FaithSieve is a Lean‑assisted framework that fine‑grains natural‑language mathematical proofs into local reasoning units, extracts typed proof obligations, and verifies them with formal evidence gated by semantic alignment. It introduces two expert‑verified datasets—ProofLoc‑Olympiad and ProofLoc‑University—to benchmark first‑error localization. On these benchmarks, FaithSieve outperforms direct‑judging baselines, achieving 81.43% and 84.5% exact first‑error accuracy respectively.
By Ziyu Wang, Qiming Dai, Yishan Wu, Zaiwen Wen
arXiv:2608. 14221v1 Announce Type: new Abstract: Autoformalization is commonly framed as translating natural-language mathematical statements into machine-verifiable formal languages such as Lean 4.
By Lushi Pu, Weiming Zhang, Xinheng Xie, Zixuan Fu, Bingxiang He, Hengyu Zhao, Hongya Lyu, Xin Li, Jie Zhou, Yudong Wang
arXiv:2605. 19723v2 Announce Type: replace-cross Abstract: Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems.
By Husnain Amjad, Raja Khurram Shahzad, Aamir Shahzad, Mehwish Fatima
arXiv:2606. 31134v1 Announce Type: new Abstract: While Large Language Models (LLMs) have demonstrated exceptional capabilities in mathematical reasoning, they frequently produce subtle errors that evade human detection.
By Arshia Soltani Moakhar, Iman Gholami, Max Springer, Mahdi JafariRaviz, MohammadTaghi Hajiaghayi
arXiv:2609.15145v1 Announce Type: new
Abstract: The reasoning ability of large language models (LLMs) is a critical factor for practical LLM-based applications. To investigate the current reasoning c...
By Runa Yoshida, Kosuke Nishida, Kyosuke Nishida
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
MathAdv is a diagnostic benchmark for formal theorem proving that covers 13 undergraduate- and graduate-level mathematics domains. It includes Lean 4 proofs and up to three auxiliary tasks—multiple-choice questions, fill-in-the-blank problems, and expert-crafted transformations—to probe knowledge, informal reasoning, and robustness to problem presentation. Evaluation of current theorem provers shows formalization is a major bottleneck, performance varies by domain, natural-language guidance can help or hinder models, and equivalent reformulations reveal significant robustness gaps.
By Jiaxin Yuan, Connor Martinez Lockhart, Xiaoyu Liu, Jiaqi Wang, Chenghao Deng, Xiayimei Han, Vlasios Mastrantonis, Dmitrii Gudin, Shaopeng Zhu, Abdirisak Abdullahi Mohamed, Bilal Hamdi Aytekin, Jiewen Lang, Zezheng Song, Furong Huang
The paper introduces GAP, a methodology that automatically generates mathematically equivalent variants of existing math problems using surface renames and kernel rewrites. Applying GAP to all 1,051 William Lowell Putnam Competition problems creates PutnamGAP, a 6,306-item dataset with 5,255 unseen variants. Evaluation of 18 commercial and open-source LLMs shows accuracy drops across all models, especially under kernel rewrites, indicating a persistent weakness in transferring proof plans to new mathematical settings.
By Yuren Hao, Xiang Wan, ChengXiang Zhai
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:2608. 10916v1 Announce Type: cross Abstract: Autoformalisation (AF) systems map natural language reasoning steps into formal statements in a proof assistant such as Lean.
By Rob Cornish, Iacopo Ghinassi, Po-Hung Yeh, Shuqi Liu, Qiyuan Xu, Haoxuan Yin, Dominik Wagner, Wenda Li, Yee Whye Teh, Luke Ong
NL2AGBench is a benchmark that evaluates how well large language models can translate English geometry problems into the formal language required by AlphaGeometry’s theorem‑proving engine. The study tests ten state‑of‑the‑art LLMs, comparing executable translation accuracy, syntactic correctness, and error types, and finds a large gap between closed‑source and open‑source models. The authors also propose an error taxonomy and test mitigation strategies such as few‑shot prompting, fine‑tuning, and human‑guided hinting, which improve performance across model families.
By Samuel Xiao, Judy Song, Rory Hu, Ziliang Zong
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