How do physicists reconstruct what really happened in a particle collision? Through calculations that are so challenging that, in some cases, they simply can’t be done. Yet.

An unexpected connection has emerged between the results of physics experiments and an important, seemingly unrelated set of numbers in pure mathematics.

The latest effort to overhaul math and science education offers a fundamental rethinking of the basic structure of knowledge. But will it be given time to work?

Computer scientists can prove certain programs to be error-free with the same certainty that mathematicians prove theorems.

Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures.

A satellite spotted a burst of light just as gravitational waves rolled in from the collision of two black holes. Was the flash a cosmic coincidence, or do astrophysicists need to rethink what black holes can do?

The physicist Subir Sachdev borrows tools from string theory to understand the puzzling behavior of high-temperature superconductors.

Three years ago, a solitary mathematician released an impenetrable proof of the famous *abc* conjecture. At a recent conference dedicated to the work, optimism mixed with bafflement.

A new breakthrough that bridges number theory and geometry is just the latest triumph for a close-knit group of mathematicians.