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

Shaoxiong Zhan, Yanlin Lai, Ziyu Lu, Dahua Lin, Ziqing Yang, Fei Tan · Aug 7, 2025 · Citations: 0

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Low trust

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Best use

Background context only

What to verify

Validate the evaluation procedure and quality controls in the full paper before operational use.

Evidence quality

Low

Derived from extracted protocol signals and abstract evidence.

Abstract

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.

Abstract-only analysis — low confidence

All signals on this page are inferred from the abstract only and may be inaccurate. Do not use this page as a primary protocol reference.

This paper looks adjacent to evaluation work, but not like a strong protocol reference.
The available metadata is too thin to trust this as a primary source.
The abstract does not clearly describe the evaluation setup.

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Should You Rely On This Paper?

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

Background context only.

Main weakness

This paper looks adjacent to evaluation work, but not like a strong protocol reference.

Trust level

Low

Usefulness score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Weak / implicit signal

Usefulness for eval research

Adjacent candidate

Extraction confidence 25%

If you are doing eval pipeline work, start here:

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What We Could Verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

missing

None explicit

No explicit feedback protocol extracted.

"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."

Evaluation Modes

missing

None explicit

Validate eval design from full paper text.

"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."

Quality Controls

missing

Not reported

No explicit QC controls found.

"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."

Benchmarks / Datasets

partial

MATH 500, GSM8K, Olympiadbench

Useful for quick benchmark comparison.

"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."

Reported Metrics

missing

Not extracted

No metric anchors detected.

"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."

Human Feedback Details

Uses human feedback: No
Feedback types: None
Rater population: Not reported
Expertise required: Math, Coding

Evaluation Details

Evaluation modes:
Agentic eval: None
Quality controls: Not reported
Evidence quality: Low
Use this page as: Background context only

Protocol And Measurement Signals

Benchmarks / Datasets

MATH-500GSM8KOlympiadbench

Reported Metrics

No metric terms were extracted from the available abstract.

Research Brief

Metadata summary

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.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key Takeaways

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.

Researcher Actions

Compare this paper against others mentioning GSM8K.
Check the full text for explicit evaluation design choices (raters, protocol, and metrics).
Use related-paper links to find stronger protocol-specific references.

Caveats

Generated from abstract + metadata only; no PDF parsing.
Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

GSM8K

Research Summary

Contribution Summary

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.
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.

Why It Matters For Eval

Existing synthesis methods largely rely on transforming human-written templates, limiting both diversity and scalability.
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.

Researcher Checklist

Gap: Human feedback protocol is explicit

No explicit human feedback protocol detected.
Gap: Evaluation mode is explicit

No clear evaluation mode extracted.
Gap: Quality control reporting appears

No calibration/adjudication/IAA control explicitly detected.
Pass: Benchmark or dataset anchors are present

Detected: MATH-500, GSM8K, Olympiadbench
Gap: Metric reporting is present

No metric terms extracted.

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