# Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models

arXiv: https://arxiv.org/abs/2502.17387 · HTML: https://mlsanity.com/paper/2502.17387/

## Key facts

- Cited by 109 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 36 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 29 of 29)

- [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)
- [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)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Bag of Tricks for Efficient Text Classification](https://mlsanity.com/paper/1607.01759/) (2016)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [SemDeDup: Data-efficient learning at web-scale through semantic deduplication](https://mlsanity.com/paper/2303.09540/) (2023)
- [Learning Word Vectors for 157 Languages](https://mlsanity.com/paper/1802.06893/) (2018)
- [Emergent Complexity and Zero-shot Transfer via Unsupervised Environment Design](https://mlsanity.com/paper/2012.02096/) (2020)
- [A Survey on Data Selection for Language Models](https://mlsanity.com/paper/2402.16827/) (2024)
- [Prioritized Level Replay](https://mlsanity.com/paper/2010.03934/) (2020)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!](https://mlsanity.com/paper/2502.07374/) (2025)
- [Towards System 2 Reasoning in LLMs: Learning How to Think With Meta Chain-of-Thought](https://mlsanity.com/paper/2501.04682/) (2025)
- [GLoRe: When, Where, and How to Improve LLM Reasoning via Global and Local Refinements](https://mlsanity.com/paper/2402.10963/) (2024)
- [Scaling Test-Time Compute Without Verification or RL is Suboptimal](https://mlsanity.com/paper/2502.12118/) (2025)
- [NaturalReasoning: Reasoning in the Wild with 2.8M Challenging Questions](https://mlsanity.com/paper/2502.13124/) (2025)
- [Efficient Online Data Mixing For Language Model Pre-Training](https://mlsanity.com/paper/2312.02406/) (2023)
- [T1: Advancing Language Model Reasoning through Reinforcement Learning and Inference Scaling](https://mlsanity.com/paper/2501.11651/) (2025)
- [Surveying the Effects of Quality, Diversity, and Complexity in Synthetic Data From Large Language Models](https://mlsanity.com/paper/2412.02980/) (2024)
- [HARP: A challenging human-annotated math reasoning benchmark](https://mlsanity.com/paper/2412.08819/) (2024)
- [Metastable Dynamics of Chain-of-Thought Reasoning: Provable Benefits of Search, RL and Distillation](https://mlsanity.com/paper/2502.01694/) (2025)
- [Examining False Positives under Inference Scaling for Mathematical Reasoning](https://mlsanity.com/paper/2502.06217/) (2025)

## Built on by (most cited first, 30 of 109)

- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [Beyond Binary Rewards: Training LMs to Reason About Their Uncertainty](https://mlsanity.com/paper/2507.16806/) (2025)
- [Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving](https://mlsanity.com/paper/2507.23726/) (2025)
- [Stabilizing MoE Reinforcement Learning by Aligning Training and Inference Routers](https://mlsanity.com/paper/2510.11370/) (2025)
- [MOPD: Multi-Teacher On-Policy Distillation for Capability Integration in LLM Post-Training](https://mlsanity.com/paper/2606.30406/) (2026)
- [Can Large Reasoning Models Self-Train?](https://mlsanity.com/paper/2505.21444/) (2025)
- [Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles](https://mlsanity.com/paper/2505.19914/) (2025)
- [Advancing Multimodal Reasoning: From Optimized Cold Start to Staged Reinforcement Learning](https://mlsanity.com/paper/2506.04207/) (2025)
- [Reward Reasoning Model](https://mlsanity.com/paper/2505.14674/) (2025)
- [Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experience](https://mlsanity.com/paper/2512.17260/) (2025)
- [How Far are VLMs from Visual Spatial Intelligence? A Benchmark-Driven Perspective](https://mlsanity.com/paper/2509.18905/) (2025)
- [SwS: Self-aware Weakness-driven Problem Synthesis in Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.08989/) (2025)
- [Diversity-Aware Policy Optimization for Large Language Model Reasoning](https://mlsanity.com/paper/2505.23433/) (2025)
- [100 Days After DeepSeek-R1: A Survey on Replication Studies and More Directions for Reasoning Language Models](https://mlsanity.com/paper/2505.00551/) (2025)
- [The Open Proof Corpus: A Large-Scale Study of LLM-Generated Mathematical Proofs](https://mlsanity.com/paper/2506.21621/) (2025)
- [Is It Thinking or Cheating? Detecting Implicit Reward Hacking by Measuring Reasoning Effort](https://mlsanity.com/paper/2510.01367/) (2025)
- [How do LLMs Compute Verbal Confidence](https://mlsanity.com/paper/2603.17839/) (2026)
- [Hybrid Reinforcement: When Reward Is Sparse, It's Better to Be Dense](https://mlsanity.com/paper/2510.07242/) (2025)
- [ReForm: Reflective Autoformalization with Prospective Bounded Sequence Optimization](https://mlsanity.com/paper/2510.24592/) (2025)
- [DeepDistill: Enhancing LLM Reasoning Capabilities via Large-Scale Difficulty-Graded Data Training](https://mlsanity.com/paper/2504.17565/) (2025)
- [Language Models Can Learn from Verbal Feedback Without Scalar Rewards](https://mlsanity.com/paper/2509.22638/) (2025)
- [From Problem-Solving to Teaching Problem-Solving: Aligning LLMs with Pedagogy using Reinforcement Learning](https://mlsanity.com/paper/2505.15607/) (2025)
- [ARES: Multimodal Adaptive Reasoning via Difficulty-Aware Token-Level Entropy Shaping](https://mlsanity.com/paper/2510.08457/) (2025)
- [PaCoRe: Learning to Scale Test-Time Compute with Parallel Coordinated Reasoning](https://mlsanity.com/paper/2601.05593/) (2026)
- [QeRL: Beyond Efficiency -- Quantization-enhanced Reinforcement Learning for LLMs](https://mlsanity.com/paper/2510.11696/) (2025)
- [OpenDataArena: A Fair and Open Arena for Benchmarking Post-Training Dataset Value](https://mlsanity.com/paper/2512.14051/) (2025)
- [BOTS: A Unified Framework for Bayesian Online Task Selection in LLM Reinforcement Finetuning](https://mlsanity.com/paper/2510.26374/) (2025)
- [EvoTrainer: Co-Evolving LLM Policies and Training Harnesses for Autonomous Agentic Reinforcement Learning](https://mlsanity.com/paper/2606.03108/) (2026)

## Abstract (arXiv)

Increasing interest in reasoning models has led math to become a prominent testing ground for algorithmic and methodological improvements. However, existing open math datasets either contain a small collection of high-quality, human-written problems or a large corpus of machine-generated problems of uncertain quality, forcing researchers to choose between quality and quantity. In this work, we present Big-Math, a dataset of over 250,000 high-quality math questions with verifiable answers, purposefully made for reinforcement learning (RL). To create Big-Math, we rigorously filter, clean, and curate openly available datasets, extracting questions that satisfy our three desiderata: (1) problems with uniquely verifiable solutions, (2) problems that are open-ended, (3) and problems with a closed-form solution. To ensure the quality of Big-Math, we manually verify each step in our filtering process. Based on the findings from our filtering process, we introduce 47,000 new questions with verified answers, Big-Math-Reformulated: closed-ended questions (i.e. multiple choice questions) that have been reformulated as open-ended questions through a systematic reformulation algorithm. Compared to the most commonly used existing open-source datasets for math reasoning, GSM8k and MATH, Big-Math is an order of magnitude larger, while our rigorous filtering ensures that we maintain the questions most suitable for RL. We also provide a rigorous analysis of the dataset, finding that Big-Math contains a high degree of diversity across problem domains, and incorporates a wide range of problem difficulties, enabling a wide range of downstream uses for models of varying capabilities and training requirements. By bridging the gap between data quality and quantity, Big-Math establish a robust foundation for advancing reasoning in LLMs.