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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.

In a watershed moment for cryptography, computer scientists have proposed a solution to a fundamental problem called “program obfuscation.”

Working on the centuries-old twin primes conjecture, two solitary researchers and a massive collaboration have made enormous advances over the last six months.

How do you know if a quantum computer is doing what it claims? A new protocol offers a possible solution and a boost to quantum cryptography.

Two young mathematicians are illuminating a frontier in the study of rational solutions to polynomial equations: the cubics.

A virtually unknown researcher has made a great advance in one of mathematics’ oldest problems, the twin primes conjecture.