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. “There is no absolute randomness in ...

Microsoft Math Solver is a free tool that uses AI to recognize both printed and handwritten math. It’s particularly strong with geometric proofs and interactive graphing, and it pulls learning ...

The authors do not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and have disclosed no relevant affiliations beyond their ...