A Triumvirate of AI Driven Theoretical Discovery

TL;DR

This paper reviews AI-driven approaches to mathematical discovery, categorizing methods into top-down, bottom-up, and meta-mathematics, and discusses how human-AI collaboration enhances theoretical progress.

Contribution

It provides a comprehensive categorization and comparison of AI methods in mathematical discovery, highlighting the complementary role of human expertise and AI.

Findings

AI approaches have advanced in mathematical discovery

Hybrid human-AI methods are promising for future research

Current AI methods are not replacing but augmenting human theorists

Abstract

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.