Symplectic geometry

Mathematicians think abstract tools from a field called symplectic geometry might help with planning missions to far-off moons and planets.

Eugenio Calabi, who died on September 25, conceived of novel geometric objects that later became fundamental to string theory.

The prize-winning geometer feels most fulfilled when exploring the fertile ground where constraint meets creation.

Recent explorations of unique geometric worlds reveal perplexing patterns, including the Fibonacci sequence and the golden ratio.

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.