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 ...

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 ...

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 ...

Baez called for the development of new mathematics — he called it “green” math — to better capture the workings of Earth’s biosphere and climate. For his part, he sought to apply category theory, a ...

Homotopy theory is a cornerstone of modern algebraic topology, concerned with the study of spaces up to continuous deformations. This approach characterises topological spaces by their intrinsic ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...