Learning to be simple

Journal article

In this work we employ machine learning to understand structured mathematical data involving finite groups and derive a theorem about necessary properties of generators of finite simple groups. We create a database of all two-generated subgroups of the symmetric group on n-objects and conduct a classification of finite simple groups among them using shallow feed-forward neural networks. We show that this neural network classifier can decipher the property of simplicity with varying accuracies depending on the features. Our neural network model leads to a natural conjecture concerning the generators of a finite simple group. We subsequently prove this conjecture. This new toy theorem comments on the necessary properties of generators of finite simple groups. We show this explicitly for a class of sporadic groups for which the result holds. Our work further makes the case for a machine motivated study of algebraic structures in pure mathematics and highlights the possibility of generating new conjectures and theorems in mathematics with the aid of machine learning.

Authors: He, Y; Jejjala, V; Challenger, M; Sharnoff, E

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: AI for Science
• Volume: 1
• Issue: 2
• Article number: 025006
• Publication date: 2025-11-20
• Acceptance date: 2025-11-07
• DOI: 10.1088/3050-287x/ae1d98
• EISSN: 3050287X
• ISSN: 3050287X
• Language: English
• Keywords: AI for mathematics; simple finite groups; AI-assisted conjectures