aloks16/mathreasoning

---
pretty_name: MathReasoning
language:
- en
license: apache-2.0
tags:
- mathematics
- reasoning
- education
- synthetic
- chain-of-thought
- problem-solving
- NCERT
- competitive-exams
- advanced maths
task_categories:
- text-generation
- question-answering

size_categories:
- 1M<n<10M
paperswithcode_id: null
dataset_info:
features:
- name: prompt
dtype: string
- name: response
dtype: string
splits:
- name: train
num_examples: 3129768
---

# MathReasoning

The **MathReasoning Dataset** is a large-scale, high-quality dataset (~3.13M rows) focused on mathematics, logical reasoning, and problem-solving. It is primarily generated through synthetic distillation techniques, complemented by curated open-source educational content. The dataset is designed to train and evaluate language models in mathematical reasoning, quantitative problem-solving, and structured chain-of-thought tasks across domains from basic arithmetic to advanced mathematics.

## Summary

• **Domain**: Mathematics, Reasoning, Education
• **Scale**: ~3.13M rows, comprehensive mathematical coverage
• **Source**: Generated using distillation techniques with open-source educational content
• **Goal**: Train and evaluate reasoning-capable LLMs for mathematical problem-solving
• **Languages**: English (academic/mathematical focus)
• **License**: Apache 2.0

## Examples

Here are some representative examples from the dataset:

```json
{
"prompt": "Solve: 2x + 5 = 15. Find x.",
"response": "Step 1: Subtract 5 from both sides → 2x = 10. Step 2: Divide both sides by 2 → x = 5."
}

{
"prompt": "Evaluate the integral ∫ (x^2) dx.",
"response": "The antiderivative of x² is (x³/3) + C. Final Answer: (x³/3) + C."
}

{
"prompt": "Five friends sit in a row. A sits to the left of B, but not next to C. If D is at one end and E is next to B, find the seating arrangement.",
"response": "Through elimination and logical reasoning, the arrangement is: D - A - C - B - E."
}
```

## Loading & Usage

```python
from datasets import load_dataset

dataset = load_dataset("169Pi/mathreasoning")

print(dataset["train"][0])
```

## Data Preview

| prompt | response |
|--------|----------|
| In the study of topology, determine the conditions under which the following statements hold true: 1. The real line $\Bbb R$ is homeomorphic to $\Bbb R^n$. 2. The unit circle $\Bbb S^1$ is homeomorphic to $\Bbb S^n$. Provide a clear proof for each case. | To address the first statement, suppose there exists a homeomorphism $f: \Bbb R \to \Bbb R^n$. Let $A = (-\infty, 0) \cup (0, \infty)$. Observe that $\Bbb R^n \setminus \{f(0)\}$ is connected for $n > 1$ because removing a single point from an $n$-dimensional Euclidean space with $n > 1$ does not disconnect it... |
| Explain why the expectation of a random variable X can be less than a real number 'a' even if X is always less than 'a'. | Even though X is always less than 'a', there may be a small probability that X takes on values much smaller than 'a'. This can lead to the expectation of X being less than 'a', as the small probability of extreme negative values can have a significant impact on the overall average. |

## Dataset Structure

| Field | Type | Description |
|-------|------|-------------|
| prompt | string | Math problem or reasoning question |
| response | string | Step-by-step solution and final answer |

## Splits & Statistics

• **Train**: 3,129,768 rows

## Mathematical Coverage

### 1. Arithmetic & Number Systems
- Addition, subtraction, multiplication, division
- Fractions, decimals, ratios, percentages
- Number theory basics (LCM, HCF, modular arithmetic)

### 2. Algebra
- Linear & quadratic equations
- Inequalities, polynomials, factorisation
- Progressions (AP, GP, HP)

### 3. Geometry & Mensuration
- Euclidean geometry, triangles, circles
- Coordinate geometry
- Area, volume, perimeter, trigonometry basics

### 4. Advanced Mathematics
- Calculus (limits, differentiation, integration basics)
- Probability & statistics
- Vectors and matrices

### 5. Logical Reasoning & Puzzles
- Deductive reasoning, analogies, pattern recognition
- Word problems, seating arrangements, mathematical puzzles
- Olympiad-style logical challenges

## Question Types

- **Numerical Problems:** direct calculations and answers
- **Step-by-Step Derivations:** chain-of-thought explanations
- **Proof-Style Explanations:** logical/mathematical proofs
- **Word Problems & Puzzles:** reasoning-heavy, multi-step logic

## Use Cases

• **Model Fine-Tuning for Mathematics** → Enhancing math-solving capabilities of LLMs
• **Reasoning Skill Development** → Training models for step-by-step problem solving (Chain-of-Thought)
• **STEM Education** → Assisting students and teachers with structured math Q&A
• **Exam Preparation** → Practice resource for school exams, competitive tests (JEE, Olympiad)
• **EdTech Applications** → Creating intelligent math tutors for adaptive learning
• **Automated Solution Generation** → Step-wise solutions for educational platforms
• **Evaluation & Benchmarking** → Testing LLM performance in mathematical reasoning
• **Cognitive Research** → Studying AI quantitative reasoning and symbolic problem-solving

## Dataset Creation Process

1. **Synthetic Generation (majority)** → Distilled math Q&A aligned with NCERT syllabus and competitive exam styles
2. **Open-Source Material (minority)** → Curated from freely available educational question banks
3. **Validation Pipeline** → Step-by-step validation for accuracy, logical flow, and clarity
4. **Quality Control** → Removed duplicates, ensured correctness of solutions

## Key Features

• **Mathematics-Focused Coverage** → Basic arithmetic to advanced problem-solving
• **Domain Richness** → School curriculum (NCERT Class 6–12), competitive exams (JEE, Olympiad)
• **Reasoning-Centric** → Designed for structured step-by-step mathematical reasoning
• **Hybrid Source** → Primarily synthetic (distilled), supplemented by open-source content
• **Cleaned & Filtered** → Comprehensive quality assurance and validation

## Impact

MathReasoning is among the largest open-source mathematics reasoning datasets (~3.1M Q&A pairs), making it a flagship resource for advancing open-source AI in mathematical reasoning, education, and benchmarking.

## License

This dataset is released under the **Apache 2.0 License**, allowing free use, modification, and distribution for research and commercial purposes.

## Limitations & Ethical Considerations

• **Synthetic Data**: Primarily generated through distillation techniques, may contain model-specific biases
• **Educational Focus**: Designed for learning and evaluation, not to replace human mathematical instruction
• **Quality Assurance**: While extensively validated, users should verify critical applications independently
• **Domain Scope**: Focused on school-level and competitive exam mathematics
• **Bias Mitigation**: Content is mathematical/logical in nature, minimising subjective biases

## Citation

```bibtex
@misc{169pi2025mathreasoning,
title = {mathreasoning},
author = {169Pi AI Team},
year = {2025},
howpublished = {\url{https://huggingface.co/datasets/169Pi/mathreasoning}},
}
```

## About 169Pi

We are an emerging company building the AI ecosystem, like the Alpie-core suite of models, datasets and more. Our mission is to advance open-source AI research by releasing large-scale, high-quality reasoning datasets across multiple domains (mathematics, education, medical, and more). The MathReasoning Dataset represents our commitment to enhancing mathematical reasoning capabilities in AI systems.

## Community & Contributions

• **Issues & Discussions**: Open issues or start discussions on the HuggingFace dataset page
• **Contributions**: Pull requests welcome for error reporting, quality improvements, and dataset extensions
• **Fine-tuning Results**: Share your model results and improvements with the community
• **Collaboration**: Researchers, developers and organisations are encouraged to contribute

---

*The MathReasoning Dataset represents a significant contribution to mathematical AI research, education, and reasoning-focused model development.*