# Exposing the Achilles' Heel: Evaluating LLMs Ability to Handle Mistakes in Mathematical Reasoning

arXiv: https://arxiv.org/abs/2406.10834 · HTML: https://mlsanity.com/paper/2406.10834/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 39 references that are in the map.
- First posted on arXiv 16 Jun 2024.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Is Self-Repair a Silver Bullet for Code Generation?](https://mlsanity.com/paper/2306.09896/) (2023)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)
- [ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning](https://mlsanity.com/paper/2212.07919/) (2022)
- [Time Travel in LLMs: Tracing Data Contamination in Large Language Models](https://mlsanity.com/paper/2308.08493/) (2023)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [MathBench: Evaluating the Theory and Application Proficiency of LLMs with a Hierarchical Mathematics Benchmark](https://mlsanity.com/paper/2405.12209/) (2024)
- [Small Language Models Need Strong Verifiers to Self-Correct Reasoning](https://mlsanity.com/paper/2404.17140/) (2024)
- [Have LLMs Advanced Enough? A Challenging Problem Solving Benchmark For Large Language Models](https://mlsanity.com/paper/2305.15074/) (2023)
- [Alice in Wonderland: Simple Tasks Showing Complete Reasoning Breakdown in State-Of-the-Art Large Language Models](https://mlsanity.com/paper/2406.02061/) (2024)
- [ARB: Advanced Reasoning Benchmark for Large Language Models](https://mlsanity.com/paper/2307.13692/) (2023)
- [Large Language Models in Education: Vision and Opportunities](https://mlsanity.com/paper/2311.13160/) (2023)
- [Can LLMs Solve longer Math Word Problems Better?](https://mlsanity.com/paper/2405.14804/) (2024)
- [What Makes Math Word Problems Challenging for LLMs?](https://mlsanity.com/paper/2403.11369/) (2024)

## Built on by (most cited first, 13 of 13)

- [Inner Thinking Transformer: Leveraging Dynamic Depth Scaling to Foster Adaptive Internal Thinking](https://mlsanity.com/paper/2502.13842/) (2025)
- [FINEREASON: Evaluating and Improving LLMs' Deliberate Reasoning through Reflective Puzzle Solving](https://mlsanity.com/paper/2502.20238/) (2025)
- [PromptHive: Bringing Subject Matter Experts Back to the Forefront with Collaborative Prompt Engineering for Educational Content Creation](https://mlsanity.com/paper/2410.16547/) (2024)
- [Reliable Proof Generation with LLMs via Analogical Retrieval and Symbolic Verification: A Case Study in Euclidean Geometry](https://mlsanity.com/paper/2505.14479/) (2025)
- [The Achilles' Heel of LLMs: How Altering a Handful of Neurons Can Cripple Language Abilities](https://mlsanity.com/paper/2510.10238/) (2025)
- [Tracking the Limits of Knowledge Propagation: How LLMs Fail at Multi-Step Reasoning with Conflicting Knowledge](https://mlsanity.com/paper/2601.15495/) (2026)
- [ArenaBencher: Automatic Benchmark Evolution via Multi-Model Competitive Evaluation](https://mlsanity.com/paper/2510.08569/) (2025)
- [A Mechanistic Study of Transformers Training Dynamics](https://mlsanity.com/paper/2410.24050/) (2024)
- [DeduCE: Deductive Consistency as a Framework to Evaluate LLM Reasoning](https://mlsanity.com/paper/2504.07080/) (2025)
- [Automatic Replication of LLM Mistakes in Medical Conversations](https://mlsanity.com/paper/2512.20983/) (2025)
- [Let Experts Feel Uncertainty: A Multi-Expert Label Distribution Approach to Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2602.04678/) (2026)
- [When Tokenization is Secretly Output Supervision](https://mlsanity.com/paper/2609.01386/) (2026)
- [Does CoT-Pass@k Really Check the CoT? A Multilingual Mathematical Audit](https://mlsanity.com/paper/2609.32622/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have been applied to Math Word Problems (MWPs) with transformative impacts, revolutionizing how these complex problems are approached and solved in various domains including educational settings. However, the evaluation of these models often prioritizes final accuracy, overlooking the crucial aspect of reasoning capabilities. This work addresses this gap by focusing on the ability of LLMs to detect and correct reasoning mistakes. We introduce a novel dataset MWP-MISTAKE, incorporating MWPs with both correct and incorrect reasoning steps generated through rule-based methods and smaller language models. Our comprehensive benchmarking reveals significant insights into the strengths and weaknesses of state-of-the-art models, such as GPT-4o, GPT-4, GPT-3.5Turbo, and others. We highlight GPT-o's superior performance in mistake detection and rectification and the persistent challenges faced by smaller models. Additionally, we identify issues related to data contamination and memorization, impacting the reliability of LLMs in real-world applications. Our findings emphasize the importance of rigorous evaluation of reasoning processes and propose future directions to enhance the generalization and robustness of LLMs in mathematical problem-solving.