arXiv:2606. 18119v1 Announce Type: new Abstract: To assess the ability of current AI systems to correctly solve research-level mathematics problems, we tested several AI systems on a set of ten problems in a broad range of mathematical fields; these problems arose naturally in the research process of the contributors.
By Mohammed Abouzaid, Nikhil Srivastava, Rachel Ward, Lauren Williams
The paper announces a new lower bound of 0.8559 for the Steiner ratio, improving on the previous 0.824 bound for the Gilbert‑Pollak Conjecture. It introduces an AI system that uses large language models to generate rule‑constrained geometric lemmas, which are then turned into executable verification functions that certify the bound. The approach relies on only thousands of LLM calls, highlighting the feasibility of LLM‑based methods for advanced mathematical research.
By Yisi Ke, Tianyu Huang, Yankai Shu, Di He, Jingchu Gai, Liwei Wang
arXiv:2606. 10806v1 Announce Type: new Abstract: Moonshine is an autonomous agent whose central objective is to generate mathematical conjectures.
By Xiaoyang Chen, Xiang Jiang
Simon Willison reports that OpenAI used an unreleased model to produce a claimed resolution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. The claim has been met with controversy, as NYU professor Tristan Buckmaster and mathematician Levent Alpöge—who had been working on related problems with Claude and Codex—accused OpenAI of using their unpublished work. OpenAI has denied accessing their data and has offered to wait for Buckmaster’s publication, but will not include Alpöge as a co‑author due to a competitive relationship with his employer.
OpenAI shares new results on long-standing open problems in mathematics and theoretical computer science, including advances in geometry, cryptography, and complexity.
On the Navier–Stokes Millennium Prize Problem introduces an impressive result from OpenAI, who used an unreleased model to produce a resolution to the Navier–Stokes existence and smoothness problem, o...