Random graphs provide a mathematical framework for modelling networks in which connections between nodes occur with prescribed probabilities. Classical models such as the Erdős–Rényi graph establish ...

Graphs are everywhere. In discrete mathematics, they are structures that show the connections between points, much like a public transportation network. Mathematicians have long sought to develop ...

At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student. The proof joined a long list of mathematical results that Sah, who turned 21 ...

AlphaProof and AlphaGeometry 2 are steps toward building systems that can reason, which could unlock exciting new capabilities. AI models can easily generate essays and other types of text. However, ...

You can probably think of a time when you’ve used math to solve an everyday problem, such as calculating a tip at a restaurant or determining the square footage of a room. But what role does math play ...

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 ...

Random graphs provide a mathematical framework for modelling networks whose links are established according to probabilistic rules. Classical ensembles such as the Erdős–Rényi model and the ...