A straightforward conjecture about runners moving around a track turns out to be equivalent to many complex mathematical ...

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.

Microscopic crystals extracted from meteorites could help settle a debate about the birth of our patch of the Milky Way.

It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question.

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 ...

Growing tissues can crack, break, and dissociate to form structures that can later withstand immense forces.

Quantum entanglement is thought to be one of the trickiest concepts in science, but the core issues are simple. And once understood, entanglement opens up a richer understanding of concepts such as ...

The Fields medalist Vladimir Voevodsky has died at 51. This 2015 article describes his computer-aided quest to eliminate human error and rewrite the century-old rules ...

Every Tuesday, editor in chief Samir Patel sits down with writers and editors to discuss our most thought-provoking stories in science and math. Audio editions of Quanta’s stories with Susan Valot ...

A straightforward conjecture about runners moving around a track turns out to be equivalent to many complex mathematical questions. Three new proofs mark the first significant progress on the problem ...

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 ...

It’s been 162 years since Bernhard Riemann posed a seminal question about the distribution of prime numbers. Despite their best efforts, mathematicians have made very little progress on the Riemann ...