Learning to be Simple
Yang-Hui He Vishnu Jejjala Challenger Mishra Em Sharnoff
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 2-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.