evanto/Incube-large-math-dataset

InCube - Large Math Dataset

Overview

This dataset contains over 175 million mathematical questions and their answers, designed for training and evaluating machine learning models on mathematical reasoning tasks. It spans 17 different types of mathematical operations with varying levels of complexity.

Dataset Details

Size

• Total examples: ~175 million
• File format: JSON
• Examples per operation: ~10 million (with some variation due to mathematical constraints)
• Value range: -1000 to 1000

Operations Included

Operation	Symbol	Description	Example
Addition	+	Adding two numbers	"5 + 3 ="
Subtraction	-	Subtracting one number from another	"9 - 4 ="
Multiplication	*	Multiplying two numbers	"6 * 7 ="
Division	/	Dividing one number by another	"20 / 4 ="
Square	^2	Raising a number to the power of 2	"3^2 ="
Cube	^3	Raising a number to the power of 3	"4^3 ="
Exponentiation	^	Raising a number to an arbitrary power	"2^5 ="
Modulo	%	Remainder after division	"17 % 5 ="
Square Root	√	Square root of a number	"√64 ="
Absolute Value	|	Absolute value of a number	"|-5| ="
Factorial	!	Product of all positive integers ≤ n	"5! ="
GCD	gcd	Greatest common divisor	"gcd(12, 18) ="
LCM	lcm	Least common multiple	"lcm(4, 6) ="
Logarithm	log	Base-10 logarithm	"log(100) ="
Natural Log	ln	Natural logarithm	"ln(e^3) ="
Sine	sin	Sine of an angle in degrees	"sin(30) ="
Cosine	cos	Cosine of an angle in degrees	"cos(60) ="
Tangent	tan	Tangent of an angle in degrees	"tan(45) ="

Question Formats

Each operation has questions presented in 4 different formats:

1. Symbolic format: Using mathematical notation (e.g., "5 + 3 =")
2. Standard word format: Using standard terminology (e.g., "What is 5 plus 3?")
3. Alternative word format: Using alternative terminology (e.g., "What is the addition of 5 and 3?")
4. Additional formats: Various other phrasings (e.g., "Sum of 5 and 3", "Calculate 5 plus 3")

Data Structure

The dataset is provided as a JSON file with the following structure:

[
  {
    "question": "5 + 3 =",
    "answer": "8"
  },
  {
    "question": "What is the square root of 16?",
    "answer": "4"
  },
  ...
]

Usage Examples

Loading the Dataset in Python

import json

with open('large_math_dataset.json', 'r') as f:
    dataset = json.load(f)

# Access a sample question
sample = dataset[0]
print(f"Question: {sample['question']}")
print(f"Answer: {sample['answer']}")

Loading with Hugging Face Datasets

from datasets import load_dataset

dataset = load_dataset("your-username/incube-large-math-dataset")
print(dataset['train'][0])

Generation Method

This dataset was generated programmatically using Python. The generation process:

1. Defines 17 mathematical operations with their symbolic and verbal representations
2. Generates values within the range of -1000 to 1000
3. Applies special handling for certain operations (e.g., ensuring division results in integers)
4. Creates questions in multiple formats
5. Computes answers and stores the question-answer pairs

License

This dataset is released under the MIT License.

Citation

If you use this dataset in your research, please cite it as:

@misc{incube-large-math-dataset,
  author = {Abhiram},
  title = {InCube Large Math Dataset},
  year = {2025},
  publisher = {Hugging Face},
  howpublished = {\\url{https://huggingface.co/datasets/evanto/incube-large-math-dataset}}
}

Limitations

• The dataset focuses on exact, deterministic mathematical operations
• Some operations (like factorial) are limited to smaller numbers to avoid overflow
• Square roots are limited to perfect squares for integer results
• Trigonometric functions are rounded to 4 decimal places