Researchers have developed a compact, low-cost convolutional spectrometer that delivers lab-grade precision for applications ...

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 ...

Enterprise AI agents have a new production failure mode, and it is not the model. As enterprises move from single-layer RAG to hybrid retrieval architectures, the same underlying data produces ...

“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 ...

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 ...

The world’s first major private geoengineering start-up must have known it’d have skeptics. The basic premise—dimming the sun to artificially cool the planet—has been called reckless by scientists 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 ...

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 ...

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 ...

The offensive line looked like it would be a stable situation heading into the offseason but season-ending injuries late in the season can always run on to the next season. Bears offensive linemen ...