Kevin Hartnett

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.

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.

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.

Zeta values seem to connect distant geometric worlds. In a new proof, mathematicians finally explain why.

Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.

By 1913, Albert Einstein had nearly completed general relativity. But a simple mistake set him on a tortured, two-year reconsideration of his theory. Today, mathematicians still grapple with the issues he confronted.