Place any number of dots on a two-dimensional plane—say, a piece of paper—and measure the distance between each pair. If you rearrange the dots, how many pairs could be positioned exactly the same ...

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 ...

OpenAI's AI model solved the unit distance problem posed by Paul Erdos in 1946 The AI found a counterexample disproving Erdos's conjecture on unit-distance pairs The solution shows unit-distance pairs ...

“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 ...

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 ...

After 80 years of fruitless struggle by human mathematicians, a major geometry conjecture has at last been solved—via a straightforward query to a chatbot. “No previous AI-generated proof has come ...

OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdős in 1946. If this sounds ...

Abstract: Approximate message passing (AMP) algorithms break a (high-dimensional) statistical problem into manageable parts and then repeatedly solve each part in turn, akin to alternating projections ...

The counterterrorism and targeted violence prevention fields are beginning to recognize that artificial intelligence is changing the threat environment. Much of the current attention is focused on how ...

Owners’ complaints related to the ICCU, including losing power while driving, hurt the brands' reliability scores in Consumer Reports' rankings. Here's what to do if your car has problems. The ICCU is ...

Five years ago, mathematicians Dawei Chen and Quentin Gendron were trying to untangle a difficult area of algebraic geometry involving differentials, elements of calculus used to measure distance ...