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A new proof shows why an uncountably infinite number of Möbius strips will never fit into a three-dimensional space.

Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.

In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.

In math, sometimes the most common things are the hardest to find.

An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”

Zeta values seem to connect distant geometric worlds. In a new proof, mathematicians finally explain why.

Decades after physicists happened upon a stunning mathematical coincidence, researchers are getting close to understanding the link between two seemingly unrelated geometric universes.

Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives?