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 ...

One July afternoon in 2024, Ryan Williams set out to prove himself wrong. Two months had passed since he’d hit upon a startling discovery about the relationship between time and memory in computing.

As a goal, quantum supremacy 1 is unlike most algorithmic tasks because it is defined not in terms of a particular problem to be solved but in terms of what classical computers cannot do. This is like ...

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 ...