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A Triumvirate of AI Driven Theoretical Discovery

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arxiv 2405.19973 v1 pith:25W5WNI7 submitted 2024-05-30 math.HO cs.AIhep-thphysics.hist-ph

Yang-Hui He This is my paper · ORCID
classification math.HOcs.AIhep-thphysics.hist-ph
keywords discoverysciencestheoreticalalgorithmsmathematicalyearsadvancesapproach
verification ladder T0 review T1 audit T2 compute T3 formal
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Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the rigorous definitions, derivations, and proofs, in contrast to the experimental sciences which rely on the modelling of data with error-bars. In this Perspective, we categorize the approaches to mathematical discovery as "top-down", "bottom-up" and "meta-mathematics", as inspired by historical examples. We review some of the progress over the last few years, comparing and contrasting both the advances and the short-comings in each approach. We argue that while the theorist is in no way in danger of being replaced by AI in the near future, the hybrid of human expertise and AI algorithms will become an integral part of theoretical discovery.

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Cited by 3 Pith papers

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