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PaperclipPerfector  3d ago (text post)   10787 thread views

Culture War Roundup for the week of August 31, 2026

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The practice of mathematics involves writing proofs in a heavily intuitive manner, and their verification in turn involves people who have been socialised to share the same intuitions, which is a process that rarely involves proper reduction to the axiomatic basics but more often looks like "your elders and betters assert that it is trivial and look at you with mild disappointment, and all your peers seem to already have gotten it, so get on with it and flog your brain into producing the 'this is obviously true' qualium already"

One of the best professors I had would sometimes in his lectures go "Proof (1. Attempt): [...] and therefore the proposition is proven ... wrong! The proof I gave had a flaw! Can anyone see what the problem is?" When no one could, he explained the flaw, gave a 2. Attempt, which fixed the flaw, but there was another unfixed flaw, and only the third attempt was the real proof.

He also constantly asked questions to the students, he was really committed to teaching actual thinking.

He also held a lecture once where he gave no sample solutions to the exercises. The exercise was always supposed to be the students discussing what they came up with, with the assistant only supervising, and the exam was just a selection of the exercise problems. One of my prouder moments was when my solution was simpler than the one the assistant had in mind, and I was eventually able to convince him it was correct.

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