Computer scientists established a new boundary on computationally verifiable knowledge. In doing so, they solved major open problems in quantum mechanics and pure mathematics.
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.
We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”
New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.