uw-math-ai/theorem-search-dataset-permissive

Theorem Search Dataset

The largest open corpus of informal mathematical theorems: 1,239,720 theorem statements with natural-language slogans from 197,889 papers, designed for semantic theorem retrieval.

Paper: Semantic Search over 9 Million Mathematical Theorems

Demo: huggingface.co/spaces/uw-math-ai/theorem-search

Benchmark results

On 110 test queries written by research mathematicians, our best pipeline (Qwen3-Embedding-8B on DeepSeek-V3.1 slogans) outperforms all existing tools for finding theorems in the literature:

Method	Theorem Hit@20	Paper Hit@20
arXiv Search	--	2.7%
Google Search (site:arxiv.org)	--	37.8%
ChatGPT 5.2 w/ Search	19.8%	--
Gemini 3 Pro	27.0%	--
Ours (Qwen3 8B)	45.0%	56.8%

Why this dataset?

Mathematicians and AI proof assistants need to find whether a specific result already exists in the literature. Existing tools (Google Scholar, arXiv search, LLMs with web access) operate at the paper level, forcing users to manually scan documents for individual statements. This dataset enables theorem-level semantic search by pairing every theorem with a concise natural-language slogan.

Dataset summary

	Count
Theorems	1,239,720
Papers	197,889
Slogans	1,239,720
Test queries (human-written)	110

Sources (by number of theorems): arXiv (1,238,975), Open Logic Project (745).

Note on dataset size: The full corpus described in our paper contains over 9.2 million theorems from approximately 690,000 arXiv papers. This dataset releases only the subset with licenses compatible with CC BY 4.0: arXiv papers under CC0, CC BY 4.0, CC BY 3.0, or CC Public Domain, plus the Open Logic Project (CC BY 4.0). Sources with ShareAlike, GFDL, or no open license are excluded. The full 9.2M-theorem corpus powers the live demo.

Files

File	Rows	Size	Description
paper.parquet	197,889	137 MB	Paper metadata (title, authors, abstract, arXiv categories, citations, etc.)
theorem.parquet	1,239,720	247 MB	Theorem statements in LaTeX (name, body, label, parsing method)
theorem_slogan.parquet	1,239,720	179 MB	Natural-language slogans generated by DeepSeek-V3.1
theorems-test.parquet	110	12 KB	Human-written test queries with ground-truth theorem matches

Schema

paper.parquet

Column	Type	Description
paper_id	string	Unique paper identifier (arXiv ID or source-specific tag)
title	string	Paper title
authors	string	List of authors
link	string	URL to the paper
last_updated	string	Last update date (arXiv papers)
summary	string	Paper abstract
journal_ref	string	Journal reference, if published
primary_category	string	Primary arXiv category (e.g., math.AG)
categories	string	All arXiv categories
citations	int	Citation count (where available)
source	string	Provenance: arXiv or Open Logic Project
license	string	License of the source paper

theorem.parquet

Column	Type	Description
theorem_id	int	Unique theorem identifier
paper_id	string	Foreign key to paper.parquet
name	string	Theorem name as displayed in source (e.g., "Theorem 3.1")
body	string	Full theorem statement in LaTeX
label	string	LaTeX \label{} tag from the source
link	string	Direct URL to the theorem (where available)
parsing_method	string	How the theorem was extracted: plastex, tex, regex, or manual

theorem_slogan.parquet

Column	Type	Description
slogan_id	int	Unique slogan identifier
theorem_id	int	Foreign key to theorem.parquet
model	string	LLM used to generate the slogan (DeepSeek-V3.1)
prompt_id	string	Prompt variant used (body-only-v1)
slogan	string	Natural-language summary of the theorem

theorems-test.parquet

Column	Type	Description
query	string	Natural-language query written blind by a research mathematician
theorem number	string	Ground-truth theorem identifier (e.g., "Theorem 3.1")
paper title	string	Title of the paper containing the target theorem
link to paper on arxiv	string	arXiv URL of the target paper

How theorems were extracted

Theorems were parsed from LaTeX sources using three strategies, applied in fallback order:

1. plasTeX (956,194 theorems): LaTeX sources are converted into a structured node tree using plasTeX. Theorem environments are identified and their name, number, and body extracted from node metadata.
2. TeX logging (296,239 theorems): A custom LaTeX package is injected that logs theorem data during compilation, capturing the theorem type, number, and body.
3. Regex (88,607 theorems): Regular expressions identify theorem delimiter tokens (\begin{theorem}...\end{theorem}, \proclaim...\endproclaim, etc.) and extract the body.

The remaining 43 theorems were entered manually. Author-defined macros (e.g., \R for \mathbb{R}) are expanded in theorem bodies. Malformed extractions (e.g., truncated bodies shorter than 8 characters) are filtered out.

How slogans were generated

Each theorem body is passed to DeepSeek-V3.1 with a prompt instructing the model to produce a concise, declarative English description of the theorem's main result, avoiding symbolic notation, proof details, and references to the surrounding document. Temperature is fixed at 0.2 with a maximum of 1024 output tokens.

Test set

The test set contains 110 queries written by four research mathematicians (Giovanni Inchiostro, Dori Bejleri, Michele Pernice, Ignacio Tejeda) across 14 arXiv tags, primarily Algebraic Geometry (math.AG), Analysis (math.AP), and Geometric Measure Theory (math.CA, math.MG).

Quick start

import pandas as pd

# Load the dataset
papers = pd.read_parquet("paper.parquet")
theorems = pd.read_parquet("theorem.parquet")
slogans = pd.read_parquet("theorem_slogan.parquet")
test = pd.read_parquet("theorems-test.parquet")

# Join theorems with their slogans
df = theorems.merge(slogans, on="theorem_id")

# Example: find all theorems from the Stacks Project "Algebra" chapter
paper_theorems = df[df["paper_id"] == "00AO"]
for _, row in paper_theorems.head(3).iterrows():
    print(f"{row['name']}: {row['slogan'][:100]}...")

# Using Hugging Face datasets
from datasets import load_dataset

ds = load_dataset("uw-math-ai/theorem-search-dataset")

Citation

@article{alexander2026semantic,
  title  = {Semantic Search over 9 Million Mathematical Theorems},
  author = {Alexander, Luke and Leonen, Eric and Szeto, Sophie and Remizov, Artemii and Tejeda, Ignacio and Inchiostro, Giovanni and Ilin, Vasily},
  journal= {arXiv preprint arXiv:2602.05216},
  year   = {2026},
  doi    = {10.48550/arXiv.2602.05216},
  url    = {https://arxiv.org/abs/2602.05216}
}

Contact

For questions or issues, contact Vasily Ilin.