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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.

Psychedelic drugs can trigger characteristic hallucinations, which have long been thought to hold clues about the brain’s circuitry. After nearly a century of study, a possible explanation is crystallizing.

New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.”

By squeezing fluids into flat sheets, researchers can get a handle on the strange ways that turbulence feeds energy into a system instead of eating it away.

New results emerging from graph theory prove that the way a population is organized can guarantee the eventual triumph of natural selection — or permanently thwart it.

Being able to think like a physicist helps Carina Curto, a mathematician-turned-neuroscientist, pull insights about the human brain out of theoretical models.

How many colors do you need to color an infinite plane so that no points 1 unit apart are the same color?

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.