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Illustation for "The Slippery Math of Causation"
insights puzzle

Solution: ‘The Slippery Math of Causation’

The all-too-intuitive picture of a straight arrow going from cause to effect is far too simplistic to describe the real world.

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

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?

Illustation for "The Slippery Math of Causation"
insights puzzle

The Slippery Math of Causation

If a forest is burning and we don’t know what’s responsible, does it have a cause?

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

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.

Art for "Three Decades Later, Mystery Numbers Explained"
Abstractions blog

Three Decades Later, Mystery Numbers Explained

Zeta values seem to connect distant geometric worlds. In a new proof, mathematicians finally explain why.