Geometry

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.

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.