  Many intellectual endeavors require mathematical problem solving, but this
skill remains beyond the capabilities of computers. To measure this ability in
machine learning models, we introduce MATH, a new dataset of 12,500 challenging
competition mathematics problems. Each problem in MATH has a full step-by-step
solution which can be used to teach models to generate answer derivations and
explanations. To facilitate future research and increase accuracy on MATH, we
also contribute a large auxiliary pretraining dataset which helps teach models
the fundamentals of mathematics. Even though we are able to increase accuracy
on MATH, our results show that accuracy remains relatively low, even with
enormous Transformer models. Moreover, we find that simply increasing budgets
and model parameter counts will be impractical for achieving strong
mathematical reasoning if scaling trends continue. While scaling Transformers
is automatically solving most other text-based tasks, scaling is not currently
solving MATH. To have more traction on mathematical problem solving we will
likely need new algorithmic advancements from the broader research community.
