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: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:2603.00889v2 Announce Type: replace-cross
Abstract: Large Language Models (LLMs) have exhibited remarkable reasoning capabilities, largely enabled by supervised fine-tuning (SFT)- and reinforce...
By Xinyu Zhu, Yihao Feng, Yanchao Sun, Xianzhi Du, Pingzhi Li, Olli Saarikivi, Yun Zhu, Yu Meng
arXiv:2609.38409v1 Announce Type: new
Abstract: Recent progress in large language model reasoning has been driven by benchmarks and reinforcement learning environments with automatically verifiable r...
By \.Ibrahim Ethem Deveci, Funda Tan \c{C}al{\i}k, Bar{\i}\c{s} Deniz Sa\u{g}lam, Duygu Ataman
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. 10254v1 Announce Type: new Abstract: While Large Language Models (LLMs) have achieved near-perfect performance in \emph{solving} high-school mathematics, their ability to \emph{evaluate} the diverse reasoning processes of real human students remains under-examined.
By Yiteng Mao, Kenan Xu, Yijia Lyu, Wenhao Li, Jianlong Chen, Xiangfeng Wang
arXiv:2605. 03344v2 Announce Type: replace-cross Abstract: Retrieval-augmented generation (RAG) has proven effective for knowledge-intensive tasks, but is widely believed to offer limited benefit for reasoning-intensive problems such as math and code generation.
By Negar Arabzadeh, Wenjie Ma, Sewon Min, Matei Zaharia
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
The paper argues that large language models (LLMs) organize their internal mathematical reasoning by reusable reasoning approaches rather than by the benchmark topics they are tested on. Using a generation‑replay protocol, the authors extract activation‑importance signatures from eight models across five math sources, cluster these signatures, and find that the resulting groups align more closely with reasoning approaches than with topics. The study shows that changing the requested reasoning approach shifts cluster assignments, while paraphrasing the prompt does not, underscoring the primacy of approach over topic in LLM reasoning.
By Sajad Goudarzi, Samaneh Zamanifard, Moloud Nasiri, Hamed Rahimian
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
arXiv:2607. 14582v1 Announce Type: new Abstract: Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition.
By Junjie Zhang, Jiayu Liu, Wenbin Liu, Zhenya Huang, Doudou Wang, Yan Jiang, Leiye Xu, Tao Xiong, Wen Huang, Qi Liu, Guoping Hu, Enhong Chen, Mengping Zhang, Xiangdong Ye