saved
The math that OpenAI keeps for itself
Hraness wrote this summary from a saved copy of the source. Quotations are taken word for word from the source.
gist
Daniel Paleka compares OpenAI's 700-plus released math results with arXiv by field and finds statistics, ML theory, optimization and numerical analysis almost absent. He suspects labs withhold the math closest to their own training work, argues math capability will keep outpacing other domains, and urges former mathematicians to pose big research questions now.
ideas
- Missing fields. Those four fields make up 20% of arXiv theorems but under 1% of OpenAI's results, a gap that shrinks but stays statistically significant when only papers solving open problems are counted.
- Not ignorance. OpenAI researchers clearly know optimization open problems, as Sebastien Bubeck's 2025 GPT-5 Pro convex-optimization bound showed, so withholding for advantage is a plausible explanation.
- Compute in, math out. Synthetic data, cheap verification and easy curricula remove the bottlenecks facing other fields, so math ability grows fastest whenever labs spend compute.
- Ask questions now. Proving deep learning theorems is still not worth it, but researchers should think big and prepare the right questions before AI wields mathematics humans cannot follow.
quotes
“Precisely, OpenAI has published very few results on statistics, ML theory, optimization, and numerical analysis.”
“You can create synthetic data. Verification is cheap. Curriculum learning is trivial.”
“Now is the time of research proposals.”