Geometry

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.

After more than three centuries, a geometry problem that originated with a royal bet has been solved.

The amplituhedron, a shape at the heart of particle physics, appears to be deeply connected to the mathematics of paper folding.

Using a relatively young theory, a team of mathematicians has started to answer questions whose roots lie at the very beginning of mathematics.

After finding the homeschooling life confining, the teen petitioned her way into a graduate class at Berkeley, where she ended up disproving a 40-year-old conjecture.

A team of mathematicians based in Vienna is developing tools to extend the scope of general relativity.

After just a few months of work, a complete newcomer to the world of sphere packing has solved one of its biggest open problems.

A tetrahedron is the simplest Platonic solid. Mathematicians have now made one that’s stable only on one side, confirming a decades-old conjecture.