[archibaldJ]

I was looking around but couldn't find the piece my prof sent me 5 years ago.

It was a piece from a mathematician's diary about walking and coming up with proofs. There is something about a changing enviroment and being on the move that's very fascinating to me.

I guess that one mathematician who likes to sit in libraries probably sits there just for sitting there ;)

[joaorico]

Alain Connes, Fields medalist, talks about going on walks while reading math books in a particular way (and 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

[yarky]

Walking helps thinking, that is a well known fact, which I also learned from a mathematician who kept sharing in class how many problems he solved while walking his dog. He would always start his phrases with "while I was walking my dog I realized ...".

There seems to be a lot of research on this topic btw.