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Re:In Mathematics, It Often Takes a Good Map to Find Answers by sabas123 on Wednesday June 03, 2020 @05:39PM (#23409122)
It was a good read, thank you for sharing.

> "It was an interesting experience exchanging cultures. It became dramatically clear how much proofs depend on the audience. We prove things in a social context and address them to a certain audience. Parts of this proof I could communicate in two minutes to the topologists, but the analysts would need an hour lecture before they would begin to understand it. Similarly, there were some things that could be said in two minutes to the analysts that would take an hour before the topologists would begin to get it. And there were many other parts of the proof which should take two minutes in the abstract, but that none of the audience at the time had the mental infrastructure to get in less than an hour"

I wonder if we would ever get to a point where we would find an effective and desirable mental infrastructure such that this wouldn't happen.

Re:In Mathematics, It Often Takes a Good Map to Find Answers by ssivark on Wednesday June 03, 2020 @06:22PM (#23409581)
Category theory is supposed to be one such tool, even though some find it very abstract. It's very much in the spirit of finding analogies among theories and analogies among analogies. (I swear I'm not trolling :P) I'm still working on my understanding of category theory, but somebody who has the mathematical fortitude might enjoy: http://groupoids.org.uk/pdffiles/Analogy-and-Comparison.pdf

In general better abstractions(similar ideas as in a recent discussion of Peter Naur's "Programming as theory building").