How can you have a proof without proving anything? Mathematicians found a way and, in the process, came to blows over it – ...

Grok 4.5 constructed a counterexample proving hypercontractivity fails on the 4-sphere, closing a decades-old gap in ...

Physicists have built a real-number version of quantum mechanics that makes all the same predictions as the standard theory, ...

The system operates entirely in the background. Sellers manage their discoverability and business information—menus, ...

Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary ...

Srikanth Nadhamuni argues that AI can dismantle India's procedural complexity, but only if it is built the way Aadhaar was: for everyone. AI has the potential to simplify procedural complexities in ...

For generations, mathematicians have tried and failed to solve an 80-year-old problem. In May, an artificial intelligence (AI) model successfully tackled it. OpenAI, the maker of ChatGPT, said one of ...

Mathematician Will Sawin discusses his experience reviewing and refining a mathematical proof devised by OpenAI's internal model—and what that could mean for mathematics.

In mid-May, OpenAI announced that an internal AI model had disproved the Erdős unit distance conjecture, a famous problem in discrete geometry that had stumped human mathematicians for the last 80 ...

AI can rifle through enormous libraries of information to connect far-flung ideas—conceptual leaps remain a purely human skill. The planar unit distance problem, or Erdős problem 90, has intrigued ...

Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary ...