A 150-year-old conundrum about how to group people has been solved, but many puzzles remain.

A mathematician who has analyzed card shuffling for decades is tackling one final nemesis: “smooshing.”

Researchers are on the trail of a mysterious connection between number theory, algebra and string theory.

A year after tackling how close together prime number pairs can stay, mathematicians have now made the first major advance in 76 years in understanding how far apart primes can be.

Subhash Khot’s bold conjecture is helping mathematicians explore the precise limits of computation.

Maryam Mirzakhani, who became the first woman Fields medalist for drawing deep connections between topology, geometry and dynamical systems, has died of cancer at the age of 40. This is our 2014 profile of her life and work.

Artur Avila’s solutions to ubiquitous problems in chaos theory have “changed the face of the field,” earning him Brazil’s first Fields Medal.

The search for artistic truth and beauty has led Manjul Bhargava to some of the most profound recent discoveries in number theory, which have helped earn him the Fields Medal.

A daring speculation offers a potential way forward in one of the great unsolved problems of mathematics: the behavior of the Navier-Stokes equations for fluid flow.