Kevin Hartnett

Researchers are getting close to building a quantum computer that can perform tasks a classical computer can’t. Here’s what the milestone will mean.

Neven’s law states that quantum computers are improving at a “doubly exponential” rate. If it holds, quantum supremacy is around the corner.

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.

In practice, quantum computers can’t run many programs that classical computers can, because they’re not allowed to selectively forget information. A new algorithm for multiplication shows a way around that problem.

These games combine quantum entanglement, infinity and impossible-to-calculate winning probabilities. But if researchers can crack them, they’ll reveal deep mathematical secrets.

Recent progress on the “sum product” problem recalls a celebrated mathematical result that revealed the power of miniature number systems.

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.

In math, sometimes the most common things are the hardest to find.

What’s easy for a computer to do, and what’s almost impossible? Those questions form the core of computational complexity. We present a map of the landscape.