An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.

The nearest neighbor problem asks where a new point fits into an existing data set. A few researchers set out to prove that there was no universal way to solve it. Instead, they found such a way.

The mathematician Caucher Birkar was born on a subsistence farm and raised in the middle of the brutal war between Iran and Iraq. After fleeing to England, he has gone on to impose order on a wild landscape of mathematical equations.

The mathematician Alessio Figalli is rarely in one place for very long. But his work has established the stability of everything from crystals to weather fronts by using concepts derived from Napoleonic fortifications.

18-year-old Ewin Tang has proven that classical computers can solve the “recommendation problem” nearly as fast as quantum computers. The result eliminates one of the best examples of quantum speedup.

What’s easy for a computer to do, and what’s almost impossible? Those questions form the core of computational complexity. We present a map of the landscape.

Computer scientists have been searching for years for a type of problem that a quantum computer can solve but that any possible future classical computer cannot. Now they’ve found one.

A century ago, the great mathematician David Hilbert posed a probing question in pure mathematics. A recent advance in optimization theory is bringing Hilbert’s work into a world of self-driving cars.

Mathematicians have disproved the strong cosmic censorship conjecture. Their work answers one of the most important questions in the study of general relativity and changes the way we think about space-time.