Asaf Karagila responds to OpenAI's claim that the Partition Principle does not imply the Axiom of Choice by rejecting the quality and presentation of their preprint. He reports skimming the paper (but not the massive Lean code) and finds the exposition muddled, terminology awkward, and several lemmas oddly stated or out of place. Citations rely on unpublished lecture notes - including Karagila’s own - instead of established references, and the writeup reads like hundreds of incomprehensible "solutions" dumped on readers. Were this submitted to a journal, Karagila argues, it would deserve a desk rejection for failing to communicate clearly; the mathematical community cannot be expected to sift through poorly organized claims.
Karagila frames the episode as a broader problem about how AI outputs enter mathematics: he accepts AI as a tool but insists on standards, peer input, and transparency (for example, declaring AI use or providing chat logs to reviewers). He warns that flashy press releases create media and policy misperceptions, risking funding and public belief that human mathematicians can be replaced. Rather than praise, companies must consult domain experts and improve presentation; until then Karagila refuses to reward or invest time in OpenAI’s claimed solution.
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