RealMath-Eval: Why SOTA Judges Struggle with Real Human Reasoning

Computer Science > Artificial Intelligence [Submitted on 8 Jun 2026] RealMath-Eval: Why SOTA Judges Struggle with Real Human Reasoning Yiteng Mao, Kenan Xu, Yijia Lyu, Wenhao Li, Jianlong Chen, Xiangfeng Wang 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. To bridge this gap, we introduce \textbf{RealMath-Eval}, a rigorously annotated benchmark of 224 real-world exam responses from high schools. Our initial evaluation reveals that even state-of-the-art LLM judges struggle significantly on this task, exhibiting a high Mean Squared Error (\sim2.96) against expert human grading. To probe a plausible explanation, we contrast this performance with a control setting where the same judges evaluate synthetic LLM-generated solutions. We identify a stark ``Evaluation Gap'': judges are considerably more accurate and consistent on synthetic text (MSE \sim1.17) but struggle to generalize to authentic student reasoning. Through semantic embedding analysis, we find that synthetic errors suffer from a ``structural collapse'' into predictable, low-dimensional linear subspaces, whereas human errors form a more diverse error space. Furthermore, generative probability probes suggest that human reasoning involves significantly higher information-theoretic surprisal, indicating that student reasoning transitions are more out-of-distribution for current models. Finally, we find that surface-level style transfer fails to close this gap. Our findings suggest that current LLM evaluation pipelines relying heavily on synthetic data may not adequately capture the diversity of authentic student mathematical reasoning. Comments: Code available at this https URL , Data available at this https URL Subjects: Artificial Intelligence (cs.AI); Computation and Language (cs.CL) Cite as: arXiv:2606.10254 [cs.AI]   (or arXiv:2606.10254v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2606.10254 Focus to learn more Submission history From: Yiteng Mao [view email] [v1] Mon, 8 Jun 2026 23:40:34 UTC (12,095 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-06 Change to browse by: cs cs.CL References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)