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 ...

We spend a lot of time thinking about the difficult people in our lives—the friend who can't take feedback, the partner who always has to be right, the coworker who turns everything into a fight. But ...

Liam Price just cracked a 60-year-old problem that world-class mathematicians have tried and failed to solve. He’s 23 years old and has no advanced mathematics training. What he does have is a ChatGPT ...

Abstract: In this work, we extend the simplex algorithm of linear programming for finding a local minimum of a concave quadratic function subject to box constraints. In order to test the performance ...

The original version of this story appeared in Quanta Magazine. In 1939, upon arriving late to his statistics course at UC Berkeley, George Dantzig—a first-year graduate student—copied two problems ...

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 ...

The leading approach to the simplex method, a widely used technique for balancing complex logistical constraints, can’t get any better. In 1939, upon arriving late to his statistics course at the ...

If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle the easiest pieces first. But this kind of sorting has a cost.

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 ...

The original version of this story appeared in Quanta Magazine. For computer scientists, solving problems is a bit like mountaineering. First they must choose a problem to solve—akin to identifying a ...

When the greatest mathematician alive unveils a vision for the next century of research, the math world takes note. That’s exactly what happened in 1900 at the International Congress of Mathematicians ...