Erica Klarreich

Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.

To the surprise of experts in the field, a postdoctoral statistician has solved one of the most important problems in high-dimensional convex geometry.

A cryptographic master tool called indistinguishability obfuscation has for years seemed too good to be true. Three researchers have figured out that it can work.

After 44 years, there’s finally a better way to find approximate solutions to the notoriously difficult traveling salesperson problem.

Three mathematicians have resolved a fundamental question about straight paths on the 12-sided Platonic solid.

Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.

In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.

It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway.