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.
number theory
Mathematician Proves Huge Result on ‘Dangerous’ Problem
Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades.
number theory
Mathematicians Catch a Pattern by Figuring Out How to Avoid It
We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”
geometry
Mathematicians Cut Apart Shapes to Find Pieces of Equations
New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.
Abstractions blog
Google and IBM Clash Over Milestone Quantum Computing Experiment
Today Google announced that it achieved “quantum supremacy.” Its chief quantum computing rival, IBM, said it hasn’t. The disagreement hinges on what the term really means.