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To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape.

It’s “a definitive study for all time, like writing the final book,” says one researcher who’s mapping out new classes of geometric structures.

Two “rare jewels” have illuminated a mysterious multidimensional object that connects a huge variety of mathematical work.

After her untimely death, Maryam Mirzakhani’s life is best remembered through her work.

Kaisa Matomäki has proved that properties of prime numbers over long intervals hold over short intervals as well. The techniques she uses have transformed the study of these elusive numbers.

John Nash’s notion of equilibrium is ubiquitous in economic theory, but a new study shows that it is often impossible to reach efficiently.

A California housewife who in the 1970s discovered four new types of tessellating pentagons is dead at 94.

A French mathematician has completed the classification of all convex pentagons, and therefore all convex polygons, that tile the plane.

Big advances in math can happen when mathematicians move ideas into areas where they seem like they shouldn’t belong.