What's up in
Mathematician Hurls Structure and Disorder Into Century-Old Problem
A new paper shows how to create longer disordered strings than mathematicians had thought possible, proving that a well-known recent conjecture is “spectacularly wrong.”
New Proof Reveals That Graphs With No Pentagons Are Fundamentally Different
Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.
Undergraduate Math Student Pushes Frontier of Graph Theory
At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.
Disorder Persists in Larger Graphs, New Math Proof Finds
David Conlon and Asaf Ferber have raised the lower bound for multicolor “Ramsey numbers,” which quantify how big graphs can get before patterns inevitably emerge.
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.”