Representation theory transforms abstract algebra groups into things like simpler matrices. The field’s founder left a list of 43 problems for others to study, iterate on, and prove. One ...

The situation is most dire at public colleges, which are the most likely to require abstract algebra as a precondition for a degree in every field, including art and theater.

Samuel Eilenberg of Columbia University and Saunders Mac Lane of the University of Chicago developed category theory in the 1940s to build a bridge between abstract algebra (the generalization of ...