Abstractions blog
Graced With Knowledge, Mathematicians Seek to Understand
A landmark proof in computer science has also solved an important problem called the Connes embedding conjecture. Mathematicians are working to understand it.
topology
Mathematics as a Team Sport
When 50 mathematicians spend a week in the woods, there’s no telling what will happen. And that’s the point.
Abstractions blog
‘Rainbows’ Are a Mathematician’s Best Friend
“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.
computational complexity
Landmark Computer Science Proof Cascades Through Physics and Math
Computer scientists established a new boundary on computationally verifiable knowledge. In doing so, they solved major open problems in quantum mechanics and pure mathematics.
combinatorics
Rainbow Proof Shows Graphs Have Uniform Parts
Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones.
Multimedia
The Map of Mathematics
Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.
fluid dynamics
Mathematicians Prove Universal Law of Turbulence
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
A startling experimental discovery about how fluids behave started a wave of important mathematical proofs.
fluid dynamics
Famous Fluid Equations Spring a Leak
Researchers have spent centuries looking for a scenario in which the Euler fluid equations fail. Now a mathematician has finally found one.