Algebraic structures, encompassing groups, rings, fields and modules, have long formed the backbone of modern mathematics. Category theory, with its focus on objects and morphisms, provides a unifying ...

The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is ...

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 ...

Emily Riehl thinks hard about objects that don't exist in the material world yet mysteriously seem to underlie many things that do. These objects have no concrete existence of their own, but they do ...

Math as both profession and course of study can be a hard sell, something even Don Draper might have trouble pitching. The field unites numbers, theories, and ideas that, yes, can be physically ...

Mathematical logic, set theory, lattices and universal algebra form an interconnected framework that underpins much of modern mathematics. At its heart, mathematical logic provides rigorous formal ...

The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is ...