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

Millions of mobile phone users in the United States remain exposed to a well-documented surveillance technique: fake cell ...

Over the past decade, Professor L. Mahadevan's Soft Math Lab at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) has helped establish how the ancient Japanese paper arts ...

Artificial intelligence is mastering the kinds of projects that have long helped to build the careers of young mathematicians. What does that mean for their future? Credit...Illustrations by Yoshi ...

Think about placing dots on a flat surface. You want as many pairs as possible to be separated by the same distance. For any amount of dots, what is the greatest possible number of pairs that can be ...

The aerospace and defense sector is in the middle of one of the most significant wealth creation cycles in its history. Defense budgets are at multi-decade highs. Private space companies that spent ...

A dude named Lenin assures us that his five year plan will be completed in 4 years and that progress is inevitable. Just tell me how many hundreds of thousands you ...

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 ...

“If you are a mathematician,” one of the world’s leading mathematicians recently wrote, “you may want to make sure you are sitting down before reading further.” And you’ll definitely need to sit down ...

It started almost by accident. At my startup Dwelly, I constantly push the limits of what AI tools can actually do. One day I just typed into a chat: “Can you prove P ≠ NP?”—referring to the problem ...

Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects. By introducing ...

A 150-year-old rule in geometry has been proven wrong. Mathematicians found two different doughnut-shaped surfaces that look identical when measured locally but are actually different overall. For ...