- Published on
OpenAI, the Partition Principle, and Mathematics
- Authors
- Name
- DeepHorus
OpenAI has released a preprint claiming that the Partition Principle does not imply the Axiom of Choice, a long-standing open problem in set theory. The announcement drew attention from a set theorist who has worked on the problem for over 15 years. He said multiple people asked him about it, and the number kept increasing.
The set theorist wrote he would not send Sam Altman a bottle of whisky, despite a promise on his Problems page. He is not entirely against AI as a tool, but generally avoids using it for mathematics. He uses LLMs for consolidating information, infographics, and proofreading emails, but says a framework for AI in mathematics is missing.
The preprint itself, he said, was poor: unclear, muddled, and strangely structured. Terminology was "a bit off," and it included theorems he would not expect to be proved, stated in unusual ways. Lemma 7.4 and Lemma 8.1 were not the kind of results one would expect in such a paper.
The references also concerned him. One of his papers on the Bristol model was cited for a basic introduction to symmetric extensions, a choice he disagreed with. At least three unpublished, unrefereed, non-arXiv lecture notes were used, including his own.
He contrasted the OpenAI paper with typical set theory papers, which he can usually skim to understand the strategy. For papers on his expertise, the Axiom of Choice, he can quickly grasp what authors did or intended. With OpenAI's Partition Principle paper, that was impossible.
If submitted to a journal, the preprint should receive a desk rejection for quality, he argued. The onus is on authors to make their work accessible, just as a paper in Swedish would likely be rejected by the Proceedings of the American Mathematical Society. The post had no comments at the time.
