Papers › Measuring Mathematical Problem Solving With the MATH Dataset

Measuring Mathematical Problem Solving With the MATH Dataset

5 Mar 2021arXiv:2103.03874archive 2025-07-28

Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, Jacob Steinhardt

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.

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Tasks

MathMath Word Problem SolvingMathematical Problem-SolvingMathematical ReasoningText Generation

Datasets

Introduced by this paper, per the archive.

AMPSMATH

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Math Word Problem Solving MATH GPT-2 (1.5B) Accuracy 6.9 #122 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-2 (1.5B) Parameters (Billions) 1.5 #122 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-2 (0.7B) Accuracy 6.4 #123 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-2 (0.7B) Parameters (Billions) 0.7 #123 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-2 (0.3B) Accuracy 6.2 #124 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-2 (0.3B) Parameters (Billions) 0.3 #124 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-3 13B Accuracy 5.6 #125 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-3 13B Parameters (Billions) 13 #125 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-2 (0.1B) Accuracy 5.4 #127 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-2 (0.1B) Parameters (Billions) 0.1 #127 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-3-175B (few-shot) Accuracy 5.2 #128 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-3-175B (few-shot) Parameters (Billions) 175 #128 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-3-13B (few-shot) Accuracy 3.0 #132 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-3-13B (few-shot) Parameters (Billions) 13 #132 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-3 2.7B Accuracy 2.9 #134 of 135 Archive leaderboard report
Math Word Problem Solving MATH GPT-3 2.7B Parameters (Billions) 2.7 #134 of 135 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Methods

Absolute Position EncodingsAdamAttentionBPEDense ConnectionsDropoutLabel SmoothingLayer NormalizationLinear LayerMulti-Head AttentionPosition-Wise Feed-Forward LayerResidual ConnectionSoftmaxTransformer

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