Geometry

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.

The links between math, music and art have been explored for thousands of years. Sarah Hart is now turning a mathematical eye to literature.

Researchers are discovering the shortest knots and fattest Möbius strips, among other “optimal shapes.”

Landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

Mathematicians prove a theorem that illuminates the geometry of universes with tiny amounts of mass.

High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible.

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.