Geometry

Grothendieck is revered in the world of math; outside of it, he’s known for his unusual life, if he’s known at all. But what were his actual mathematical contributions?

The sunlight-collecting organelles known as chloroplasts solve a packing problem: how to optimize photosynthesis without sustaining damage from dangerously intense rays.

A straightforward conjecture about runners moving around a track turns out to be equivalent to many complex mathematical questions. Three new proofs mark the first significant progress on the problem in decades.

The Bonnet problem asks when just a bit of information is enough to uniquely identify a whole surface.

Explore a shape that can’t pass through itself, a teenage prodigy, and two new kinds of infinity.

By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most powerful tools.

Mathematicians have broken through a long-standing barrier in the study of “minimizing surfaces,” which play an important role in both math and physics.

In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation for modern geometry and physics.

Despite their wide variety of sizes, niches and shapes, sharks scale geometrically, pointing to possible fundamental constraints on evolution.