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 ...

A Palestinian boy sits at the site of an overnight Israeli military strike on structures and tents housing displaced families, killing ten Palestinians, in Gaza City, Thursday. Credit: AFP/OMAR ...

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 ...

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 ...

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 ...

Dr Jin Cheng (Jess Hong) pulls a Sir Isaac Newton move in the VR game in "3 Body Problem." Credit: Netflix If you're the type of person who yells "wey-oh!" if someone in a TV show says the name of the ...

Follow this section to personalize your feed and get instant alerts. WHY FOLLOW? Update your preferences in Account Settings Personalized Content Follow this tag to personalize your feed and get ...

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 ...

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 ...

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 ...