真·博士水平，GPT-5首次给出第四矩定理显式收敛率，数学教授只点拨了一下

Core Insights - GPT-5 has successfully extended the qualitative fourth moment theorem to a quantitative form with explicit convergence rates, marking a significant advancement in mathematical research [1][6][8]. Group 1: Research Achievements - OpenAI's GPT-5 Pro improved the known boundary value in convex optimization from 1/L to 1.5/L within minutes [6]. - The research led by three mathematics professors aimed to test GPT-5's ability to generalize the qualitative fourth moment theorem to include explicit convergence rates, covering both Gaussian and Poisson cases [8][14]. Group 2: Interaction with Researchers - During the initial interaction, GPT-5 provided a correct overall conclusion but made errors in reasoning that could invalidate the proof, which were later corrected through further questioning by researchers [10][12]. - GPT-5 was able to format the results into a research paper, including an introduction, main theorem statements, detailed proofs, and references, demonstrating its capability in academic writing [12]. Group 3: Further Exploration - Researchers sought to extend the findings to the Poisson case, prompting GPT-5 to recognize structural differences between Gaussian and Poisson scenarios [14][15]. - After initial missteps, GPT-5 was guided to consider non-negativity in the Poisson case, leading to a more accurate reformulation of the theorem [16][17]. Group 4: Publication Challenges - The authors initially intended to list GPT-5 as a co-author but were informed by arXiv that AI cannot be credited as an author, resulting in a submission without GPT-5's name [18].