OpenAI recently released a preprint announcing that the Partition Principle does not imply the Axiom of Choice, a claim that has long been studied in set theory. Mathematician Asaf Karagila, who describes himself as 'famously interested in this problem,' noted that the announcement prompted multiple inquiries from colleagues, highlighting the attention such a result attracts within the mathematical community.
Karagila criticized the preprint's exposition as fundamentally flawed, describing it as 'unclear, muddled, and has a strange structure.' He pointed out terminology that is 'a bit off,' unexpected theorems such as Lemma 7.4 and Lemma 8.1 being stated in odd ways, and problematic references including one of his own papers on the Bristol model used for a basic introduction of symmetric extensions—a reference he says he would not have chosen—as well as at least three unpublished, unrefereed lecture notes. According to him, the paper's quality is so low that 'if this was an academic paper submitted to a journal, it should be issued a desk rejection'.
Beyond technical shortcomings, Karagila argued that releasing such poorly written works creates an unreasonable burden on mathematicians who must divert time from their own research to evaluate them, asking 'When am I supposed to sift through a badly written paper? Why should I bother, when they don't bother to communicate better?' He also warned that when the public, funding bodies, and policy makers—who are not academics or experts—encounter these results, they may mistakenly believe AI can replace human mathematical expertise, which he likened to 'replacing the chef with the kitchen tools'.
Consequently, Karagila stated he will not be sending Sam Altman a bottle of whisky as previously promised on his Problems page, nor does he plan to spend time trying to make sense of the paper. He emphasized that producers have an onus to communicate clearly rather than expecting readers to decipher opaque work.