One of the biggest stories in science is quietly playing out in the world of abstract mathematics. Over the course of last year, researchers fulfilled a decades-old dream when they unveiled a proof of ...

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 ...

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 original version of this story appeared in Quanta Magazine. In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last ...

A mathematical proof has finally debunked the idea that we live in a simulation, according to a group of international researchers. The theory that the universe could be a computer programme has been ...