Curated Math Reasoning Dataset

• Curated mathematical reasoning datasets are rigorously filtered collections of validated math problems paired with detailed solutions for benchmarking algorithmic reasoning.
• They employ multi-stage curation processes including source filtering, deduplication, and expert validation to ensure clarity, diversity, and accuracy.
• These datasets support fine-grained evaluation and advanced model training through annotated metadata, multiple modalities, and comprehensive reasoning chains.

A curated mathematical reasoning dataset is a rigorously filtered and structured collection of mathematical problems paired with solutions, engineered to benchmark, train, or analyze algorithmic reasoning—particularly for LLMs and multimodal systems. Such datasets are distinguished by meticulous quality control, diverse topical coverage, and explicit metadata, often supporting targeted supervision, evaluation, and robust ablation in mathematical reasoning research.

1. Fundamental Attributes and Motivation

Curated mathematical reasoning datasets address the limitations of raw or synthetic corpora by enforcing problem validity, coverage, diversity, and annotational rigor. Critical motivations include:

• Ensuring Problem Validity: Removing malformed, ambiguous, or unsolvable items through formal and semantic validation pipelines (Shen et al., 20 May 2025, Tang et al., 5 Mar 2024).
• Supporting Fine-Grained Evaluation: Enabling comprehensive analysis across topics, difficulty levels, modalities (text, code, images), and linguistic domains (Sobhani et al., 16 Oct 2025, Duan et al., 13 Oct 2025, Feng et al., 8 Aug 2025).
• Facilitating Model Training and Benchmarking: Supplying high-caliber examples for supervised fine-tuning, instruction tuning, reinforcement learning, and chain-of-thought (CoT) optimization (Tang et al., 5 Mar 2024, Duan et al., 13 Oct 2025, Albalak et al., 24 Feb 2025, He et al., 15 Apr 2025).

These datasets form the empirical backbone for state-of-the-art mathematical LLMs, neuro-symbolic systems, and multimodal architectures.

2. Curation Methodologies and Quality Control

Curation processes are multi-staged and systematic, often including some or all of the following:

• Source Selection and Filtering: Aggregating problems from competitions, textbooks, publicly available repositories, and web-scraped corpora, followed by strict filtration based on mathematical completeness, unique verifiability, non-copy contamination, and topic balance (Zhao et al., 25 Mar 2025, Albalak et al., 24 Feb 2025, Tang et al., 5 Mar 2024).
• Deduplication and Decontamination: Applying both semantic (embedding-based) and string-based deduplication, removing overlap with public test sets to avoid contamination (Zhao et al., 25 Mar 2025, He et al., 15 Apr 2025, Albalak et al., 24 Feb 2025).
• Validation Pipelines: Incorporating expert human review, automated symbolic equivalence checking (e.g., Math-Verify), multi-model cross-verification, and condition-by-condition logical checks for contradiction or underspecification (Shen et al., 20 May 2025, Zhao et al., 25 Mar 2025, He et al., 15 Apr 2025).
• Error Typology: Explicit error-type labeling (instruction error, linguistic error, minimal domain/underspecification, contradiction, completeness) for negative instances, enabling detailed failure analysis (Shen et al., 20 May 2025).
• Multi-Agent and Ensemble Generation (for synthetic sets): Using multi-agent LLM systems for extraction and human-in-the-loop adjudication, critical for high-difficulty or derivation-focused corpora (Liu et al., 2 Jun 2025).

3. Dataset Structures, Modalities, and Annotations

Modern mathematical reasoning datasets exhibit rich structure:

• Entry Format: Each example typically comprises a formally stated problem (in standardized LaTeX or Markdown), a stepwise reasoning trace (CoT or full derivation), and a canonical answer (numeric, symbolic, or code-executable) (Duan et al., 13 Oct 2025, Tang et al., 5 Mar 2024, Zhao et al., 25 Mar 2025).
• Metadata: Datasets are annotated with tags for topic, difficulty, question type, language, and provenance, and may include granularity (single-step, multi-step, proof vs. computation), reasoning chain length, and token/step-level statistics (Zhao et al., 25 Mar 2025, He et al., 15 Apr 2025, Shen et al., 20 May 2025).
• Multimodality: Advanced datasets integrate images (diagrams, real photos), code (Python for symbolic computation or plotting), and even formal logic (Lean theorems), supporting both language and vision-based approaches (Duan et al., 13 Oct 2025, Feng et al., 8 Aug 2025, Cao et al., 20 Jun 2025).
• Multilinguality and Alignment: For robust cross-lingual research, curated sets may feature parallel question-solution pairs across diverse languages, ensuring linguistic as well as mathematical alignment (Sobhani et al., 16 Oct 2025).

Dataset	Entries	Key Modalities	Special Features
MathScaleQA	2M	Text, step-by-step CoT	Graph-based topic/KP sampling
AM-DeepSeek-R1	411K math	Text, CoT, answer	Severe deduplication, RL focus
DeepMath-103K	103K	Text, 3x CoT per item	High difficulty, min. levels 5–10
Math-VR	178K	Text, images, code, 2lang	Visual reasoning, code-plots
STORM-BORN	2K/100	Text, LaTeX, derivations	Human-analyst filtered, deriv.
CLEVR-Math	680K	Synthetic images, text	Compositional, scene-prog labels

4. Evaluation Protocols and Benchmarks

Curated datasets are paired with rigorous evaluation methodologies:

• Canonical Answer Matching: Numeric or symbolic equivalence (module symbolic simplification) for closed-form answers (Albalak et al., 24 Feb 2025, Zhao et al., 25 Mar 2025).
• Stepwise/Process Scoring: Partial credit for intermediate steps, LLM-based or rule-based process verifiers, and customized metrics such as “process score” (PS) (Duan et al., 13 Oct 2025).
• Multimodal Scoring: Evaluation of both answer correctness and visual-manipulation fidelity (e.g., code-driven images rendered and compared) (Duan et al., 13 Oct 2025, Shi et al., 16 Oct 2025).
• Proof-Generating Protocols: Pass@k on autoformalization tasks, metricizing the proportion of theorems proved within k attempts in formal logic datasets (Cao et al., 20 Jun 2025, Biyani et al., 30 Nov 2025).
• Difficulty and Coverage Disaggregation: Analysis over question types, Chapman difficulty bins, topic/subdomain slices, and single- vs. multi-step solutions (He et al., 15 Apr 2025, Zhao et al., 25 Mar 2025, Tang et al., 5 Mar 2024).

5. Representative Datasets and Case Studies

• MathScaleQA employs a concept-graph–based synthetic pipeline, scaling to 2M problems with explicit coverage of 2,018 topics and 8,892 knowledge points, with each problem paired to an Alpaca-style instruction-response trace (Tang et al., 5 Mar 2024).
• AM-DeepSeek-R1-Distilled-1.4M (math subset) provides 411K reasoning traces, rigorously deduplicated and verified, emphasizing long chains and hard examples; it is uniquely suited for training models with extended mathematical CoT (Zhao et al., 25 Mar 2025).
• Big-Math systematically links scale to RL usability, with 251K problems filtered for answer verifiability and open-endedness, including conversion of multiple-choice to open-form problems (Big-Math-Reformulated, 47K) (Albalak et al., 24 Feb 2025).
• DeepMath-103K targets high-difficulty, decontaminated problems, each with three solution chains, supporting RL and supervised paradigms, and directly advancing pass@k scores on elite benchmarks (He et al., 15 Apr 2025).
• CLEVR-Math and multimodal suites (e.g., Math-VR, MathCanvas, MATH-Vision, MV-MATH) pioneer the integration of images, code, and scene-graph reasoning, exposing unique challenges in compositionality and vision–language fusion (Lindström et al., 2022, Duan et al., 13 Oct 2025, Shi et al., 16 Oct 2025, Wang et al., 22 Feb 2024, Wang et al., 28 Feb 2025).

6. Applications, Limitations, and Future Directions

Curated mathematical reasoning datasets underpin advances across:

• Supervised and RL Training: Elevating LLMs’ mathematical proficiency, especially for long-form CoT and tool use, by providing granular, verifiable supervision (Tang et al., 5 Mar 2024, He et al., 15 Apr 2025, Zhao et al., 25 Mar 2025).
• Multilingual and Multimodal Reasoning: Benchmarking model generalization and robustness across languages and input modalities (Duan et al., 13 Oct 2025, Sobhani et al., 16 Oct 2025, Feng et al., 8 Aug 2025).
• Mathematical Formalization and Auto-Theorem Proving: Enabling research in Lean/Coq formalizations with parallel natural–formal pairs and domain-specific structure (Cao et al., 20 Jun 2025, Biyani et al., 30 Nov 2025).

Limitations persist in:

• Synthetic-Data Noise: Large synthetic sets may inherit inaccuracies or blandness from prompt-based LLM sampling, requiring extensive filtering (Tang et al., 5 Mar 2024).
• Gap in Human-Like Creativity and Heuristics: Even the most curated sets may not match the depth of human mathematical intuition or non-algorithmic reasoning (addressed by STORM-BORN’s multi-agent–plus–human-expert pipeline) (Liu et al., 2 Jun 2025).
• Tool Ecosystem Weakness: Verifiability and step-level supervision depend on robust symbolic engines, automated code-execution, or formal logic verifiers, which may limit corpus breadth, particularly for open-ended proof tasks (Shen et al., 20 May 2025, Cao et al., 20 Jun 2025).

Future research will expand dataset scale and diversity (e.g., via code, image, and multilingual axes), sharpen formalization schemas, and couple data curation with active research into verifiability, process-level scoring, and cross-domain generalization (Duan et al., 13 Oct 2025, Shen et al., 20 May 2025, Liu et al., 2 Jun 2025).