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Mathematicians have solved the century-old triangulation conjecture, a major problem in topology that asks whether all spaces can be subdivided into smaller units.

Researchers have found a set of rules for imbuing flat surfaces with curvature, enabling them to form a virtually unlimited range of three-dimensional structures.

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.

New research suggests physicists, computers and brains employ the same procedure to tease out important features from among other irrelevant bits of data.

A potent theory has emerged explaining a mysterious statistical law that arises throughout physics and mathematics.

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

Martin Hairer was named a 2014 Fields medalist for an epic masterpiece in stochastic analysis that colleagues say “created a whole world.”

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.