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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Comfortable folk theories of technical work do harm by filling the space where a better understanding could go, making its absence invisible. “Yes of course we know how to do science! We are scientists!” But clearly you didn’t, because you go so much of it wrong.
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Some sciences are upgrading their understanding, which I am optimistic will lead to better science.https://meaningness.com/metablog/upgrade-your-cargo-cult …
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Does the folk theory of mathematics also cause trouble? Here I am less confident, because math rarely has replication crises. However, this paper suggests to me that more and better math might get done if it were upgraded: https://personalpages.manchester.ac.uk/staff/hung.bui/ideal.pdf …pic.twitter.com/XSbDWXhDpz
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"Of course we know how to do mathematics! We are mathematicians!" But there's good evidence you don't, and so you can't teach it clearly, and you can't reflect on whether you are doing it well or badly. https://personalpages.manchester.ac.uk/staff/hung.bui/ideal.pdf …pic.twitter.com/YsL16YdGVe
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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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Replying to @Meaningness @XenaProject and
A much better source than polemicists (which you might have heard of) is William Thurston, himself at the forefront of a recent mathematical renaissance, https://arxiv.org/abs/math/9404236 …. It still feels true today
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Thurston’s paper is a classic, yes. Yes, it’s obvious that The Ideal Mathematician is satirical, but it points out what seem to be real phenomena as well.
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Replying to @Meaningness @mathemamitka and
Whenever the topic “so how does math actually work” comes up, the same handful of sources always get mentioned (Thurston, Rota, Tao, Hadamard, Lakatos). That there are so few suggests an unwillingness to examine the question, perhaps because the answer is unattractive.
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