Fractals

A new paper establishes a long-conjectured bound about the size of the overlap between sets of lines and points.

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

Mark Braverman has spent his career translating thorny problems into the language of information complexity.

The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.

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

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

By folding fractals into 3-D objects, a mathematical duo hopes to gain new insight into simple equations.

Nature has revealed peculiar mathematical objects that connect order and chaos.