計算機科学：人工知能を使って数学上の問題を解く

A machine learning framework that can help mathematicians to discover new conjectures and theorems is presented in Nature this week. The framework, developed by DeepMind, has facilitated the discovery of two new conjectures in different areas of pure mathematics. The study demonstrates how machine learning can be integrated into existing workflows to support mathematical research.

A key goal for the practice of pure mathematics is to uncover patterns between mathematical objects and to use these connections to formulate conjectures: statements that are suspected to be true, but have not yet been rigorously proved. Since the 1960s, mathematicians have used computers to aid the discovery of patterns and formulation of conjectures, but artificial intelligence systems are not commonly used in theoretical mathematical research.

DeepMind teamed up with mathematicians to build a machine learning framework for assisting with mathematical research. Their algorithms search for potential patterns and relations between mathematical objects and try to make sense of them. Then the mathematicians take over, using the observations to guide their intuition towards potential conjectures. Application of this approach to two areas of pure mathematics led to the discovery of a new theorem in topology (the study of the properties of geometric shapes) and a new conjecture in representation theory (the study of algebraic systems), Alex Davies and colleagues report. They conclude that their framework could encourage future collaborations between the fields of mathematics and artificial intelligence.