Core Insights - OpenAI's GPT-5 Pro demonstrated the ability to independently derive new mathematical conclusions, specifically in the field of convex optimization, by providing a more precise threshold and proof for a boundary problem compared to the original paper [1][4]. Group 1: GPT-5 Pro's Achievements - GPT-5 Pro was able to refine the boundary condition from 1/L to 1.5/L using advanced inequality techniques within 17.5 minutes, while human researchers took 25 minutes to verify the proof [21][22]. - The model's approach involved transforming the optimization curve's convexity problem into proving the monotonic decrease of function value differences, utilizing Bregman divergence and co-coercivity inequalities [24][34]. Group 2: Research Context - The original paper discussed whether the optimization curve generated by gradient descent on smooth convex functions is convex, concluding that the convexity depends on the choice of step size [6][9]. - Key findings included specific ranges for step sizes that guarantee convexity and conditions under which non-convexity may occur [9][10]. Group 3: Competitive Dynamics - Following GPT-5 Pro's findings, the original authors updated their paper to establish a precise boundary of 1.75/L, closing previously unexplored intervals [34]. - This update indicates a competitive landscape in mathematical research where AI can contribute significantly, but human researchers can still respond and refine findings rapidly [4][34].

作者丨 机器之心 编辑丨 机器之心 点击下方 卡片 ，关注" 具身智能之心 "公众号 >> 点击进入→ 具身 智能之心 技术交流群 更多干货，欢迎加入国内首个具身智能全栈学习社区 ： 具身智能之心知识星球 (戳我) ， 这里包含所有你想要的。 恭喜获奖者。 RSS（Robotics: Science and Systems，机器人科学与系统会议）是机器人领域顶级学术会议，自 2005 年起每年举办一次，该会议旨在促进机器人领域的科学研究和 技术应用的发展。 今年大会已于 6 月 21 日至 25 日在美国洛杉矶举行。杰出 Demo 论文奖、杰出系统论文奖、杰出学生论文奖、杰出论文奖多个奖项已经公布。 地址：https://roboticsconference.org/program/awards/ 杰出 Demo 论文奖 论文标题：Demonstrating MuJoCo Playground 论文链接：https://www.roboticsproceedings.org/rss21/p020.pdf 论文主页：https://playground.mujoco.org/ 机构：UC 伯克利、Google ...