# Benchmarking LLMs' Mathematical Reasoning with Unseen Random Variables Questions

arXiv: https://arxiv.org/abs/2501.11790 · HTML: https://mlsanity.com/paper/2501.11790/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 31 of its 73 references that are in the map.
- First posted on arXiv 20 Jan 2025.

## Placed in

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

## Builds on (most cited first, 30 of 31)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Understanding the planning of LLM agents: A survey](https://mlsanity.com/paper/2402.02716/) (2024)
- [Benchmark Data Contamination of Large Language Models: A Survey](https://mlsanity.com/paper/2406.04244/) (2024)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [Evaluation of OpenAI o1: Opportunities and Challenges of AGI](https://mlsanity.com/paper/2409.18486/) (2024)
- [OlympicArena: Benchmarking Multi-discipline Cognitive Reasoning for Superintelligent AI](https://mlsanity.com/paper/2406.12753/) (2024)
- [Leakage and the Reproducibility Crisis in ML-based Science](https://mlsanity.com/paper/2207.07048/) (2022)
- [Training on the Benchmark Is Not All You Need](https://mlsanity.com/paper/2409.01790/) (2024)
- [BeHonest: Benchmarking Honesty in Large Language Models](https://mlsanity.com/paper/2406.13261/) (2024)

## Built on by (most cited first, 7 of 7)

- [When to use Graphs in RAG: A Comprehensive Analysis for Graph Retrieval-Augmented Generation](https://mlsanity.com/paper/2506.05690/) (2025)
- [LLMs are Overconfident: Evaluating Confidence Interval Calibration with FermiEval](https://mlsanity.com/paper/2510.26995/) (2025)
- [On Path to Multimodal Historical Reasoning: HistBench and HistAgent](https://mlsanity.com/paper/2505.20246/) (2025)
- [MathReal: We Keep It Real! A Real Scene Benchmark for Evaluating Math Reasoning in Multimodal Large Language Models](https://mlsanity.com/paper/2508.06009/) (2025)
- [Scalable and Reliable Evaluation of AI Knowledge Retrieval Systems: RIKER and the Coherent Simulated Universe](https://mlsanity.com/paper/2601.08847/) (2025)
- [VeRA: Renewing Reasoning Benchmarks with Executable Specifications](https://mlsanity.com/paper/2602.13217/) (2026)
- [Credit Cards, Confusion, Computation, and Consequences: What Can We Uncover About Language Model Reasoning?](https://mlsanity.com/paper/2607.26952/) (2026)

## Abstract (arXiv)

Recent studies have raised significant concerns regarding the reliability of current mathematics benchmarks, highlighting issues such as simplistic design and potential data contamination. Consequently, developing a reliable benchmark that effectively evaluates large language models' (LLMs) genuine capabilities in mathematical reasoning remains a critical challenge. To address these concerns, we propose RV-Bench, a novel evaluation methodology for Benchmarking LLMs with Random Variables in mathematical reasoning. Specifically, we build question-generating functions to produce random variable questions (RVQs), whose background content mirrors original benchmark problems, but with randomized variable combinations, rendering them "unseen" to LLMs. Models must completely understand the inherent question pattern to correctly answer RVQs with diverse variable combinations. Thus, an LLM's genuine reasoning capability is reflected through its accuracy and robustness on RV-Bench. We conducted extensive experiments on over 30 representative LLMs across more than 1,000 RVQs. Our findings propose that LLMs exhibit a proficiency imbalance between encountered and ``unseen'' data distributions. Furthermore, RV-Bench reveals that proficiency generalization across similar mathematical reasoning tasks is limited, but we verified it can still be effectively elicited through test-time scaling.