OpenAI manuscript claims to prove the Hausdorff dimension conjecture for Kakeya sets in four dimensions, advancing Wang Hong's three-dimensional result

On October 7, OpenAI publicly released 722 mathematical manuscripts at once, of which two numbered 074 total 272 pages, claiming to prove the three-dimensional Kakeya maximal function conjecture and the Hausdorff dimension conjecture for Kakeya sets in four dimensions, with the author field listing only OpenAI. The three-dimensional paper strengthens the set version result of Wang Hong and Joshua Zahl to the maximal function version; the four-dimensional paper directly pushes the dimension lower bound, previously stuck around 3 point something, to 4, and cites a lemma from the three-dimensional paper. Neither paper has been formalized in Lean, nor has either undergone peer review; OpenAI stated in the README that some unformalized results may have issues. The four-dimensional paper only proves the Hausdorff dimension version and does not resolve the four-dimensional maximal function conjecture; for five dimensions and above, it only gives lower bounds via projections. The human mathematics association (AHM) led by Terence Tao subsequently issued a statement urging mathematicians to stop cooperating with OpenAI.