explain concepts accurately and with clarity. I remember discovering and being blown away by Richard Feynman's lectures on physics. He took a complex subject and presented the breadth of it with perfect clarity; I doubt whether anyone has ever explained the the double-slit experiment more clearly. Conversely, math textbooks, and even sources such as Wikipedia and Mathworld, while presumably perfectly accurate, are shrouded in layers of obfuscation and jargon rendering them impenetrable.

But hopefully someone's done a Feynman-esque job of bringing it all together. Hopefully. Or maybe it's just a pipe dream.

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