Computational complexity

Researchers prove that navigating certain systems of vectors is among the most complex computational problems.

Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms.

How hard is it to prove that problems are hard to solve? Meta-complexity theorists have been asking questions like this for decades. A string of recent results has started to deliver answers.

Quantum algorithms can find their way out of mazes exponentially faster than classical ones, at the cost of forgetting the path they took. A new result suggests that the trade-off may be inevitable.

A new algorithm brings together the advantages of randomness and deterministic processes to reliably construct large prime numbers.

A new paper finds a faster method for determining when two mathematical groups are the same.

Is it possible to fill space “cubically” with shapes that act like spheres? A proof at the intersection of geometry and theoretical computer science says yes.

In Shang-Hua Teng’s work, theoretical and practical questions have long been intertwined. Now he’s turning his focus to the impractical.

Random circuit sampling, a popular technique for showing the power of quantum computers, doesn’t scale up if errors go unchecked.