Microsoft Research reports that a 31‑year‑old mathematical problem, the Kannan–Lovász–Simonovits (KLS) conjecture, has been solved. The conjecture, proposed in 1995, questioned the difficulty of computing in high‑dimensional spaces and had been a major obstacle to understanding the efficiency of randomized algorithms. The new research removes this theoretical barrier, advancing knowledge about algorithmic performance in science and computing.
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.
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.
arXiv:2606. 10806v1 Announce Type: new Abstract: Moonshine is an autonomous agent whose central objective is to generate mathematical conjectures.
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Levent Alpöge—who had been working on related problems with Claude and Codex—accused OpenAI of using their unpublished work.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...
The paper reports on autonomous mathematical discovery within the Station, an open‑world multi‑agent environment where diverse AI agents pursue shared research goals without central coordination. Across 12 construction problems and two case studies, the agents produced novel results—including a new infinite family of finite‑field Kakeya sets, 604‑point kissing configurations in dimension 11, improved records for discretized Kakeya needle and sign uncertainty problems, a stronger lower bound for Erdős’s minimum‑overlap problem, and new infinite families for Book Ramsey numbers—alongside theorems and analyses that explain the constructions. All agent dialogues, proofs, and verification code are released to provide a transparent record of the discovery process.
arXiv:2608. 11195v1 Announce Type: new Abstract: AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively.
arXiv:2606. 02484v1 Announce Type: new Abstract: Recent advances in large language models and agentic AI systems have enabled significant progress in mathematical discovery, from solving competition problems to tackling research-level conjectures.
AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively. Towards this, we present an extensive case study of how AI was used to improve bounds on the Grothendieck constant $K_G$, which captures the hardness between combinatorial problems and their continuous relaxations.
arXiv:2608. 11941v1 Announce Type: new Abstract: We construct OEIS Open, a benchmark based on 492 open mathematical conjectures from the OEIS, formalized in Lean by Tsoukalas et al.
arXiv:2605. 22763v2 Announce Type: replace Abstract: Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research.