The original version of this story appeared in Quanta Magazine. One July afternoon in 2024, Ryan Williams set out to prove himself wrong. Two months had passed since he’d hit upon a startling ...

Complexity theory is a branch of computer science that studies the resources required to solve computational problems, particularly focusing on the classification of problems based on their inherent ...

Online algorithms are designed to make decisions sequentially, without complete knowledge of future inputs. In many real-world applications—from scheduling and resource allocation to network ...

Primal methods constitute a common approach to solving (combinatorial) optimization problems. Starting from a given feasible solution, they successively produce new feasible solutions with ...

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. Many aspects of modern applied research ...