This paper proposes a framework for using machine learning to guide mathematical intuition, demonstrating its application to knot theory and representation theory. In knot theory, the framework led to the discovery of a new relationship between geometric and algebraic invariants, resulting in a novel theorem. In representation theory, it contributed to a conjectured solution to the combinatorial invariance conjecture for symmetric groups, offering a potential resolution to a 40-year-old open problem.

The authors are employed by DeepMind, which funded the research. This could potentially introduce bias in the interpretation and presentation of the results, although there is no direct indication of such bias in the paper.

This paper presents a novel and potentially impactful framework for using AI to assist mathematical discovery. The framework's successful application to two distinct areas of mathematics, leading to a new theorem and a conjectured solution to a long-standing open problem, demonstrates its potential. However, limitations in generalizability and dependence on data and function complexity warrant a slightly lower rating than groundbreaking.