Multilingual Mathematics Dataset

This dataset code generates mathematical question and answer pairs in different languages, 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 in various languages.

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

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 1.2

Added more translation variations and synonym capabilities. Specify synonyms with brackets: [Synonym 1, Synonym 2, Synonym 3, etc. ].

Version 1.1

This is the updated multilingual version. New languages are added in the lang folder. The lang object translates all strings in the code specified by the language in the generate_settings.py file.

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.

Below is a list of available filters:

• linear_1d_composed
• linear_1d
• linear_2d_composed
• linear_2d
• polynomial_roots_composed
• polynomial_roots
• sequence_next_term
• sequence_nth_term
• add_or_sub_in_base
• add_or_sub
• add_sub_multiple
• div
• mixed
• mul_div_multiple
• mul
• nearest_integer_root
• simplify_surd
• differentiate_composed
• differentiate
• closest_composed
• closest
• kth_biggest_composed
• kth_biggest
• pair_composed
• pair
• sort_composed
• sort
• conversion
• time
• base_conversion
• div_remainder_composed
• div_remainder
• gcd_composed
• gcd
• is_factor_composed
• is_factor
• is_prime_composed
• is_prime

We've also included generate_to_file.py as an example of how to write the generated examples to text files. You can use this directly, or adapt it for your generation and training needs. To generate a range of questions into a directory, use:

python -m mathematics_dataset.generate_to_file --output_dir=directory_name

Note, make sure the directory does not already exist before qenerating questions to file.

Adding More Languages

Copy the template.txt file in the lang folder and rename it to lang.txt with the two-character abbreviation for your language. To change the output language, change the lang= in the generate_settings.py file to the language abbreviation.

Synonyms are enclosed in square brackets ([]). The program will automatically create all combinations possible from the provided synonyms. This is a quick way to get more variations in the problem formulations. Multiple blocks of synonyms can be included in the same template. The program parses this template and produces a list of all variations. For example:

[Calculate, Determine] 5 [times, multiplied with] 7. 

Turns into:

Calculate 5 times 7.
Calculate 5 multiplied with 7.
Determine 5 times 7.
Determine 5 multiplied with 7.

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