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
Large language models (LLMs) have achieved remarkable performance on high-school and olympiad-style mathematics, yet their capabilities on advanced mathematics remain poorly understood. Existing benchmarks, however, fall short in both scope and evaluation granularity: they provide limited disciplinary coverage and often rely on final-answer correctness or coarse judgments, leaving the validity of the reasoning process inadequately assessed.
arXiv:2606. 17581v1 Announce Type: cross Abstract: We present a dependent-type-based prover designed around the way LLMs (and humans) tend to write mathematics, complementing existing systems such as Lean and Rocq.
By Xiyu Zhai, Xinyi Chen, Yiping Wang, Runlong Zhou, Liao Zhang, Simon S. Du
Large language models produce outputs presented as discoveries - new proofs, conjectures, or molecules. Whether such an output that appears creative is truly original and effective is hard to establis...
The paper reports a specialized training pipeline for large language models to excel in competitive programming, combining problem curation, synthetic reasoning traces, supervised fine‑tuning, and reinforcement learning. Using 22,000 curated problems, the authors train two models—Nemotron‑3‑Nano‑CC (30B) and Nemotron‑3‑Ultra‑CC (550B)—and introduce GenCorrect, a test‑time refinement strategy. On the IOI 2025 benchmark, Nano‑CC scores 468 points with GenCorrect, surpassing the gold‑medal threshold, while Ultra‑CC reaches 502; in IOI 2026, a competition‑specific Ultra‑CC system scores 535.4, exceeding both the gold threshold and the top human score of 498.27, marking the first AI system to outscore the highest‑scoring human contestant on an IOI problem set.
By Aleksander Ficek, Sean Narenthiran, Mehrzad Samadi, Somshubra Majumdar, Boris Ginsburg
The paper introduces LLM-as-an-Improver, a method that uses verification feedback to enhance the candidate set in verifier-based selection. It proposes Verify–Repair–Reselect (VRR), which keeps the initial winner, generates three complementary alternatives (repaired versions of the winner and runner‑up, and a new approach), filters invalid or duplicate candidates, and then reselects the final answer. Experiments on code‑generation and reasoning benchmarks show that VRR outperforms fixed‑pool selection and can recover correct solutions even when the initial pool is entirely wrong.
By Akiyoshi Tomihari, Yuma Ichikawa
arXiv:2602. 16793v2 Announce Type: replace Abstract: In the past year, custom and unreleased math reasoning models reached gold medal performance on the International Mathematical Olympiad (IMO).
By Xingyu Dang, Rohit Agarwal, Rodrigo Porto, Anirudh Goyal, Liam H Fowl, Sanjeev Arora