Geometry

The discovery earlier this year of the “hat” tile marked the culmination of hundreds of years of work into tiles and their symmetries.

After identifying interlocking symmetries in mammalian cells, scientists can describe some tissues as liquid crystals — an observation that lays the groundwork for a fluid-dynamic theory of how tissues move.

Eugenio Calabi, who died on September 25, conceived of novel geometric objects that later became fundamental to string theory.

A new magnum opus posits the existence of a hidden mathematical link akin to the connection between electricity and magnetism.

The spatial intuition behind a three-point turn offers an on-ramp to a century-old geometry problem.

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

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.

A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square.