# ReliableMath: Benchmark of Reliable Mathematical Reasoning on Large Language Models

arXiv: https://arxiv.org/abs/2507.03133 · HTML: https://mlsanity.com/paper/2507.03133/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 43 of its 76 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Placed in

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

## Builds on (most cited first, 30 of 43)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Trustworthy LLMs: a Survey and Guideline for Evaluating Large Language Models' Alignment](https://mlsanity.com/paper/2308.05374/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [Do Large Language Models Know What They Don't Know?](https://mlsanity.com/paper/2305.18153/) (2023)
- [GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers](https://mlsanity.com/paper/2402.19255/) (2024)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)

## Built on by (most cited first, 8 of 8)

- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [BrokenMath: A Benchmark for Sycophancy in Theorem Proving with LLMs](https://mlsanity.com/paper/2510.04721/) (2025)
- [Stop Before You Fail: Operational Capability Boundaries for Mitigating Unproductive Reasoning in Large Reasoning Models](https://mlsanity.com/paper/2509.24711/) (2025)
- [Not All Proofs Are Equal: Evaluating LLM Proof Quality Beyond Correctness](https://mlsanity.com/paper/2605.10379/) (2026)
- [RIDE: Difficulty Evolving Perturbation with Item Response Theory for Mathematical Reasoning](https://mlsanity.com/paper/2511.04120/) (2025)
- [Feedback Indices to Evaluate LLM Responses to Rebuttals for Multiple Choice Type Questions](https://mlsanity.com/paper/2601.03285/) (2026)
- [TIPS: Topological Ill-Posedness Probing and Steering in Large Language Models](https://mlsanity.com/paper/2606.23590/) (2026)
- [FlowEdit: Information-Theoretic Control of LLM Reasoning Flows for Ill-posed Problems Involving Conflicts](https://mlsanity.com/paper/2607.20500/) (2026)

## Abstract (arXiv)

Although demonstrating remarkable performance on reasoning tasks, Large Language Models (LLMs) still tend to fabricate unreliable responses when confronted with problems that are unsolvable or beyond their capability, severely undermining the reliability. Prior studies of LLM reliability have primarily focused on knowledge tasks to identify unanswerable questions, while mathematical reasoning tasks have remained unexplored due to the dearth of unsolvable math problems. To systematically investigate LLM reliability in mathematical reasoning tasks, we formulate the reliability evaluation for both solvable and unsolvable problems. We then develop a ReliableMath dataset which incorporates open-source solvable problems and high-quality unsolvable problems synthesized by our proposed construction workflow with human evaluations. Experiments are conducted on various LLMs with several key findings uncovered. LLMs fail to directly identify unsolvable problems and always generate fabricated responses. When instructing LLMs to indicate unsolvability using a reliable prompt, the reliability of larger-sized LLMs remains on solvable problems, but notably improves on unsolvable problems yet still falls short of solvable problems. However, small LLMs rarely show any progress despite employing reliable prompts. Therefore, we further propose an alignment strategy to enhance small LLMs' reliability, which can significantly improve LLM reliability performances on both in-domain and out-of-domain tasks.