Mathematics

The triangle angle sum theorem makes working with triangles easy. What happens when you can’t rely on it?

Infinite sums are among the most underrated yet powerful concepts in mathematics, capable of linking concepts across math’s vast web.

Paul Nelson has solved the subconvexity problem, bringing mathematicians one step closer to understanding the Riemann hypothesis and the distribution of prime numbers.

A surprising new solution to Leonhard Euler’s famous “36 officers puzzle” offers a novel way of encoding quantum information.

A new result shows that quantum information can theoretically be protected from errors just as well as classical information can.

Decades ago, a mathematician posed a warmup problem for some of the most difficult questions about prime numbers. It turned out to be just as difficult to solve, until now.

Mathematicians and computer scientists answered major questions in topology, set theory and even physics, even as computers continued to grow more capable.

A new paper shows how to create longer disordered strings than mathematicians had thought possible, proving that a well-known recent conjecture is “spectacularly wrong.”

More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective.