Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.

By 1913, Albert Einstein had nearly completed general relativity. But a simple mistake set him on a tortured, two-year reconsideration of his theory. Today, mathematicians still grapple with the issues he confronted.

Two teams of researchers have made significant progress toward proving the black hole stability conjecture, a critical mathematical test of Einstein’s theory of general relativity.

Even with no one in charge, army ants work collectively to build bridges out of their bodies. New research reveals the simple rules that lead to such complex group behavior.

New algorithms show how swarms of very simple robots can be made to work together as a group.

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge.

The mathematician Richard Schwartz finds the hidden depth lurking in simple mathematical puzzles.

Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense.

A famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics.