The paper presents a method for training Nemotron 3 Ultra to generate proofs for difficult Olympiad mathematics. By fine‑tuning two specialist checkpoints with supervised learning and reinforcement learning, the authors evaluate how checkpoint selection, verification, and refinement affect performance. The resulting open‑model pipeline, which operates entirely in natural language without external tools, achieved 30 out of 42 points at IMO 2026, meeting the gold‑medal threshold, and the authors release the checkpoints, training data, code, solutions, and a new benchmark of 200 problems.
By Ivan Moshkov, Stephen Ge, George Armstrong, Wei Du, Sadegh Mahdavi, Igor Gitman
AdvancedMathBench is a new benchmark suite that evaluates large language models on advanced mathematical proof generation and verification. It includes ProverBench, with 245 problems from undergraduate to doctoral qualifying‑exam levels, and VerifierBench, which tests models’ ability to judge proof validity using 888 expert‑annotated trajectories. The suite features an automatic verification pipeline trained on expert data, and results show that even state‑of‑the‑art models perform poorly, highlighting a gap between generation and verification skills.
By Lingkai Kong, Zijian Wu, Yuzhe Gu, Haiteng Zhao, Zhouqi Hua, Wenyong Huang, Shuang Sun, Zhicheng Xiong, Xiaotian Zhang, Shuya Zhao, Yan Wang, Disheng Xu, Wenwei Zhang, Kai Chen
arXiv:2608.21356v1 Announce Type: cross
Abstract: For sixty years, machine verification has been a major cost overhead, affordable only for exceptional artifacts. Here we report that generative AI in...
By Jason Hickey
arXiv:2608. 15979v1 Announce Type: new Abstract: Large language models produce outputs presented as discoveries - new proofs, conjectures, or molecules.
By Eric Xie, Wenqian Ye, Aidong Zhang
arXiv:2602.02377v3 Announce Type: replace
Abstract: While large language models (LLMs) have achieved strong performance on mathematical problems with verifiable answers, many advanced problems are pr...
By Haotong Yang, Zitong Wang, Shijia Kang, Siqi Yang, Wenkai Yu, Xu Niu, Yike Sun, Yi Hu, Zhouchen Lin, Muhan Zhang
arXiv:2608. 00004v1 Announce Type: cross Abstract: Grading natural-language mathematical proofs is a recurring cost in evaluating math-reasoning systems, and frontier LLM judges are expensive.
By Benjamin Grayzel