GPT-5.6 프롬프트 하나로 볼록 최적화 30년 격차 해소

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Become a Redditor and join one of thousands of communities. × 681 682 683 After OpenAI’s CDC proof announcement, GPT-5.6 used a similar prompt to close a 30-year gap in convex optimization, verified in Lean   ( self.math ) submitted  2 days ago   *  by  pkerger TL;DR: In a single 148 min session, with a prompt modeled after the one OpenAI used to prove CDC, GPT 5.6 Sol Pro supplied a proof that closed a complexity gap in convex optimization that has existed since 1996. The result was formally verified in Lean. Links to everything and thoughts on AI capabilities are at the bottom of this post. Disclosure: I am the author of the preprint and Lean repository linked below. I have a PhD in applied mathematics and am a teaching prof in IEOR at UC Berkeley. The result has not yet been peer reviewed. Following the recent announcement that GPT-5.6 Sol Pro had produced a proof of the Cycle Double Cover Conjecture, I adapted the prompting methodology used in that project to a problem in convex optimization. After 148 minutes of uninterrupted work, GPT-5.6 Sol Pro produced the main argument for a lower bound that I had been unable to prove myself (and a lot of my past work has been proving complexity lower bounds in different settings). The problem concerns deterministic zeroth-order convex optimization: Let B_d be the Euclidean unit ball in ℝᵈ, and consider all convex, 1-Lipschitz functions f: B_d → ℝ. An algorithm may query any point x ∈ B_d, and receives only the exact real number f(x), no other information (but the algorithm "knows" that f is convex and Lipschitz). The algorithm is otherwise completely unrestricted, and can use unlimited computation and memory. These function-value-only problems arise naturally when