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 ...

At an event for pharmaceutical executives, biotech founders, and researchers yesterday, Anthropic announced Claude Science, a ...

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 ...

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 ...

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 ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...