Algebraic structures—such as groups, rings, modules and Lie algebras—provide formal frameworks for operations and symmetries that underpin vast areas of mathematics and its applications. Category ...

On a crisp fall New England day during my junior year of college, I was walking past a subway entrance when a math problem caught my eye. A man was standing near a few brainteasers he had scribbled on ...

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 ...

Emily Riehl sees similarities between the viola, which she grew up playing, and the mathematical field of higher category theory, in which she is currently a leading participant. She thinks of the two ...