Symmetry

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.

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

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

The proof establishes new conditions that cause connected oscillators to sway in sync.

Simple math can help explain the complexities of the newly discovered aperiodic monotile.

A new phase of matter called a “time crystal” plays with our expectations of thermodynamics. The physicist Vedika Khemani talks with Steven Strogatz about its surprising quantum behavior.

In all bilaterally symmetrical animals, from humans down to simple worms, nerves cross from one side of the body to the opposite side of the brain. Geometry may explain why.

So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.