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?

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

Mathematicians have long pondered the reach of a grazing goat tied to a fence, only finding approximate answers until now.

An exercise in pure mathematics has led to a wide-ranging theory of how the world comes together.

Struggling with math problems that can’t be solved helps us better understand the ones we can.