Representation theory studies the ways in which abstract algebraic objects—groups, rings, algebras and categories—can act by linear transformations on vector spaces or modules. By encoding an ...

The original version of this story appeared in Quanta Magazine. In 2003, a German graduate student named Britta Späth encountered the McKay conjecture, one of the biggest open problems in the ...

String theory began over 50 years ago as a way to understand the strong nuclear force. Since then, it’s grown to become a theory of everything, capable of explaining the nature of every particle, ...