Computational complexity

When checking that solutions to certain problems are correct, it turns out, you can’t get around the inherent complexity of the quantum world.

A graduate student recently harnessed the complexity of mathematical proofs to create a powerful new tool in cryptography.

Henry Yuen is developing a new mathematical language to describe problems whose inputs and outputs aren’t ordinary numbers.

Explore the year’s most surprising computational revelations, including a new fundamental relationship between time and space, an undergraduate who overthrew a 40-year-old conjecture, and the unexpectedly effortless triggers that can turn AI evil.

Researchers have used metamathematical techniques to show that certain theorems that look superficially distinct are in fact logically equivalent.

Mary Wootters discusses how error-correcting codes work, and how they are essential for reliable communication and storage.

In theory, quantum physics can bypass the hard mathematical problems at the root of modern encryption. A new proof shows how.

An attack on a fundamental proof technique reveals a glaring security issue for blockchains and other digital encryption schemes.

One computer scientist’s “stunning” proof is the first progress in 50 years on one of the most famous questions in computer science.