arXiv AI By Yuren Hao, Xiang Wan, ChengXiang Zhai

An Investigation of Robustness of LLMs in Mathematical Reasoning: Benchmarking with Mathematically-Equivalent Transformation of Advanced Mathematical Problems

Read the original on arXiv AI →

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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

arXiv Computation and Language
Aug 27

MathAdv: What Theorem Provers Know, Reason, Formalize, and Generalize

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
arXiv AI
Jul 24

Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving

arXiv:2607. 20520v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly evaluated on mathematical problem solving, yet prior work often treats representationally equivalent formulations as interchangeable and conflates reasoning errors with interface failures.

By Sagnik Nath, Edith Aurora Graf, Liang Zhang, Diego Zapata-Rivera
arXiv AI
Sep 25

LiveMathematicianBench: A Live Benchmark for Research-Level Mathematical Reasoning with Proof Sketches

LiveMathematicianBench is a dynamic multiple‑choice benchmark for research‑level mathematical reasoning, built from recent arXiv papers published after model training cutoffs. It introduces a thirteen‑category logical taxonomy of theorem types and uses a proof‑sketch‑guided distractor pipeline to create plausible but invalid answer choices, enhancing sensitivity to genuine reasoning. Evaluation shows current large language models perform poorly, with the best model scoring 43.5% overall and only 17.6% under substitution‑resistant conditions, indicating the benchmark’s difficulty and realism.

By Linyang He, Qiyao Yu, Hanze Dong, Baohao Liao, Xinxing Xu, Micah Goldblum, Jiang Bian, Nima Mesgarani
arXiv Machine Learning
Oct 3

The Missing Primitive: Diagnosing and Repairing Mathematical Reasoning in Large Language Models

arXiv:2610. 02191v1 Announce Type: new Abstract: While Large Language Models (LLMs) have demonstrated striking capabilities on frontier mathematical problems, it remains unclear whether they possess the structural mathematical understanding underlying their solutions.

By Shuo Xing, Zilin Dai, Chengyuan Qian, Fangzhou Lin, Wenjing Chen, Ping He, Pan Lu, Alvaro Velasquez, Mohit Bansal, Zhengzhong Tu
arXiv AI
Jun 24

Benchmarking LLMs' Mathematical Reasoning with Unseen Random Variables Questions

arXiv:2501. 11790v5 Announce Type: replace-cross Abstract: Recent studies have raised significant concerns regarding the reliability of current mathematics benchmarks, highlighting issues such as simplistic design and potential data contamination.

By Zijin Hong, Hao Wu, Su Dong, Junnan Dong, Yilin Xiao, Yujing Zhang, Zhu Wang, Feiran Huang, Linyi Li, Hongxia Yang, Xiao Huang