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

arXiv: https://arxiv.org/abs/2606.10254 · HTML: https://mlsanity.com/paper/2606.10254/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 13 of 13)

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- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [JudgeBench: A Benchmark for Evaluating LLM-based Judges](https://mlsanity.com/paper/2410.12784/) (2024)
- [Phi-4-reasoning Technical Report](https://mlsanity.com/paper/2504.21318/) (2025)
- [RewardBench 2: Advancing Reward Model Evaluation](https://mlsanity.com/paper/2506.01937/) (2025)
- [KaLM-Embedding: Superior Training Data Brings A Stronger Embedding Model](https://mlsanity.com/paper/2501.01028/) (2025)
- [MASLab: A Unified and Comprehensive Codebase for LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2505.16988/) (2025)

## Abstract (arXiv)

While Large Language Models (LLMs) have achieved near-perfect performance in solving high-school mathematics, their ability to evaluate the diverse reasoning processes of real human students remains under-examined. To bridge this gap, we introduce 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 (~2.96) 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 ~1.17) 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.