# PromptCoT: Synthesizing Olympiad-level Problems for Mathematical Reasoning in Large Language Models

arXiv: https://arxiv.org/abs/2503.02324 · HTML: https://mlsanity.com/paper/2503.02324/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 40 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Scaling Synthetic Data Creation with 1,000,000,000 Personas](https://mlsanity.com/paper/2406.20094/) (2024)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (2024)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)
- [GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers](https://mlsanity.com/paper/2402.19255/) (2024)
- [OpenWebMath: An Open Dataset of High-Quality Mathematical Web Text](https://mlsanity.com/paper/2310.06786/) (2023)
- [MAmmoTH2: Scaling Instructions from the Web](https://mlsanity.com/paper/2405.03548/) (2024)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)
- [Common 7B Language Models Already Possess Strong Math Capabilities](https://mlsanity.com/paper/2403.04706/) (2024)
- [Can Large Language Models Reason and Plan?](https://mlsanity.com/paper/2403.04121/) (2024)
- [Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning](https://mlsanity.com/paper/2403.02333/) (2024)
- [From the Least to the Most: Building a Plug-and-Play Visual Reasoner via Data Synthesis](https://mlsanity.com/paper/2406.19934/) (2024)

## Built on by (most cited first, 22 of 22)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Reinforcing Spatial Reasoning in Vision-Language Models with Interwoven Thinking and Visual Drawing](https://mlsanity.com/paper/2506.09965/) (2025)
- [Beyond Pass@1: Self-Play with Variational Problem Synthesis Sustains RLVR](https://mlsanity.com/paper/2508.14029/) (2025)
- [SwS: Self-aware Weakness-driven Problem Synthesis in Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.08989/) (2025)
- [Leanabell-Prover: Posttraining Scaling in Formal Reasoning](https://mlsanity.com/paper/2504.06122/) (2025)
- [BrokenMath: A Benchmark for Sycophancy in Theorem Proving with LLMs](https://mlsanity.com/paper/2510.04721/) (2025)
- [MathSmith: Towards Extremely Hard Mathematical Reasoning by Forging Synthetic Problems with a Reinforced Policy](https://mlsanity.com/paper/2508.05592/) (2025)
- [A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Law](https://mlsanity.com/paper/2505.02665/) (2025)
- [Sparks of Tabular Reasoning via Text2SQL Reinforcement Learning](https://mlsanity.com/paper/2505.00016/) (2025)
- [PromptCoT 2.0: Scaling Prompt Synthesis for Large Language Model Reasoning](https://mlsanity.com/paper/2509.19894/) (2025)
- [EvolProver: Advancing Automated Theorem Proving by Evolving Formalized Problems via Symmetry and Difficulty](https://mlsanity.com/paper/2510.00732/) (2025)
- [ScaleDiff: Scaling Difficult Problems for Advanced Mathematical Reasoning](https://mlsanity.com/paper/2509.21070/) (2025)
- [Visual Latents Know More Than They Say: Unsilencing Latent Reasoning in MLLMs](https://mlsanity.com/paper/2605.02735/) (2026)
- [How Well Do Large Reasoning Models Translate? A Comprehensive Evaluation for Multi-Domain Machine Translation](https://mlsanity.com/paper/2505.19987/) (2025)
- [QueST: Incentivizing LLMs to Generate Difficult Problems](https://mlsanity.com/paper/2510.17715/) (2025)
- [Scaling Reasoning without Attention](https://mlsanity.com/paper/2505.22425/) (2025)
- [DynaAct: Large Language Model Reasoning with Dynamic Action Spaces](https://mlsanity.com/paper/2511.08043/) (2025)
- [Syn-GRPO: Self-Evolving Data Synthesis for MLLM Perception Reasoning](https://mlsanity.com/paper/2511.19343/) (2025)
- [InfoSynth: Information-Guided Benchmark Synthesis for LLMs](https://mlsanity.com/paper/2601.00575/) (2026)
- [D'ej`aQ: Open-Ended Evolution of Diverse, Learnable and Verifiable Problems](https://mlsanity.com/paper/2601.01931/) (2026)
- [SAGE: Semantic Anchor-Guided Evolution for Grounded Medical QA Data Synthesis](https://mlsanity.com/paper/2610.08093/) (2026)
- [MagicBeanStalk: Escaping the RLVR Zero Advantage Trap with Recursive Data Synthesis](https://mlsanity.com/paper/2610.12659/) (2026)

## Abstract (arXiv)

The ability of large language models to solve complex mathematical problems has progressed significantly, particularly for tasks requiring advanced reasoning. However, the scarcity of sufficiently challenging problems, particularly at the Olympiad level, hinders further advancements. In this work, we introduce PromptCoT, a novel approach for automatically generating high-quality Olympiad-level math problems. The proposed method synthesizes complex problems based on mathematical concepts and the rationale behind problem construction, emulating the thought processes of experienced problem designers. We provide a theoretical analysis demonstrating that an optimal rationale should maximize both the likelihood of rationale generation given the associated concepts and the likelihood of problem generation conditioned on both the rationale and the concepts. Our method is evaluated on standard benchmarks including GSM8K, MATH-500, and AIME2024, where it consistently outperforms existing problem generation methods. Furthermore, we demonstrate that PromptCoT exhibits superior data scalability, consistently maintaining high performance as the dataset size increases, outperforming the baselines. The implementation is available at https://github.com/zhaoxlpku/PromptCoT.