AI-driven research in pure mathematics and theoretical physics

Abstract

The past five years have seen a dramatic increase in the usage of artificial intelligence (AI) algorithms in pure mathematics and theoretical sciences. This might appear counter-intuitive as mathematical sciences require 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 and theoretical discovery as ‘top-down’, ‘bottom-up’ and ‘meta-mathematics’. We review the progress over the past few years, comparing and contrasting both the advances and the shortcomings of each approach. We believe that although the theorist is not in danger of being replaced by AI systems in the near future, the combination of human expertise and AI algorithms will become an integral part of theoretical research. Advances in artificial-intelligence-assisted mathematical investigations suggest that human–machine collaboration will be an integral part of future theoretical research.