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 ...

Jie Wang does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...

Debbie Passey does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond ...

When it comes to teaching math, a debate has persisted for decades: How, and to what degree, should algorithms be a focus of learning math? The step-by-step procedures are among the most debated ...