Computational complexity

Algorithms that zero in on solutions to optimization problems are the beating heart of machine reasoning. New results reveal surprising limits.

The most widely used technique for finding the largest or smallest values of a math function turns out to be a fundamentally difficult computational problem.

To understand what quantum computers can do — and what they can’t — avoid falling for overly simple explanations.

A recent paper set the fastest record for multiplying two matrices. But it also marks the end of the line for a method researchers have relied on for decades to make improvements.

Avi Wigderson and László Lovász won for their work developing complexity theory and graph theory, respectively, and for connecting the two fields.

By harnessing randomness, a new algorithm achieves a fundamentally novel — and faster — way of performing one of the most basic computations in math and computer science.

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

After 44 years, there’s finally a better way to find approximate solutions to the notoriously difficult traveling salesperson problem.

A landmark proof in computer science has also solved an important problem called the Connes embedding conjecture. Mathematicians are working to understand it.