In Mathematics, It Often Takes a Good Map to Find Answers • Hacker News Board

Re: In Mathematics, It Often Takes a Good Map to Find Answers

#21

Post by JadeNB » Thu, Jun 04, 2020, 2:36 AM UTC

mmhsieh wrote: post #7

The difficulty in coming up with a good map of mathematics is summarized by this quote by Banach: "A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies."

Discussed from a literal point of view on MO: https://mathoverflow.net/questions/13832/analogies-between-a... .

Re: In Mathematics, It Often Takes a Good Map to Find Answers

#22

Post by Errancer » Thu, Jun 04, 2020, 7:06 AM UTC

ssivark wrote: post #3

I highly recommend Bill Thurston’s gem of an article On proof and progress in mathematics https://arxiv.org/abs/math/9404236 Talks about the human aspect of pursuing mathematical research, how they shape the attitude of the field towards a problem abs are crucial in progressing towards knowledge. Should be very readable for everyone; no formal math as such.

In this topic I also highly recommend "Proofs and Refutations" by Imre Lakatos

Re: In Mathematics, It Often Takes a Good Map to Find Answers

#23

Post by rmrfstar » Thu, Jun 04, 2020, 3:04 PM UTC

Maps turn out to be useful in experimental physics too.

Here's a neat BBC piece featuring Gell-man and Feynman on Strangeness -3 [1].

[1] https://www.youtube.com/watch?v=BGeW6Nc6IMQ

Re: In Mathematics, It Often Takes a Good Map to Find Answers

#24

Post by amandavinci » Thu, Jun 04, 2020, 5:26 PM UTC

The analogy of maps and boats is just an instance of the exploration-exploitation idea. I have seen instances of this pop up every time we discuss problem solving in some form. It falls in the perennial variety of ideas that can't be revisited enough.