Mathematics Dataset

This dataset code generates mathematical question and answer pairs, from a range of question types at roughly school-level difficulty. This is designed to test the mathematical learning and algebraic reasoning skills of learning models.

Original paper: Analysing Mathematical Reasoning Abilities of Neural Models (Saxton, Grefenstette, Hill, Kohli).

Street Math Approximation Dataset

This repository now includes a Street Math Approximation Dataset specifically designed for training models on mental math estimation and approximation techniques. The dataset is converted to Alpaca format for instruction tuning.

Quick Start - Approximation Dataset

To generate the Alpaca-formatted approximation dataset:

python combine_dataset.py

This creates the street_math_hf_dataset/ directory with:

• train.jsonl - Training split (70%)
• validation.jsonl - Validation split (15%)
• test.jsonl - Test split (15%)
• sample.jsonl - Sample examples to preview format

Alpaca Format Structure

Each example follows the Alpaca instruction format:

{
  "instruction": "Estimate the following calculation using basic mental math and rounding techniques. Provide your approximation and briefly explain your rounding strategy.",
  "input": "22 * -394",
  "output": "**Approximation: -8700**\n\n**Method:**\n- **Round 22** to **20** (easier to multiply)\n- **Round -394** to **-400** (round number)\n\n**Reasoning:**\nThis estimation method provides a quick, practical approximation by rounding to the nearest convenient numbers for mental calculation.",
  "metadata": {
    "exact_answer": "-8668.0",
    "lower_bound": "-9535.0", 
    "upper_bound": "-7801.0",
    "difficulty": "train-easy",
    "module": "street_math__mul"
  }
}

Using with Axolotl

This dataset is optimized for training with Axolotl using the alpaca format. Simply point your Axolotl config to the generated JSONL files.

Dataset Focus

The approximation dataset emphasizes:

• Mental math techniques - Rounding strategies for quick estimation
• Practical approximation - Real-world estimation skills
• Reasoning explanation - Understanding why approximations work
• Bounded evaluation - Answers within reasonable tolerance ranges are considered correct

Example questions

Question: Solve -42*r + 27*c = -1167 and 130*r + 4*c = 372 for r.
Answer: 4

Question: Calculate -841880142.544 + 411127.
Answer: -841469015.544

Question: Let x(g) = 9*g + 1. Let q(c) = 2*c + 1. Let f(i) = 3*i - 39. Let w(j) = q(x(j)). Calculate f(w(a)).
Answer: 54*a - 30

Question: Let e(l) = l - 6. Is 2 a factor of both e(9) and 2?
Answer: False

Question: Let u(n) = -n**3 - n**2. Let e(c) = -2*c**3 + c. Let l(j) = -118*e(j) + 54*u(j). What is the derivative of l(a)?
Answer: 546*a**2 - 108*a - 118

Question: Three letters picked without replacement from qqqkkklkqkkk. Give prob of sequence qql.
Answer: 1/110

Pre-generated data

Pre-generated files

Version 1.0

This is the version released with the original paper. It contains 2 million (question, answer) pairs per module, with questions limited to 160 characters in length, and answers to 30 characters in length. Note the training data for each question type is split into "train-easy", "train-medium", and "train-hard". This allows training models via a curriculum. The data can also be mixed together uniformly from these training datasets to obtain the results reported in the paper. Categories:

• algebra (linear equations, polynomial roots, sequences)
• arithmetic (pairwise operations and mixed expressions, surds)
• calculus (differentiation)
• comparison (closest numbers, pairwise comparisons, sorting)
• measurement (conversion, working with time)
• numbers (base conversion, remainders, common divisors and multiples, primality, place value, rounding numbers)
• polynomials (addition, simplification, composition, evaluating, expansion)
• probability (sampling without replacement)

Getting the source

PyPI

The easiest way to get the source is to use pip:

$ pip install mathematics_dataset

From GitHub

Alternately you can get the source by cloning the mathematics_dataset repository:

$ git clone https://github.com/deepmind/mathematics_dataset
$ pip install --upgrade mathematics_dataset/

Generating examples

Generated examples can be printed to stdout via the generate script. For example:

python -m mathematics_dataset.generate --filter=linear_1d

will generate example (question, answer) pairs for solving linear equations in one variable.

Writing to files

We've also included generate_to_file.py to write generated examples to files. It supports both the original text format and JSON format compatible with Hugging Face datasets.

Text format (original):

python -m mathematics_dataset.generate_to_file --output_dir=./dataset_text

JSON format (Hugging Face compatible):

# Separate JSONL files per difficulty level
python -m mathematics_dataset.generate_to_file --output_dir=./dataset_json --format=json

# Single combined JSONL file
python -m mathematics_dataset.generate_to_file --output_dir=./dataset_json --format=json --single_file=True

JSON output format: Each line in the JSONL files contains:

{"input": "Solve -42*r + 27*c = -1167 and 130*r + 4*c = 372 for r.", "output": "4", "difficulty": "interpolate", "module": "algebra__linear_1d"}

This format can be directly used with Hugging Face's datasets library:

from datasets import load_dataset
dataset = load_dataset("json", data_files="interpolate.jsonl")

Additional options:

• --per_train_module=N: Number of examples per training module (default: 10)
• --per_test_module=N: Number of examples per test module (default: 10)
• --filter=pattern: Generate only modules matching the pattern
• --train_split=False: Don't split training data by difficulty

You can use these scripts directly, or adapt them for your generation and training needs.

Dataset Metadata

The following table is necessary for this dataset to be indexed by search engines such as Google Dataset Search.

property	value
name	Mathematics Dataset
url	https://github.com/deepmind/mathematics_dataset
sameAs	https://github.com/deepmind/mathematics_dataset
description	This dataset consists of mathematical question and answer pairs, from a range of question types at roughly school-level difficulty. This is designed to test the mathematical learning and algebraic reasoning skills of learning models.\n \n ## Example questions\n \n ```\n Question: Solve -42*r + 27*c = -1167 and 130*r + 4*c = 372 for r.\n Answer: 4\n \n Question: Calculate -841880142.544 + 411127.\n Answer: -841469015.544\n \n Question: Let x(g) = 9*g + 1. Let q(c) = 2*c + 1. Let f(i) = 3*i - 39. Let w(j) = q(x(j)). Calculate f(w(a)).\n Answer: 54*a - 30\n ```\n \n It contains 2 million (question, answer) pairs per module, with questions limited to 160 characters in length, and answers to 30 characters in length. Note the training data for each question type is split into "train-easy", "train-medium", and "train-hard". This allows training models via a curriculum. The data can also be mixed together uniformly from these training datasets to obtain the results reported in the paper. Categories:\n \n * **algebra** (linear equations, polynomial roots, sequences)\n * **arithmetic** (pairwise operations and mixed expressions, surds)\n * **calculus** (differentiation)\n * **comparison** (closest numbers, pairwise comparisons, sorting)\n * **measurement** (conversion, working with time)\n * **numbers** (base conversion, remainders, common divisors and multiples,\n primality, place value, rounding numbers)\n * **polynomials** (addition, simplification, composition, evaluating, expansion)\n * **probability** (sampling without replacement)
provider	property value name DeepMind sameAs https://en.wikipedia.org/wiki/DeepMind
citation	https://identifiers.org/arxiv:1904.01557