"How to solve it" for theory builders?

Question

Gowers has written a paper where he distinguishes between two cultures of mathematics: theory builders and problem solvers.

There are many textbooks on "how to solve mathematical problems", or "how to prove things", such as Pólya's books, e.g. this one. I have looked at a few of them in the past, and so far as I can remember, they tend to have a "problem solver" perspective.

Are there such "how to do mathematics" books that take a theory-builder perspective?

Grothendieck's story about how to open a nut might be an example of what you're talking about. Some of the answers here might be interesting: https://hsm.stackexchange.com/questions/3014/grothendiecks-approach-to-solving-problems — littleO, Aug 19 '19 at 19:28
I don't know if it's at all what you're asking for, but you might like Thurston's essay "On Proof and Progress in Mathematics". — Jair Taylor, Aug 19 '19 at 20:56

score 1 · Answer 1 · answered Jun 19 '21 at 02:21

1

I don't know exactly what are you looking for.

But maybe reading about history, philosophy and the biography of the mainly theory-builder of math can help you to understand how they worked.

answered Jun 19 '21 at 02:21

Corrêa H

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"How to solve it" for theory builders?

1 Answers1