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.

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.

The universe of problems that a computer can check has grown. The researchers’ secret ingredient? Quantum entanglement.

In math, sometimes the most common things are the hardest to find.