The dogma that mathematical proofs could, in principle, be turned into logical proofs remains a conjecture; it is not feasible in practice. Existing proof systems are not up to the job; can they be beefed up sufficiently? Research community disconnect!https://xenaproject.wordpress.com/2020/02/09/where-is-the-fashionable-mathematics/ …
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Resonates with
@michael_nielsen &@andy_matuschak’s point that “tools for thinking” have to be driven by the needs of expert professional users, not someone’s appealing theory of education or cognition or philosophy of math or somethingShow this thread -
(I should say that computer proof systems are occasionally useful for computer system verification. It’s “real math” that they aren’t (yet) useable for.)
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Also wonder how this might change the way mathematicians conceive of proofs, cf. Hardy (in 1928): “proofs are what Littlewood and I call gas, rhetorical flourishes designed to affect psychology, pictures on the board in the lecture, devices to stimulate the imagination of pupils”pic.twitter.com/m7LoHC4lcy
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"Real" math is not newcomer friendly. Experts in their areas usually adopt the formalism so well, that they don't even understand why their argument/paper is not comprehensible/sufficient to others. Mathematicians and proof system people are two different people after all...
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