The universe’s expansion makes cosmic distance far less intuitive than simply measuring how long light has traveled.

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, ...

Long-distance driving in a Porsche Turbo S brings performance, comfort, and endurance into focus as the road trip develops problems along the way. Rather than a track setting or short test drive, the ...

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 ...

After maintaining an impressively decisive lead in the Trans Balkan Race, it was announced last night (2 June) that Radosław Gołębiewski has been disqualified. While details were initially thin, the ...

Mathematician Will Sawin discusses his experience reviewing and refining a mathematical proof devised by OpenAI's internal model—and what that could mean for mathematics. Reading time 10 minutes Will ...

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 ...