Recently, OpenAI released 722 advanced mathematics manuscripts in one go, among which two major papers directly target a century-old problem in the mathematical world — the Kakeya Conjecture. This breakthrough not only redrew the boundaries of understanding in multi-dimensional mathematics, but also sparked deep discussion in the global academic community about what role AI should play in cutting-edge basic scientific research.
Among the released manuscripts, the two core papers respectively focus on the three-dimensional Kakeya maximal function conjecture and the full-dimensional proof of the general Kakeya set in four dimensions. Notably, the three-dimensional version is stronger than the three-dimensional Kakeya set version previously solved jointly by the young mathematician Hong Wang and Zahl; while the four-dimensional version dramatically advances the previously known dimensional lower bound for the four-dimensional Kakeya set from 3.059 to full dimension 4. It is worth noting that the entire argumentation process of these two manuscripts heavily draws upon and builds on the classical mathematical methods and conclusions previously established by Hong Wang and her collaborators.
Looking back at the research trajectory of the mathematical community, in the course of exploring the Kakeya Conjecture, the young Chinese mathematician Hong Wang once caused a global sensation with her outstanding proof of the three-dimensional Kakeya conjecture, and for a time became a popular candidate for the Fields Medal. Now, OpenAI, with its vast proof manuscripts generated with the assistance of large models, is launching a general offensive toward higher dimensions on top of this solid foundation laid by predecessors.
However, a cautious scientific attitude remains indispensable. At present, these two 175-page four-dimensional proof manuscripts are still in the stage of awaiting independent expert verification. Experts in the field point out that if the argumentation ultimately withstands scrutiny and is proven valid, it will become a historic breakthrough in the field of Kakeya Conjecture research, and will also mark that artificial intelligence has formally acquired the formidable capability to participate in, and even lead, the assault on humanity's most difficult mathematical problems.