What happens when things combine? This question lies at the heart of the Borell-Brascamp-Lieb inequality (BBL), a ...

The Langlands programme has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore.

This article gives a new and purely geometric proof for Morley’s theorem. The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a ...

We give an algebraic geometric proof of the Theorem of Ax and Kochen on p-adic diophantine equations in many variables. Unlike Ax-Kochen's proof, ours does not use any notions from mathematical logic ...

A 125-page proof posted to arXiv may represent a huge breakthrough in geometric measure theory. This problem has implications in fields like encryption, computer science, and number theory.