# Beyond Accuracy: Evaluating Strategy Diversity in LLM Mathematical Reasoning

arXiv: https://arxiv.org/abs/2605.09292 · HTML: https://mlsanity.com/paper/2605.09292/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 10 May 2026.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving](https://mlsanity.com/paper/2405.12205/) (2024)
- [Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models](https://mlsanity.com/paper/2503.21380/) (2025)
- [FIMO: A Challenge Formal Dataset for Automated Theorem Proving](https://mlsanity.com/paper/2309.04295/) (2023)
- [Enhancing LLM-Based Feedback: Insights from Intelligent Tutoring Systems and the Learning Sciences](https://mlsanity.com/paper/2405.04645/) (2024)
- [RealMath: A Continuous Benchmark for Evaluating Language Models on Research-Level Mathematics](https://mlsanity.com/paper/2505.12575/) (2025)
- [Reasoning Path Divergence: A New Metric and Curation Strategy to Unlock LLM Diverse Thinking](https://mlsanity.com/paper/2510.26122/) (2025)
- [Riemann-Bench: A Benchmark for Moonshot Mathematics](https://mlsanity.com/paper/2604.06802/) (2026)
- [Plan before Solving: Problem-Aware Strategy Routing for Mathematical Reasoning with LLMs](https://mlsanity.com/paper/2509.24377/) (2025)

## Built on by (most cited first, 1 of 1)

- [Reasoning Consensus: Structural Ensembling of LLM Reasoning via Weighted DAG Aggregation](https://mlsanity.com/paper/2607.27783/) (2026)

## Abstract (arXiv)

Large language models now achieve high final-answer accuracy on mathematical reasoning benchmarks, but accuracy alone does not capture reasoning flexibility. We introduce a strategy-level evaluation framework instantiated on 80 AMC 10/12 and AIME problems with 217 AoPS-derived reference strategy families. Model outputs are annotated for strategy identity, validity, and correctness using dual-AI coding with human adjudication. Across four frontier models, we find a pronounced decoupling between answer accuracy and strategy diversity. Under a single-solution prompt, all models achieve high accuracy (95%-100%), but under a multiple-strategy prompt they recover substantially fewer strategies than the human reference set. Gemini, DeepSeek, GPT, and Claude generate 184, 152, 151, and 110 distinct valid strategies, respectively, with the largest gaps in Geometry and Number Theory. The models collectively produce 50 benchmark-novel valid strategies, indicating both incomplete coverage of human strategies and some capacity for alternative reasoning. A repeated-run robustness check on 20 problems shows diminishing gains in discovered strategies, with the strongest model recovering only 39 of 55 AoPS-reference strategies (71%) after three runs. These findings position strategy diversity as a complementary dimension for evaluating mathematical reasoning beyond answer correctness.