# MathSmith: Towards Extremely Hard Mathematical Reasoning by Forging Synthetic Problems with a Reinforced Policy

arXiv: https://arxiv.org/abs/2508.05592 · HTML: https://mlsanity.com/paper/2508.05592/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 7 Aug 2025.

## Placed in

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

## Builds on (most cited first, 10 of 10)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Unleashing LLM Reasoning Capability via Scalable Question Synthesis from Scratch](https://mlsanity.com/paper/2410.18693/) (2024)
- [CMR Scaling Law: Predicting Critical Mixture Ratios for Continual Pre-training of Language Models](https://mlsanity.com/paper/2407.17467/) (2024)
- [PromptCoT: Synthesizing Olympiad-level Problems for Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2503.02324/) (2025)

## Built on by (most cited first, 24 of 24)

- [Natural-Language Agent Harnesses](https://mlsanity.com/paper/2603.25723/) (2026)
- [BrokenMath: A Benchmark for Sycophancy in Theorem Proving with LLMs](https://mlsanity.com/paper/2510.04721/) (2025)
- [Agentic Proposing: Enhancing Large Language Model Reasoning via Compositional Skill Synthesis](https://mlsanity.com/paper/2602.03279/) (2026)
- [Read As Human: Compressing Context via Parallelizable Close Reading and Skimming](https://mlsanity.com/paper/2602.01840/) (2026)
- [The Script is All You Need: An Agentic Framework for Long-Horizon Dialogue-to-Cinematic Video Generation](https://mlsanity.com/paper/2601.17737/) (2026)
- [Merge-of-Thought Distillation](https://mlsanity.com/paper/2509.08814/) (2025)
- [ScaleDiff: Scaling Difficult Problems for Advanced Mathematical Reasoning](https://mlsanity.com/paper/2509.21070/) (2025)
- [Grouter: Decoupling Routing from Representation for Accelerated MoE Training](https://mlsanity.com/paper/2603.06626/) (2026)
- [More Data or Better Data? A Critical Analysis of Data Selection and Synthesis for Mathematical Reasoning](https://mlsanity.com/paper/2510.07169/) (2025)
- [EternalMath: A Living Benchmark of Frontier Mathematics that Evolves with Human Discovery](https://mlsanity.com/paper/2601.01400/) (2026)
- [ReSURE: Regularizing Supervision Unreliability for Multi-turn Dialogue Fine-tuning](https://mlsanity.com/paper/2508.19996/) (2025)
- [Discovering New Theorems via LLMs with In-Context Proof Learning in Lean](https://mlsanity.com/paper/2509.14274/) (2025)
- [HACHIMI: Scalable and Controllable Student Persona Generation via Orchestrated Agents](https://mlsanity.com/paper/2603.04855/) (2026)
- [Verifier-Backed Hard Problem Generation for Mathematical Reasoning](https://mlsanity.com/paper/2605.06660/) (2026)
- [From Static to Dynamic: Adaptive Monte Carlo Search for Mathematical Process Supervision](https://mlsanity.com/paper/2509.24351/) (2025)
- [MedRule-KG: A Knowledge-Graph--Steered Scaffold for Mathematical Reasoning with a Lightweight Verifier](https://mlsanity.com/paper/2510.16309/) (2025)
- [Reverse Constitutional AI: A Framework for Controllable Toxic Data Generation via Probability-Clamped RLAIF](https://mlsanity.com/paper/2604.17769/) (2026)
- [Make LLM Learn to Synthesize from Streaming Experiences through Feedback](https://mlsanity.com/paper/2605.29940/) (2026)
- [Not All Pixels Are Equal: Pixel-wise Meta-Learning for Medical Segmentation with Noisy Labels](https://mlsanity.com/paper/2511.18894/) (2025)
- [Auxiliary-Hyperparameter-Free Sampling: Entropy Equilibrium for Text Generation](https://mlsanity.com/paper/2512.00789/) (2025)
- [IRIS: Interpolative R'enyi Iterative Self-play for Large Language Model Fine-Tuning](https://mlsanity.com/paper/2604.20933/) (2026)
- [DenoiseRL: Bootstrapping Reasoning Models to Recover from Noisy Prefixes](https://mlsanity.com/paper/2605.28421/) (2026)
- [AMTFV: Agentic Mathematical Tool-Flow Verification for LLM Self-Correction](https://mlsanity.com/paper/2607.29549/) (2026)
- [ADE: Agentic Data Evolution Framework for Human-Centered Objectives](https://mlsanity.com/paper/2608.23719/) (2026)

## Abstract (arXiv)

Large language models have achieved substantial progress in mathematical reasoning, yet their advancement is limited by the scarcity of high-quality, high-difficulty training data. Existing synthesis methods largely rely on transforming human-written templates, limiting both diversity and scalability. We propose MathSmith, a novel framework for synthesizing challenging mathematical problems to enhance LLM reasoning. Rather than modifying existing problems, MathSmith constructs new ones from scratch by randomly sampling concept-explanation pairs from PlanetMath, ensuring data independence and avoiding contamination. To increase difficulty, we design nine predefined strategies as soft constraints during rationales. We further adopts reinforcement learning to jointly optimize structural validity, reasoning complexity, and answer consistency. The length of the reasoning trace generated under autoregressive prompting is used to reflect cognitive complexity, encouraging the creation of more demanding problems aligned with long-chain-of-thought reasoning. Experiments across five benchmarks, categorized as easy & medium (GSM8K, MATH-500) and hard (AIME2024, AIME2025, OlympiadBench), show that MathSmith consistently outperforms existing baselines under both short and long CoT settings. Additionally, a weakness-focused variant generation module enables targeted improvement on specific concepts. Overall, MathSmith exhibits strong scalability, generalization, and transferability, highlighting the promise of high-difficulty synthetic data in advancing LLM reasoning capabilities. Our code and data are available at https://github.com/Jasaxion/MathSmith.