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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 conversation with the mathematical physicist Freeman Dyson on quantum electrodynamics, climate change and his latest pet project.

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.

Improvements in how densely spheres and other shapes can be packed together could lead to advances in materials science, deep space communication and theoretical physics.

To determine the nature of infinity, mathematicians face a choice between two new logical axioms. What they decide could help shape the future of mathematical truth.

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

Scientific data sets are becoming more dynamic, requiring new mathematical techniques on par with the invention of calculus.