Daniel Tubbenhauer on Computer Aided Mathematics

See https://leanprover-community.github.io/undergrad.html and Solution of the Robbins Problem by William Mccune.

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So much for the existence of proofs. There is also a very similar problem in the philosophy of mathematics concerning the existence of numbers, sets and such-like. And problems in metamathematics concern the validity of reasoning about correspondences between proofs and mathematical objects. All of these seem to me to be questions about languages and about translations between those languages.

Penelope Maddy on Objectivity in Mathematics

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