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

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

Question: Solve -42*r + 27*c = -1167 and 130*r + 4*c = 372 for r.Answer: 4Question: Calculate -841880142.544 + 411127.Answer: -841469015.544Question: 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 - 30Question: Let e(l) = l - 6. Is 2 a factor of both e(9) and 2?Answer: FalseQuestion: 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 - 118Question: Three letters picked without replacement from qqqkkklkqkkk. Give prob of sequence qql.Answer: 1/110

Pre-generated files

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

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

$ pip install mathematics_dataset

Alternately you can get the source by cloning the mathematics_datasetrepository:

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

Generated examples can be printed to stdout via thegenerate script. Forexample:

python -m mathematics_dataset.generate --filter=linear_1d

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

We've also includedgenerate_to_file.py as an example of how to write thegenerated examples to text files. You can use this directly, or adapt it foryour generation and training needs.

The following table is necessary for this dataset to be indexed by searchengines such asGoogle Dataset Search.