Kevin Hartnett

Senior Writer

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Abstractions blog

Graced With Knowledge, Mathematicians Seek to Understand

April 8, 2020

A landmark proof in computer science has also solved an important problem called the Connes embedding conjecture. Mathematicians are working to understand it.

Photo of two mathematicians drawing on a chalkboard

Mathematics as a Team Sport

March 31, 2020

When 50 mathematicians spend a week in the woods, there’s no telling what will happen. And that’s the point.

An animation showing a 3-by-3 Latin square, with numbers color coded, and the equivalent graph.
Abstractions blog

‘Rainbows’ Are a Mathematician’s Best Friend

March 18, 2020

“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.

Animation showing toy-like depictions of computer science, quantum mechanics and pure math affecting each other.
computational complexity

Landmark Computer Science Proof Cascades Through Physics and Math

March 4, 2020

Computer scientists established a new boundary on computationally verifiable knowledge. In doing so, they solved major open problems in quantum mechanics and pure mathematics.

Animated demonstration of a colorful complete graph being tiled by a smaller tree

Rainbow Proof Shows Graphs Have Uniform Parts

February 19, 2020

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones.


The Map of Mathematics

February 13, 2020

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Photo of black and white swirls of mixing paint
fluid dynamics

Mathematicians Prove Universal Law of Turbulence

February 4, 2020

By exploiting randomness, three mathematicians have proved an elegant law that underlies the chaotic motion of turbulent systems.

Abstractions blog

For Fluid Equations, a Steady Flow of Progress

January 13, 2020

A startling experimental discovery about how fluids behave started a wave of important mathematical proofs.

Animation of two rings of fluid approaching each other and colliding.
fluid dynamics

Famous Fluid Equations Spring a Leak

December 18, 2019

Researchers have spent centuries looking for a scenario in which the Euler fluid equations fail. Now a mathematician has finally found one.