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Mathematics

Photo illustration of Alessio Figalli
2018 Fields Medal and Nevanlinna Prize Winners

A Traveler Who Finds Stability in the Natural World

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.

Art for "A Math Theory for Why People Hallucinate"
neuroscience

A Math Theory for Why People Hallucinate

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.

Photo of Cohl Furey
fundamental physics

The Peculiar Math That Could Underlie the Laws of Nature

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

Photo of Jupiter for "Mathematicians Tame Turbulence in Flattened Fluids"
fluid dynamics

Mathematicians Tame Turbulence in Flattened Fluids

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.

Illustration for "Mathematics Shows How to Ensure Evolution"
mathematical biology

Mathematics Shows How to Ensure Evolution

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.

Photo of Carina Curto
Q&A

Her Key to Modeling Brains: Ignore the Right Details

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

Illustration for "Four Is Not Enough"
Quantized Academy

Four Is Not Enough

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

Art for "A Classical Math Problem Gets Pulled Into the Modern World"
algorithms

A Classical Math Problem Gets Pulled Into the Modern World

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.

Illustration of a black hole with a Cauchy horizon
general relativity

Mathematicians Disprove Conjecture Made to Save Black Holes

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.