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A comment on In Mathematics, It Often Takes a Good Map to Find Answers.

Re:In Mathematics, It Often Takes a Good Map to Find Answers by mmhsieh on Wednesday June 03, 2020 @03:47PM (#23407816)
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."

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Re:In Mathematics, It Often Takes a Good Map to Find Answers by jordigh on Wednesday June 03, 2020 @04:31PM (#23408289)
Haha, it's like Maclane said: "I did not invent category theory to talk about functors. I invented it to talk about natural transformations."

You gotta go at least to the third level of abstraction to get the real meat.

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Re:In Mathematics, It Often Takes a Good Map to Find Answers by JadeNB on Wednesday June 03, 2020 @10:36PM (#23411714)
Discussed from a literal point of view on MO: https://mathoverflow.net/questions/13832/analogies-between-a... .
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