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Artificial Intelligence and the Structure of Mathematics

arxiv.org · 24,940 words · saved by 1 readers

Recent progress in artificial intelligence (AI) is unlocking transformative capabilities for mathematics. There is great hope that AI will help solve major open problems and autonomously discover new mathematical concepts. In this essay, we further consider how AI may open a grand perspective on mathematics by forging a new route, complementary to mathematical logic, to understanding the global structure of formal proofs. We begin by providing a sketch of the formal structure of mathematics in terms of universal proof and structural hypergraphs and discuss questions this raises about the foundational structure of mathematics. We then outline the main ingredients and provide a set of criteria to be satisfied for AI models capable of automated mathematical discovery. As we send AI agents to traverse Platonic mathematical worlds, we expect they will teach us about the nature of mathematics: both as a whole, and the small ribbons conducive to human understanding. Perhaps they will shed lig

Artificial Intelligence and the Structure of Mathematics Maissam Barkeshli Meta Superintelligence Labs, Fundamental AI Research Department of Physics and Joint Quantum Institute, University of Maryland, College Park Meta Superintelligence Labs, Fundamental AI Research Department of Physics and Joint Quantum Institute, University of Maryland, College Park Michael R. Douglas Center for Mathematical Sciences and Applications, Harvard University Center for Mathematical Sciences and Applications, Harvard University Michael H. Freedman Center for Mathematical Sciences and Applications, Harvard Unive

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