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A complete classification could lead to a wealth of new materials and technologies. But some exotic phases continue to resist understanding.

By reimagining the kinks and folds of origami as atoms in a lattice, researchers are uncovering strange behavior hiding in simple structures.

Voevodsky’s friends remember him as constitutionally unable to compromise on the truth — a quality that led him to produce some of the most important mathematics of the 20th century.

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.

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry.

Three physicists have been awarded the Nobel Prize in Physics for rewriting our understanding of exotic quantum states on the surfaces of materials.

Mathematicians have had a hard time finding commonalities in large groups of random shapes — until recently.

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