symplectic geometry

More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective.

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about.

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

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.

The simple Möbius strip illustrates a deep mathematical challenge that has long tormented the field of symplectic geometry.

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.