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 ...

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 ...

Basketball: NBA Commissioner Adam Silver speaks to the media during a press conference at the St. Regis Hotel New York, NY 9/10/2025CREDIT: Erick W. Rasco (Photo by Erick W. Rasco/Sports Illustrated ...

Elizabeth Guevara is a personal finance reporter who explains the world of business and economics and how it impacts your finances. She joined Investopedia in 2024. Investopedia / Photo Composite by ...

Last week, the NBA fined the Utah Jazz $500,000 for "conduct detrimental to the league" and the Indiana Pacers $100,000 for violating the league's Player Participation Policy after both teams altered ...

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 ...

The best way to fix Americans’ cost-of-living problem is to give workers bigger raises, Federal Reserve Chair Jerome Powell said last week. The problem: That solution looks broken, too. The US job ...