English

NaturalProofs: Mathematical Theorem Proving in Natural Language

Information Retrieval 2021-06-09 v2 Machine Learning

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.

Keywords

Cite

@article{arxiv.2104.01112,
  title  = {NaturalProofs: Mathematical Theorem Proving in Natural Language},
  author = {Sean Welleck and Jiacheng Liu and Ronan Le Bras and Hannaneh Hajishirzi and Yejin Choi and Kyunghyun Cho},
  journal= {arXiv preprint arXiv:2104.01112},
  year   = {2021}
}
R2 v1 2026-06-24T00:48:32.515Z