hyperfinitism

The statement of Lemma A.1 (“For every finite simple graph, a minimum ordinary drawing can be chosen polygonal, straight near every vertex and crossing, and without crossings between edges having a common endpoint.”) is already hard to read, but I had to give up on the proof. For example, I don't know what the author means by “On each edge choose pairwise disjoint relative parameter neighborhoods, with disjoint closures, of its marked parameters, one-sided at its endpoints.” I also find “Suppose two edges vu, vw cross” problematic, since there is no explanation of what u, v, and w represent. There are numerous other flaws and the list of issues goes on... Am I the only one disappointed by the quality of the mathematical exposition in some of their preprints?

Obviously, some types of mathematical problems are particularly well suited to AI. For example, I regularly use AI to search for counterexamples to various conjectures, and my students and I know how useful it is for this purpose (needless to say, I always check its answers very carefully). So I'm not surprised that many of OpenAI's preprints report counterexamples likewise, and I imagine these were found through a large number of attempts. OpenAI's announcement has sparked considerable debate, but in my opinion, determining whether a proposition is true or false and understanding why are two different things. Crafting beautiful and rigorous exposition is yet another.

OpenAI has released many math preprints, attracting considerable attention. As a mathematician who regularly uses various AI models including OpenAI's, I had a look at some of their preprints in my own field (combinatorics, like graph theory). My impression is that the quality of the written exposition varies considerably. Even before assessing their mathematical correctness, some are so poorly written that I cannot even tell what is being claimed. (My comments concern only the written preprints, not the Lean formalizations.) For example, consider "165. Exact crossing numbers of complete and complete bipartite graphs." I find Lemma A.1 and its proof in p.11–p.12 of the following preprint ("The crossing number of complete graphs") particularly hard to follow. In my view, the exposition is not yet at a level suitable for peer review. If I were reviewing the paper, I would recommend major revisions to this part, at least. github.com/openai/math/blob/… Interestingly, the corresponding lemma in the other preprint on complete bipartite graphs appears more readable, although I have not examined that paper in detail. github.com/openai/math/blob/… How readable have you found OpenAI's preprints in your own area of mathematics? Have you noticed similar issues?