5 ms·

I highly recommend Bill Thurston’s gem of an article On proof and progress in mathematics https://arxiv.org/abs/math/9404236 https://arxiv.org/abs/math/9404236

• sabas123 6y ago
  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.
  • ssivark 6y ago
    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 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").
• raincom 6y ago
  Just finished reading Thurston's paper. A great paper esp for those in "philosophy of mathematics".
• mturmon 6y ago
  It's a great read. See also: https://news.ycombinator.com/item?id=12280139 https://news.ycombinator.com/item?id=12280139
• Errancer 6y ago
  In this topic I also highly recommend "Proofs and Refutations" by Imre Lakatos