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 ...

Richard Feynman described a decision-making problem and its solution in handwritten notes, but the meaning of the notes has been a mystery for almost 50 y. We decipher the problem and solution from ...

“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 ...

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 war in Iran has disrupted supplies of diesel, used to power trucks and heavy equipment, much more than gasoline, which is primarily used in passenger cars. By Emmett Lindner The price of diesel ...

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 ...