Algorithms

By proving a broader version of Hilbert’s famous 10th problem, two groups of mathematicians have expanded the realm of mathematical unknowability.

The library sorting problem is used across computer science for organizing far more than just books. A new solution is less than a page-width away from the theoretical ideal.

Hypothetical devices that can quickly and accurately answer questions have become a powerful tool in computational complexity theory.

Researchers got a better look at the thoughts of chatbots, amateurs learned exactly how complicated simple systems can be, and quantum computers passed an essential milestone.

Dijkstra’s algorithm was long thought to be the most efficient way to find a graph’s best routes. Researchers have now proved that it’s “universally optimal.”

Researchers are exploring new ways that quantum computers will be able to reveal the secrets of complex quantum systems.

While devising a new quantum algorithm, four researchers accidentally established a hard limit on entanglement.

Neural networks and other forms of machine learning ultimately learn by trial and error, one improvement at a time.

Computational complexity theorists have discovered a surprising new way to understand what makes certain problems hard.