Computational complexity

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.

Computer scientists established a new boundary on computationally verifiable knowledge. In doing so, they solved major open problems in quantum mechanics and pure mathematics.

The universe of problems that a computer can check has grown. The researchers’ secret ingredient? Quantum entanglement.

By chopping up large numbers into smaller ones, researchers have rewritten a fundamental mathematical speed limit.

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

18-year-old Ewin Tang has proven that classical computers can solve the “recommendation problem” nearly as fast as quantum computers. The result eliminates one of the best examples of quantum speedup.

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.