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 ...

“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 ...

AI can rifle through enormous libraries of information to connect far-flung ideas—conceptual leaps remain a purely human skill. The planar unit distance problem, or Erdős problem 90, has intrigued ...

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 ...

What Is This Subset Sum Solver? This is the world record exact subset sum solver. It holds world records across all 65 tested algorithm categories, solving the NP-complete subset sum problem from 10 ...

Is America heading toward a national debt crisis? As an economic adviser to President Biden and an economist active in mainly Democratic policy circles since the late 1980s, I’ve spent most of my ...

Company says work on Paul Erdős planar unit distance problem shows advance in AI reasoning OpenAI has claimed a further advance in AI reasoning after its technology successfully tackled an 80-year-old ...

Watching the Suns this past season, there were noticeable holes on the roster, especially in their matchup against the Thunder. The priority this offseason, as with any NBA team, should be to fill ...

The U.S. blockade of Iran continues amid an uncertain round of peace negotiations, while Congress wrestles with the ongoing Department of Homeland Security shutdown and the looming lapse of a key ...

One idle evening last October, Mehtaab Sawhney took up an old pastime. He began perusing the website erdosproblems.com, an updated record of the 1,179 conjectures left behind by the eccentric and ...