The original version of this story appeared in Quanta Magazine. If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle ...

OpenAI’s latest artificial intelligence (AI) system dropped in September with a bold promise. The company behind the chatbot ChatGPT showcased o1 — its latest suite of large language models (LLMs) — ...

If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle the easiest pieces first. But this kind of sorting has a cost.

Alan Veliz-Cuba has received funding from the Simons Foundation and the American Mathematical Society for some of his research. You can probably think of a time when you’ve used math to solve an ...