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Here's Alain Connes, Fields medalist, on how a mathematician works and should read a book [0]:

"To understand any subject, above all, a mathematician SHOULD NOT pick up a book and read it.

It is the worst error!

No, a mathematician needs to look in a book, and to read it backwards. Then, he sees the statement of a theorem. And, well, he goes for a walk. And, above all, he does not look at the book.

He says, "How the hell could I prove this?"

He goes for his walk, he takes two hours ... He comes back and he has thought about how he would have proved it. He looks at the book. The proof is 10 pages long. 99% of the proof, pff, doesn't matter.

Tak!, here's the idea!

But this idea, on paper, it looks the same as everything else that is written. But there is a place, where this little thing is written, that will immediately translate in his brain through a complete change of mental image that will make the proof.

So, this is how we operate. Well, at least some of us. Math is not learned in a book, it cannot be read from a book. There is something active about it, tremendously active.


It's a personal, individual work."

[0] https://www.youtube.com/watch?v=9qlqVEUgdgo

This approach seems very similar to working backwards when trying figure out the behavior of a function that calls other functions or libraries and when trying to a debug an issue and following the stack trace to determine the root cause of the issue. Not a perfect analogy but I find it helpful to think about it that way.

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