Y. He

Reviewing progress in the field of AI-assisted discovery for maths and theoretical physics reveals a triumvirate of different approaches.

The different approaches to making discoveries in pure mathematics and fundamental sciences such as theoretical physics can be broadly categorised as "top-down", "bottom-up" or "meta-mathematics". Assessing the recent impact of artificial intelligence on each suggests that while the theorist is in no danger of being replaced soon, combining human expertise with AI algorithms will be integral to discovery in future.

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.

On AI-driven discovery

AI-driven research in pure mathematics and theoretical physics