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I agree with the gist of your comment but I think people can benefit from books about maths. A classic example that comes to mind is Polya's "How to Solve It".
by bubblyworld 2y ago
I agree with the gist of your comment but I think people can benefit from books about maths. A classic example that comes to mind is Polya's "How to Solve It". It's about the meta of doing maths (or the tacit knowledge of a great mathematician), not about specific fields or theorems.
- almostgotcaught 2y agoYes if you know absolutely nothing about writing proofs then polya's book is good. But that's it - after that "onboarding" you're never going to see a professional mathematician reading another such book.
- bubblyworld 2y agoI still got stuff out of it during my PhD (in mathematics, though I never finished). I think you might underestimate the value of tacit-knowledge-type stuff, especially from skilled mathematicians like Polya. It's interesting to see how they tackle hard problems, and to compare it to how you would do the same - at the very least I have a much less developed philosophy about it. Terrence Tao has blog posts about his problem-solving meta as well, that are interesting (to me) for similar reasons.