Quantum computers located in a data center. Photo: Sven Hoppe/dpa (Photo by Sven Hoppe/picture alliance via Getty Images) To understand what quantum computers actually threaten, you first need to know ...

“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 ...

Sign up for Work in Progress, a newsletter where Rogé Karma investigates the mysteries of a complicated economy. As recently as five years ago, Spain was no one’s ...

So you’ve connected a device to your PC via a USB port — but Windows doesn’t recognize it. What now? Before you assume the product (or your PC port) is broken, there are several USB troubleshooting ...

De Freitas, Julian, Zeliha Oğuz Uğuralp, and Ahmet Kaan Uğuralp. "Emotional Manipulation by AI Companions." Harvard Business School Working Paper, No. 26-005, August 2025. (Revised October 2025.) ...