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 discovery about the relationship between time and memory in computing. It was a rough sketch of a mathematical proof that memory was more powerful than computer scientists believed: A small amount would be as helpful as a lot of time in all conceivable computations. That sounded so improbable that he assumed something had to be wrong, and he promptly set the proof aside to focus on less crazy ideas. Now, he’d finally carved out time to find