Erica Klarreich

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space.

The “sensitivity” conjecture stumped many top computer scientists, yet the new proof is so simple that one researcher summed it up in a single tweet.

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.

Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.

A founder of modern geometric analysis who produced “some of the most dramatic advances in mathematics in the last 40 years,” Uhlenbeck is the first woman to be awarded this top honor.

A pair of mathematicians has built on an obscure, 30-year-old mathematical theory to show that soap-filmlike minimal surfaces appear abundantly in a wide range of shapes.

Tadashi Tokieda discovers new physical phenomena by looking at the everyday world with the eyes of a child.

A new proof from the Australian science fiction writer Greg Egan and a 2011 proof anonymously posted online are now being hailed as significant advances on a puzzle mathematicians have been studying for at least 25 years.

Urmila Mahadev spent eight years in graduate school solving one of the most basic questions in quantum computation: How do you know whether a quantum computer has done anything quantum at all?