Advancing mathematics by guiding human intuition with AI.

Area of Science:

• Pure Mathematics
• Artificial Intelligence

Background:

• Mathematics traditionally relies on pattern discovery for conjectures and theorems.
• Computers have assisted mathematicians since the 1960s in pattern discovery and conjecture formulation.
• Notable examples include the Birch and Swinnerton-Dyer conjecture, a Millennium Prize Problem.

Purpose of the Study:

• To demonstrate a method for machine learning to assist mathematicians in discovering new conjectures and theorems.
• To propose a framework for using machine learning to guide mathematical intuition and discovery.

Main Methods:

• Utilizing machine learning to identify potential patterns and relationships between mathematical objects.
• Employing attribution techniques to understand these discovered patterns.
• Using these insights to guide human intuition and formulate new mathematical conjectures.

Main Results:

• Successful application of the machine-learning-guided framework to current research questions in pure mathematics.
• Discovery of a novel connection between the algebraic and geometric structures of knots.
• Identification of a candidate algorithm predicted by the combinatorial invariance conjecture for symmetric groups.

Conclusions:

• Machine learning can significantly aid in the discovery of fundamental results in pure mathematics.
• The proposed framework facilitates collaboration between mathematicians and artificial intelligence (AI).
• This synergistic approach can lead to surprising and meaningful contributions to open mathematical problems.