The European Space Agency's XMM-Newton and NASA's Chandra X-ray space telescopes have spotted the aftermath of three bright explosions echoing through the outer spiral arms of our galaxy, the Milky ...

Last month, OpenAI announced that its latest version of ChatGPT had solved a major math problem, one that had stumped experts ...

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 ...

The result is correct but challenges core norms of mathematics: checking proofs, crediting ideas and keeping research open to everyone.

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 ...

Add Yahoo as a preferred source to see more of our stories on Google. When you buy through links on our articles, Future and its syndication partners may earn a commission. The distance players have ...

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 ...

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 ...

For nearly 80 years, mathematicians have struggled to solve a classic geometry puzzle first posed by Paul Erdős in 1946: the planar unit distance problem. The question posed by the legendary Hungarian ...

A long-standing problem in discrete geometry involving how many pairs of points can be exactly one unit apart has been addressed using an artificial intelligence system developed by OpenAI, according ...

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 ...