"I used ChatGPT to solve an open problem in convex optimization." (twitter.com)

A researcher reports using ChatGPT as an active research assistant to resolve a previously open problem in convex optimization: through iterative prompting the model generated plausible lemmas, suggested proof strategies (e.g., reductions, duality transforms and inequality chains), and produced short symbolic derivations that the human then checked and tightened into a complete, publishable proof. The workflow combined model drafts with targeted prompts to fill logical gaps, automated numerical checks of edge cases the model suggested, and careful human verification of each step before formalizing the argument. The end result was a verified solution to the open question and accompanying intuition that would have taken substantially longer without the model’s rapid idea-generation. For the AI/ML community this case is a concrete demonstration that large language models can assist nontrivial mathematical research: they can propose useful intermediate results, translate high-level ideas into workable lemmas, and help triage promising proof paths. Technically, the interaction highlights strengths (pattern-matching across existing proofs, fast algebraic manipulation, hypothesis generation) and limitations (occasional hallucinated steps, brittle symbolic precision) and underscores the need for human-in-the-loop verification and reproducible prompt protocols. The outcome suggests LLMs will become practical co-researchers for theorem exploration and conjecture testing, while formal verification or rigorous peer review remains essential for final acceptance.