Mathematicians and scientists have vague folk theories of what math and science are that both are blurred ancestral memories of pre-WWII logical positivism.
These theories are totally wrong, but do little *direct* harm because they are mainly ignored in practice.
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OK, maybe mathematics DOES have a broad replicability problem! Seemingly strong evidence and arguments from
@XenaProject, whose post I tweeted yesterday. Great slides! (h/t@vonbladet,@aelkus) (“Seemingly”: I’m not qualified to have an opinion here) http://www.andrew.cmu.edu/user/avigad/meetings/fomm2020/slides/fomm_buzzard.pdf …pic.twitter.com/UDQLsKoph3
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Well it might also not, he cheerfully anti-foundationed without any obvious credentials. Also, while it's not sociologically that popular surely we *do* know what rigour is, it's when you can convince a proof verifier you are right:https://www.vice.com/en_us/article/8xwm54/number-theorist-fears-all-published-math-is-wrong-actually …
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I think I got this one from
@aelkus, but it's great: http://www.andrew.cmu.edu/user/avigad/meetings/fomm2020/slides/fomm_buzzard.pdf … - 2 more replies
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I do worry a bit that formal mathematics has a tendency to displace domain knowledge in other fields. If you squint really hard a lot of things look like subfields of mathematics, which seems to give some people license to pretend those things *are* subfields of mathematics.
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..which does remind me of convincing the villagers that their local religion is really just a subset of Christianity.
End of conversation
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