For new discoveries, everyday mysteries, and the science behind the headlines, follow NPR's ShortWave podcast . Over a century ago, the German psychologist Wolfgang Köhler conducted what became a ...

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 ...

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 ...

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 ...

If you like the idea of a ‘whodunnit’ style detective game, but one without any murder or grizzly crime, you’ll probably love Little Problems. It’s a cosy detective game, where instead of solving ...

Abstract: Maximum jump height evaluation is crucial for transmission line deicing and typically involves time-consuming processes such as dynamic numerical simulations and model experiments. Previous ...

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 ...