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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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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End of conversation
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I've only read half your article, and need to get back to going through the motions of my craft, but it resonates with me. It made me think of this book review, which is a great companion piece:https://slatestarcodex.com/2019/06/04/book-review-the-secret-of-our-success/ …
Thanks. Twitter will use this to make your timeline better. UndoUndo
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