Geometry

Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.

Math teachers have stymied students for hundreds of years by sticking goats in strangely shaped fields. Learn why one grazing goat problem has stumped mathematicians for more than a century.

The mathematician Federico Ardila takes a creative approach to the search for useful answers hiding among inconceivably huge numbers of possible ones.

To the surprise of experts in the field, a postdoctoral statistician has solved one of the most important problems in high-dimensional convex geometry.

A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.

A group of MIT undergraduates is searching for tetrahedra that tile space, the latest effort in a millennia-long inquiry. They’ve already made a new discovery.

Four mathematicians have cataloged all the tetrahedra with rational angles, resolving a question about basic geometric shapes using techniques from number theory.

Long considered solved, David Hilbert’s question about seventh-degree polynomials is leading researchers to a new web of mathematical connections.

Imagine if we lived on a cube-shaped Earth. How would you find the shortest path around the world?