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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A better understanding of what math is and how we do it might improve the rate at which mathematical understanding increases, its dissemination to other fields, and its relevance and usefulness.pic.twitter.com/POO3njXgfj
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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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yeah, I suspect that for many students who find they're "no good at" a subject (even when they're good at other similarly difficult subjects), it's because they can't catch on to the pattern of which things that discipline includes in its models and which are "irrelevant details"
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My copy of that Ideal Mathematician essay has this Wittgenstein story at the start. "If a child does not respond to the suggestive gesture, it is separated from the others and treated as a lunatic."pic.twitter.com/lFMVTXqAux
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Oh this "ideal mathematician" link is wonderful! Thanks! This is pretty much the "proper mathematician" that I've been talking about for the past year or so.
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Glad you like it! Just remembered I got it from
@drossbucket; I’ll credit her publicly now
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This essay is satirical. Many mathematicians can give quite reasonable discussions of the ambiguity of the term 'exist', most others just don't find the issue worth considering one way or another. Platonists/intuitionists/etc. are considered somewhat cranky.
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I think in physics the analogous stance is called 'shut up and calculate'. Worry about that stuff (not challenge it, but take a stance at all) is for when you're old and your research days are mostly over.
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I think one can combine two criteria given by the ideal mathematician, to get another interesting one: "A proof is something that convinces an expert, that a logical proof for the statement could be written".
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A proof to one person is obvious and to another insufficient to get them to see. All correct theorems are tautological, so a proof can only ever be an aid to help people see the tautological nature of it, and the level of help needed necessarily varies by person.
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