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A type of symmetry so unusual that it was called a “pariah” turns out to have deep connections to number theory.

Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.

To tell truth from fiction, start with quantitative thinking, argues the mathematician Rebecca Goldin.

The color of LED lights is controlled by a clumsy process. A new mathematical discovery may make it easier for us to get the hues we want.

The mathematician Svitlana Mayboroda and collaborators have figured out how to predict the behavior of electrons — a mathematical discovery that could have immediate practical effects.

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.