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Sébastien Bubeck has used one question to test AI models for two years: how long can a gradient flow path be on a convex function inside the unit ball in n dimensions? Trivial to state, brutal to solve — the best published bound, n^O(n), dates to Manselli and Pucci, 1991. Every model failed. GPT-5.6, OpenAI’s frontier reasoning model, thought for 168 minutes, beat that state of the art, and showed the Omega(d²) lower bound for this function class matches a 30-year-old algorithm’s complexity. Gap closed. Bubeck checked the proof; part is Lean-verified.

Why this one counts

The trend line is the story. In August 2025, GPT-5-pro needed 17 minutes to nudge one bound in one paper. Eleven months later, its successor retires a 30-year open problem. Add the Erdős results and cycle double cover, and frontier models doing real, verifiable math is a pattern now, not a stunt. HN: 226 points, 115 comments.

The honest caveat

Bubeck fed it a 10-page prompt distilled from a year of his own research. The model is the engine; a world-class mathematician still steers. That’s AI-for-science today — and it’s still the hardest evidence the narrative has.

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