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.
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:2605. 20531v2 Announce Type: replace-cross Abstract: Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning.
By Slim Barkallah, Luke Bailey, Kaiyue Wen, Mohammed Abouzaid, Tengyu Ma
arXiv:2609.35790v1 Announce Type: cross
Abstract: While neural theorem provers have achieved impressive milestones in formal mathematics, they largely operate on the assumption that faithful Lean 4 f...
By Thomas Hirtz, Farzad Jafarrahmani, Abdelmouksit Sagueni, Xiang Zhou, Wengping Deng, Liang Zhang
arXiv:2606. 12594v1 Announce Type: new Abstract: Modern Lean theorem provers achieve strong performance only with substantial training and inference compute, driven in part by scarce verified proof data and the long reasoning traces of formal proof search, making both supervised fine-tuning (SFT) and sampling expensive.
By Joshua Ong Jun Leang, Zheng Zhao, Mihaela C\u{a}t\u{a}lina Stoian, Qiyuan Xu, Haonan Li, Wenda Li, Shay B. Cohen, Eleonora Giunchiglia
arXiv:2606. 15258v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly capable of mathematical problem solving and can even assist with research-level proofs, yet we still lack a scalable and reproducible way to measure step-level reasoning in long proofs across diverse sources.
By Jierui Zhang, Siyuan Tan, Xinhang Li, Longzhuangzhi Lin, Dailin Li, Chengfeng Gu, Xinping Li, Yaxian Hao, Shengjia Liang, Yuxiang Ren, Wenhao Liu
Magenta is a training‑free pipeline that bridges informal natural‑language mathematical problems and formal Lean 4 verification. Given a problem in plain text, it generates an answer, translates it into a Lean 4 statement, and constructs a machine‑checked proof. The system includes a statement judge to ensure the formalisation matches the original problem and an error‑attribution judge to guide corrections, achieving perfect accuracy on olympiad benchmarks and solving all six IMO 2026 problems when combined with K2‑Horizon‑7B.
By Joshua Ong Jun Leang, Haonan Li, Zheng Zhao, Xinyi Shang, Wenda Li, Zhengzhong Liu, Erix Xing, Shay Cohen, Eleonora Giunchiglia
arXiv:2607. 11307v1 Announce Type: new Abstract: Full-proof autoformalization bridges extensive mathematical proofs in natural language with formally validated reasoning, offering a pathway to elevate the ceiling of verifiable mathematical reasoning.
By Tian-Shuo Liu, Shiyuan Zhang, Zijie Geng, Haoyu Liu, Runjie Xu, Pengyuan Wang, Lei Yuan, Yang Yu
arXiv:2606. 13782v1 Announce Type: new Abstract: Large Language Models (LLMs) have made notable progress in automated theorem proving, yet existing formal benchmarks remain limited in both mathematical coverage and difficulty.
By Lushi Pu, Weiming Zhang, Xinheng Xie, Zixuan Fu, Bingxiang He, Hongya Lyu, Xin Li, Jie Zhou, Yudong Wang
arXiv:2606. 10799v1 Announce Type: new Abstract: Large Language Models (LLMs) struggle to rigorously verify complex mathematical proofs.
By Yifeng Sun
arXiv:2606. 31002v1 Announce Type: new Abstract: Theorem-proving benchmarks evaluate proof search against fixed formal statements, but natural-language-to-Lean formalization must generate the formal statement itself.
By Ke Zhang, Patricio Gallardo Candela, Sudhir Murthy, Yi Xie, Zhi Wang, Maziar Raissi
arXiv:2607. 19407v1 Announce Type: new Abstract: Formal theorem proving has emerged as a frontier challenge for machine learning, yet the ecosystem is fragmented: proofs remain siloed across incompatible systems, limiting both training data for learning-based provers and the portability of verified results.
By Jiayi Wu, Robert Joseph George, Anima Anandkumar