Learning to be Simple
- URL: http://arxiv.org/abs/2312.05299v1
- Date: Fri, 8 Dec 2023 19:00:00 GMT
- Title: Learning to be Simple
- Authors: Yang-Hui He, Vishnu Jejjala, Challenger Mishra, Max Sharnoff
- Abstract summary: We employ machine learning to understand structured mathematical data involving finite groups.
We derive a theorem about necessary properties of generators of finite simple groups.
Our work highlights the possibility of generating new conjectures and theorems in mathematics with the aid of machine learning.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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