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A New Algorithm for Graph Crossings, Hiding in Plain Sight
Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory.
When Math Gets Impossibly Hard
Mathematicians have long grappled with the reality that some problems just don’t have solutions.
‘Rainbows’ Are a Mathematician’s Best Friend
“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.
Landmark Computer Science Proof Cascades Through Physics and Math
Computer scientists established a new boundary on computationally verifiable knowledge. In doing so, they solved major open problems in quantum mechanics and pure mathematics.
Rainbow Proof Shows Graphs Have Uniform Parts
Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones.
The Map of Mathematics
Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.
New Proof Settles How to Approximate Numbers Like Pi
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.
A 53-Year-Old Network Coloring Conjecture Is Disproved
In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.
Computer Scientists Expand the Frontier of Verifiable Knowledge
The universe of problems that a computer can check has grown. The researchers’ secret ingredient? Quantum entanglement.