  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.
