GPT-5.6, a large language model, used a prompt to solve a 30-year-old open problem in convex optimization. The achievement demonstrates AI's potential to contribute to mathematical research.
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Following OpenAI's CDC proof, GPT-5.6 uses a similar prompt to solve a convex optimization problem that had stumped the field for 30 years, verified in Lean. Is this a signal of AI independently discovering new mathematics, or a carefully engineered prompt trick?
On July 15, 2026, Reddit user pkerger posted in r/math claiming that OpenAI's GPT-5.6, using a single prompt, successfully closed a theoretical gap in convex optimization that had existed for 30 years, and the result was verified in the Lean theorem prover. The post quickly garnered 677 upvotes (95% approval rate), sparking intense debate in the math and AI communities.
According to the poster, this achievement came after OpenAI's announcement of the CDC (Continuous Deep Clustering?) proof, and GPT-5.6 used a prompt similar to that used for the CDC proof. This means the model did not start from scratch but leveraged an existing successful pattern.
The key difference is that the result is not just a model output; it has been formally verified in the Lean theorem prover. Lean is an interactive theorem prover that ensures every step of a mathematical proof is strictly correct. This means that regardless of whether GPT-5.6's reasoning process was perfect, the final conclusion is logically sound.
Several commenters (e.g., Model_Checker, bitchslayer78) acknowledged this, stating that formal verification greatly increases the credibility of the result. However, some voices pointed out that the verification might only cover the conclusion, not the complete process by which the model generated the proof.
The community quickly polarized. Supporters (e.g., Mon_Ouie, arbitrarycivilian) see this as a major breakthrough in AI mathematical reasoning, indicating that the model can discover proofs that humans have long failed to find. Skeptics (e.g., evitcele, PersonalityIll9476) question its independence: the prompt itself may have contained key ideas, and the model merely performed formal filling.
In subsequent comments, the poster pkerger admitted that the prompt design indeed borrowed from OpenAI's CDC proof method, but emphasized that the model still had to derive the specific proof steps on its own. This statement did not fully quell the controversy, as the exact content of the prompt has not been disclosed.
Additionally, some comments noted that the gap in convex optimization might not be a mainstream problem, and its significance remains to be assessed. Nevertheless, the fact that a 30-year open problem was solved by AI is itself an event worth attention.
This breakthrough is not an isolated event. Just days earlier, OpenAI announced that its model had successfully proved a theorem related to CDC (Continuous Deep Clustering?), also using Lean verification. GPT-5.6's convex optimization result is seen as a direct extension of this approach.
This 'prompt-verify' pattern is emerging as a new paradigm for AI mathematical research: first, humans design a prompting strategy, then the model generates a proof, and finally, formal tools verify it. But this also raises philosophical questions about 'who is the true discoverer.'
This report is primarily based on a Reddit post and its comments, making it a secondary source. The identity and background of the poster pkerger have not been independently verified, and OpenAI has not issued an official statement on the matter. The existence of Lean verification increases credibility, but the specific content of the prompt and the full scope of verification remain unclear.
GPT-5.6 solving a 30-year convex optimization problem, verified in Lean, marks a significant step for AI in mathematical discovery. However, prompt dependency and community controversy indicate that the boundaries of AI's independent innovation still require stricter scrutiny.
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