Arnold’s work was in an area of mathematics that concerns all the different configurations a physical system like bouncing billiard balls or orbiting planets can take. These configurations are encoded ...

They made some progress, re-proving the conjecture in two dimensions using different techniques—ones they hoped would be applicable to the three-dimensional case. But then they hit a wall. “At some ...

Carnegie Mellon University computer scientists and mathematicians have resolved the last, stubborn piece of Keller's conjecture, a geometry problem that scientists have puzzled over for 90 years. By ...

After 80 years of fruitless struggle by human mathematicians, a major geometry conjecture has at last been solved—via a straightforward query to a chatbot. “No previous AI-generated proof has come ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective. Arnold’s work was in an area of mathematics that ...