Symmetry

Mathematicians have long wondered how “shapes of constant width” behave in higher dimensions. A surprisingly simple construction has given them an answer.

What do the integers have in common with the symmetries of a triangle? In the 19th century, mathematicians invented groups as an answer to this question.

If you cover a surface with tiles, repetitive patterns always emerge — or do they? In this week’s episode, mathematician Natalie Priebe Frank and co-host Janna Levin discuss how recent breakthroughs in tiling can unlock structural secrets in the natural world.

Two mathematicians have proved a long-standing conjecture that is a step on the way toward finding the worst shape for packing the plane.

Time is all around us: in the language we use, in the memories we revisit and in our predictions of the future. But what exactly is it? The physicist and Nobel laureate Frank Wilczek joins Steve Strogatz to discuss the fundamental hallmarks of time.

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

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.