Putnam AXIOM Dataset

Dataset Summary

The Putnam AXIOM dataset is designed for evaluating large language models (LLMs) on advanced mathematical reasoning skills. It is based on challenging problems from the Putnam Mathematical Competition and contains three subsets:

Full Original (236 problems): Contains 236 problems in their original form.
Functional Original (53 problems): A selected subset of 53 original problems.
Functional Variations (265 problems): Includes modified versions of problems to prevent memorization and encourage true mathematical understanding.

Each problem includes:

Problem statement
Solution
Original problem variant (where applicable)
Answer type (e.g., numerical, proof)
Source and type of problem (e.g., Algebra, Calculus, Geometry)

Supported Tasks and Leaderboards

Mathematical Reasoning: Evaluate mathematical reasoning and problem-solving skills.
Language Model Benchmarking: Use this dataset to benchmark performance of language models on advanced mathematical questions.

Languages

The dataset is presented in English.

Dataset Structure

Data Fields

year: The year of the competition.
id: Unique identifier for each problem.
problem: The problem statement.
solution: The solution or explanation for the problem.
answer_type: The expected type of answer (e.g., numerical, proof).
source: The origin of the problem (Putnam).
type: A description of the problem’s mathematical topic (e.g., "Algebra Geometry").
original_problem: Original form of the problem, where variations exist.
original_solution: Original solution to the problem, if modified in this dataset.

Subsets

Subset	Description	Number of Problems
`full_original_236`	Complete set of 236 original problems	236
`small_original_53`	Subset of 53 original problems	53
`small_variations_265`	Modified variations for evaluation	265

Dataset Usage

from datasets import load_dataset

# Load the full dataset
dataset = load_dataset("brando/putnam-axiom-dataset")

# Access each subset
full_original = dataset["full_original_236"]
small_original = dataset["small_original_53"]
small_variations = dataset["small_variations_265"]

# Example usage: print the first problem from the full original subset

print(full_original[0])

Citation

If you use this dataset, please cite it as follows:

@article{fronsdal2024putnamaxiom,
  title={Putnam-AXIOM: A Functional and Static Benchmark for Measuring Higher Level Mathematical Reasoning},
  author={Kai Fronsdal and Aryan Gulati and Brando Miranda and Eric Chen and Emily Xia and Bruno de Moraes Dumont and Sanmi Koyejo},
  journal={NeurIPS 2024 Workshop on MATH-AI},
  year={2024},
  month={October},
  url={https://openreview.net/pdf?id=YXnwlZe0yf},
  note={Published: 09 Oct 2024, Last Modified: 09 Oct 2024},
  keywords={Benchmarks, Large Language Models, Mathematical Reasoning, Mathematics, Reasoning, Machine Learning},
  abstract={As large language models (LLMs) continue to advance, many existing benchmarks designed to evaluate their reasoning capabilities are becoming less challenging. These benchmarks, though foundational, no longer offer the complexity necessary to evaluate the cutting edge of artificial reasoning. In this paper, we present the Putnam-AXIOM Original benchmark, a dataset of 236 challenging problems from the William Lowell Putnam Mathematical Competition, along with detailed step-by-step solutions. To address the potential data contamination of Putnam problems, we create functional variations for 53 problems in Putnam-AXIOM. We see that most models get a significantly lower accuracy on the variations than the original problems. Even so, our results reveal that Claude-3.5 Sonnet, the best-performing model, achieves 15.96% accuracy on the Putnam-AXIOM original but experiences more than a 50% reduction in accuracy on the variations dataset when compared to its performance on corresponding original problems.},
  license={Apache 2.0}
}

License

This dataset is licensed under the Apache 2.0.

Datasets:

Putnam-AXIOM
/

putnam-axiom-dataset

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