Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects. By introducing ...

Key Laboratory of Optimization Theory and Applications, School of Mathematics and Information, China West Normal University, Nanchong, China. This paper proposes a symmetric alternating direction ...

Some readers may solve the problem procedurally: line up the two numbers, add the ones column, carry the one, and add the tens to get 43. Others might instead notice a creative shortcut: 29 + 14 is ...

In a dark room, in the middle of the night, a woman lies dreaming. Suddenly, her eyes beneath their lids dart crisply left-right, left-right. The eye signal means she knows she’s dreaming. Lucid ...

At a secret meeting in 2025, some of the world's leading mathematicians gathered to test OpenAI's newest large language model, o4-mini. Experts at the meeting were amazed by how much the model's ...

Amateur mathematicians are using artificial intelligence chatbots to solve long-standing problems, in a move that has taken professionals by surprise. While the problems in question aren’t the most ...

In October 2024, news broke that Facebook parent company Meta had cracked an "impossible" problem that had stymied mathematicians for a century. In this case, the solvers weren't human. An artificial ...

We are moving from a world of institutional dependency to one of personal responsibility. The question is no longer, “What can we do for people?” but, “How can we equip people to do more for ...

The busy box that is your brain is hard at work all day long—and it doesn’t quit when you’re asleep. Not only does your brain fill your slumber with dreams, it also goes right on solving the problems ...

Consider someone who’s perfectly content with their office chair. It’s not ergonomic, it doesn’t have lumbar support, but it works. Then, during a meeting or a visit to a friend’s office, they sit in ...

Sven, a sales leader, received a call from a major customer who was furious. Their order arrived late, the product was damaged, and to top it off, their invoice didn’t reflect the volume discount ...