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 ...

The laws of physics that concern heat and work could gain a firmer mathematical footing thanks to “gauge theory”, which ...

It’s been 250 years since the signing of the Declaration of Independence — a milestone that invites not just celebration, but reflection. To illustrate two and a half centuries of U.S. history, Here & ...

Your browser does not support the audio element. In January 2025 I was in Santa Clara, California writing some JavaScript to perform some reporting. I wanted to be ...

A Mathematician with early access to XAI Grok 4.20, found a new Bellman function for one of the problems he had been working on with my student N. Alpay. Not an Erdős problem, but original research.

There is a rule in mathematics that feels so obvious it barely seems worth stating. Yet accepting it leads to objects with no size, spheres that duplicate themselves, and sets that cannot be measured ...

When a delicate object crashes onto the floor, most people expect it to shatter into several pieces. What they might not know, however, is that the sizes of those fragments—whether from a broken plate ...

Thirty years ago today, Netscape Communications and Sun Microsystems issued a joint press release announcing JavaScript, an object scripting language designed for creating interactive web applications ...

Here’s what you’ll learn when you read this story: Object Arjuna 2025 PN7 was thought to be a meteorite in an Earthlike orbit, but that is now being questioned. The new hypothesis suggests that 2025 ...