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arXiv · 2104.01112

NaturalProofs: Mathematical Theorem Proving in Natural Language

Sean Welleck·Jiacheng Liu·Ronan Le Bras·Hannaneh Hajishirzi·Yejin Choi·Kyunghyun Cho
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Abstract

Understanding and creating mathematics using natural mathematical language - the mixture of symbolic and natural language used by humans - is a challenging and important problem for driving progress in machine learning. As a step in this direction, we develop NaturalProofs, a multi-domain corpus of mathematical statements and their proofs, written in natural mathematical language. NaturalProofs unifies broad coverage, deep coverage, and low-resource mathematical sources, allowing for evaluating both in-distribution and zero-shot generalization. Using NaturalProofs, we benchmark strong neural methods on mathematical reference retrieval and generation tasks which test a system's ability to determine key results that appear in a proof. Large-scale sequence models show promise compared to classical information retrieval methods, yet their performance and out-of-domain generalization leave substantial room for improvement. NaturalProofs opens many avenues for research on challenging mathematical tasks.

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Sean Welleck, Jiacheng Liu, Ronan Le Bras, Hannaneh Hajishirzi, Yejin Choi, Kyunghyun Cho. 2021-03-24. NaturalProofs: Mathematical Theorem Proving in Natural Language. https://arxiv.org/abs/2104.01112

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