# Do LLMs Exhibit Coherent Knowledge Structures in Mathematical Reasoning? A Perspective from Knowledge Space Theory

arXiv: https://arxiv.org/abs/2609.05245 · HTML: https://mlsanity.com/paper/2609.05245/

## 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 12 of its 35 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Placed in

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

## Builds on (most cited first, 12 of 12)

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- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Knowledge Fusion of Large Language Models](https://mlsanity.com/paper/2401.10491/) (2024)
- [AI-Assisted Generation of Difficult Math Questions](https://mlsanity.com/paper/2407.21009/) (2024)
- [What Defines Good Reasoning in LLMs? Dissecting Reasoning Steps with Multi-Aspect Evaluation](https://mlsanity.com/paper/2510.20603/) (2025)
- [Automate Knowledge Concept Tagging on Math Questions with LLMs](https://mlsanity.com/paper/2403.17281/) (2024)
- [Behavior-Aware Item Modeling via Dynamic Procedural Solution Representations for Knowledge Tracing](https://mlsanity.com/paper/2604.08260/) (2026)

## Abstract (arXiv)

Human knowledge is inherently structured and interdependent: mastery of a concept requires prior mastery of its prerequisites, a principle formalized by Knowledge Space Theory (KST). While LLMs achieve strong performance on complex reasoning tasks, it remains unclear whether they exhibit coherent, human-like knowledge structure. We introduce a KST-grounded framework for evaluating LLM knowledge structure in mathematical reasoning, using it as a normative framework to analyze whether LLM behavior adheres to principled knowledge dependencies. Evaluating eight open- and closed-source LLMs against real human learners, we find that (1) LLMs do not adhere to human knowledge structure -- they frequently violate knowledge dependencies and fail to leverage related knowledge provided in context to improve performance on dependent questions; (2) LLMs do not share a consistent knowledge structure among themselves, as reflected by low overlap in their knowledge distributions. Furthermore, these structural deficiencies remain largely invisible to accuracy-based and LLM-as-judge evaluations. Together, our results provide behavioral evidence that current LLMs knowledge does not follow a human-like structure.