Learning Algebraic Structures: Preliminary Investigations
This work addresses the problem of applying AI to abstract algebra, offering preliminary insights into automated learning of mathematical structures, though it is incremental with limited scope.
The paper investigates whether AI can learn algebraic structures, specifically finite groups and rings, by training on small datasets to identify simple groups from Cayley tables and match addition and multiplication tables, achieving success for small-sized structures.
We employ techniques of machine-learning, exemplified by support vector machines and neural classifiers, to initiate the study of whether AI can "learn" algebraic structures. Using finite groups and finite rings as a concrete playground, we find that questions such as identification of simple groups by "looking" at the Cayley table or correctly matching addition and multiplication tables for finite rings can, at least for structures of small size, be performed by the AI, even after having been trained only on small number of cases. These results are in tandem with recent investigations on whether AI can solve certain classes of problems in algebraic geometry.