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At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.

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.

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory.

Mathematicians have long grappled with the reality that some problems just don’t have solutions.

“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.

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 have proved that copies of smaller graphs can always be used to perfectly cover larger ones.

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.

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