How did Ernest Ryu use ChatGPT to solve a research problem related to Nesterov acceleration?

Ryu picked a difficult, open version of a problem related to Nesterov acceleration that had resisted others but might admit a short proof. Over three evenings, he iteratively worked with ChatGPT: when the model produced an initial proof with a calculation mistake, he corrected it, preserved the correct intermediate steps in a growing prompt, abandoned dead ends, and pushed it toward other approaches until it cracked the problem. He described the process as maze running and estimated ChatGPT accelerated his exploration by 3x to 10x.

Ernest Ryu used ChatGPT as a research collaborator on a mathematics problem tied to Nesterov acceleration, a technique for speeding up optimization. He deliberately chose a version of the problem that was open long enough that others had attempted it, but simple enough that a short proof might exist. Working for three consecutive nights from 8pm to midnight, he guided the model until it solved the problem on the third night. Their collaboration resembled real research: ChatGPT produced an initial proof containing a calculation mistake, so Ryu iterated by correcting the error, keeping the valid intermediate steps in an increasingly long prompt, discarding unsuccessful lines of attack, and steering the model toward other approaches. Ryu characterized the work as maze running, with ChatGPT helping him move down promising corridors and open doors much faster, roughly 3 to 10 times faster than without it.