Jordana Cepelewicz

A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.

Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.

A series of new papers describes how to fully characterize key dynamical systems with relatively little data.

For the first time, mathematicians have proved that planetary orbits in a solar system will always be unstable.

In 50 years of searching, mathematicians found only one example of a “subspace design” in a vector space. A new proof reveals that there are infinitely more out there.

Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical physics.

Is it possible to fill space “cubically” with shapes that act like spheres? A proof at the intersection of geometry and theoretical computer science says yes.

Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong.

For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. A new computer-assisted proof marks a major breakthrough in that quest.