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 ...

Alan Milburn says youth unemployment has no quick fixes – an idea with an important lesson for those thinking about how to rejoin the EU Mainstream politicians are rarely direct. It is part of the ...

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 ...

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 ...

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 ...

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 ...

In this video I will work through 22 different examples of solving two-step equations using a worksheet I created for my students. I will use the properties of equality, inverse operations, and ...

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 ...

David Cutler is in the spotlight for his work on a tasty-sounding mathematics problem. In January, the New York Times featured a research paper authored by Cutler and Neil Sloane, the founder of The ...

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 ...