Jordana Cepelewicz

For decades, a small group of mathematicians has patiently unraveled the mystery of what was once math’s most popular picture. Their story shows how technology transforms even the most abstract mathematical landscapes.

Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?

On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics.

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

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.