GPT-5.6 Sol proves Omega(d^2) lower bound for convex optimization, closing 30-year complexity gap

Short summary

GPT-5.6 Sol reportedly proved an Omega(d^2) lower bound for convex optimization over bounded Lipschitz functions, closing a 30-year gap in complexity theory. The proof took ~148 minutes of sustained reasoning and matches the upper bound of a three-decade-old algorithm, settling the complexity of this problem class. This follows GPT-5.6 Sol Ultra's proof of the Cycle Double Cover Conjecture eight days earlier, suggesting a pattern of AI models tackling long-standing open mathematical problems.

• •GPT-5.6 Sol produced a proof of the Omega(d^2) lower bound for convex Lipschitz optimization, closing a 30-year complexity gap
• •The proof took ~148 minutes of sustained reasoning, not pattern matching, and was guided by a researcher's prompt framework built over a year of failed attempts
• •This is the second major math result from GPT-5.6 in a month, following the Cycle Double Cover Conjecture proof, signaling industrialized mathematical discovery

Generated with AI, which can make mistakes.