Quantum error-correcting codes are an essential ingredient to protect quantum information in a quantum computer from errors due to coupling to an external environment. Recent progress 1,2,3,4,5 has ...

In ancient Greece, Euclid showed that if you agree on a small list of preliminary principles, or axioms, you can use deductive reasoning to reveal all sorts of new mathematical truths. But although ...

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Researchers at Stanford and Caltech have found some critical reasoning failures in advanced AI models. LLMs are great at recognizing patterns, but they have trouble with basic logic, social reasoning, ...

This year has seen some amazing advancements in fundamental mathematics. Researchers have made breakthroughs in geometry, topology, chaos theory, and more. And a startling three of our top 10 ...

You’d be surprised how many young people can’t read this. One of its conclusions tells the sad tale. “Between 2020 and 2025, the number of students whose math skills fall below high school level has ...

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions. But now ...

Mathematical proof debunks the idea that the universe is a computer simulation by Patty Wellborn, University of British Columbia edited by Gaby Clark, reviewed by Robert Egan Editors' notes ...

The original version of this story appeared in Quanta Magazine. At the turn of the 20th century, the renowned mathematician David Hilbert had a grand ambition to bring a more rigorous, mathematical ...

Mehrdad (He/Him) is a writer at GameRant. He started writing about video games when he was a high-school student. He loves playing competitive FPS games such as Rainbow Six Siege. In between, you can ...