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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.

Prime numbers are endlessly fascinating to number theorists and math enthusiasts. This month’s puzzle explores primes by cooking up a whimsical dish of grilled snake ribs.

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

The mathematical concept of parity and the fatal flaw of serial multiplication can help explain why having two sexes usually works better than having one or three.

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.

Mathematical insights into how RNA helps viruses pull together their protein shells could guide future studies of viral behavior and function.

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