Imagine a world where artificial intelligence not only understands language but creates with it, where quantum systems no longer feel like an enigma but a solvable puzzle. It might sound like science ...

Building on a landmark algorithm, researchers propose a way to make a smaller and more noise-tolerant quantum factoring circuit for cryptography. The most recent email you sent was likely encrypted ...

The original version of this story appeared in Quanta Magazine. 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 ...

If someone asks you to determine whether two objects are the same, it might seem like a trivial request. In most everyday cases, a quick glance is enough for you to render an accurate judgment. But in ...

Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms. All of modern mathematics is built on ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...