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.
Abstractions blog
Mathematicians Begin to Tame Wild ‘Sunflower’ Problem
A major advance toward solving the 60-year-old sunflower conjecture is shedding light on how order begins to appear as random systems grow in size.
foundations of mathematics
With Category Theory, Mathematics Escapes From Equality
Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.
prime numbers
Big Question About Primes Proved in Small Number Systems
The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.