Developer Uses AI to Extend OpenAI's Math Research, Proves 13 Dimensions Optimal with Lean Verification
Moretheevu · reddit · 2026-10-08
The author set out to see if AI could push OpenAI's recent mathematical research further rather than just explain it, and shipped two open-source projects.
- A new result: OpenAI showed a strange geometric effect works in 10-dimensional shapes; with AI's help the author proved 13 dimensions is optimal within this family of shapes.
- A practical tool, curveball-error-budget: for researchers who shuffle networks to test whether patterns are meaningful, the tool computes how much shuffling is needed to hit a chosen error bound instead of relying on guesswork.
Proofs in both projects are checked with Lean, a formal proof system (the second project's software isn't formally verified end-to-end). The author admits they expected nothing useful and notes formal verification doesn't prove novelty but gives much stronger grounds for trusting the math.
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