MathZero, The Classification Problem, and Set-Theoretic Type Theory

By David A. McAllester. 2020

4 citations recorded by the source corpus.

AlphaZero learns to play go, chess and shogi at a superhuman level through self play given only the rules of the game. This raises the question of whether a similar thing could be done for mathematics -- a MathZero. MathZero would require a formal foundation and an objective. We propose the foundation of set-theoretic dependent type theory and an objective defined in terms of the classification problem -- the problem of classifying concept instances up to isomorphism. The natural numbers arise as the solution to the classification problem for finite sets. Here we generalize classical Bourbaki set-theoretic isomorphism to set-theoretic dependent type theory. To our knowledge we give the first isomorphism inference rules for set-theoretic dependent type theory with propositional set-theoretic equality. The presentation is intended to be accessible to mathematicians with no prior exposure to type theory.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Program Analysis & Verification

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Citations in the corpus

Measuring Mathematical Problem Solving With the MATH Dataset (2021, background): “While most other text-based tasks are already nearly solved by enormous Transformers, MATH is notably different.”