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Semantic Search Over 9 million Mathematical Theorems

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# Semantic Search over 9 Million Mathematical Theorems

**Luke Alexander, Eric Leonen, Sophie Szeto, Artemii Remizov, Ignacio Tejeda, Giovanni Inchiostro, Vasily Ilin**

[![arXiv](https://img.shields.io/badge/arXiv-2602.05216-b31b1b.svg)](https://arxiv.org/abs/2602.05216)
[![HF Paper](https://img.shields.io/badge/HF-Paper-yellow.svg)](https://huggingface.co/papers/2602.05216)
[![Dataset](https://img.shields.io/badge/Dataset-Theorem_Search-blue.svg)](https://huggingface.co/datasets/uw-math-ai/theorem-search-dataset)
[![Demo](https://img.shields.io/badge/Demo-Live-green.svg)](https://huggingface.co/spaces/uw-math-ai/theorem-search)
[![MathGPT](https://img.shields.io/badge/MathGPT-Custom_GPT-74aa9c.svg)](https://chatgpt.com/g/g-6994f4d1eb7c8191a1a8b6aad90e1449-mathgpt)
[![Website](https://img.shields.io/badge/Website-theoremsearch.com-teal.svg)](https://theoremsearch.com)

---

## Overview

Mathematicians and math prover agents need fast and efficient theorem search.  
We release **[Theorem Search](https://huggingface.co/spaces/uw-math-ai/theorem-search)** over all of arXiv, the Stacks Project, and six other sources.

Our search is **2× more accurate than frontier LLMs**, with only **4 second latency**.

Feedback is welcome.

---

## Retrieval Performance (Hit@10)

| Model | Theorem-level | Paper-level |
|-------|--------------:|------------:|
| Google Search | — | 0.378 |
| ChatGPT 5.2 | 0.180 | — |
| Gemini 3 Pro | 0.252 | — |
| **Ours** | **0.432** | **0.505** |

Theorem-level = retrieval of exact theorem statements  
Paper-level = retrieval of the correct paper containing the theorem

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---

## API

TheoremSearch provides a production REST API for semantic theorem search.**Example:**

```bash
curl https://api.theoremsearch.com/search \
  -H "Content-Type: application/json" \
  -d '{
        "query": "smooth DM stack codimension one",
        "n_results": 5
      }'
```

Returns a JSON object containing theorem-level results with metadata and similarity scores.

## MCP

TheoremSearch is also available as an MCP tool for AI agents with a single tool `theorem_search`. Endpoint: `https://api.theoremsearch.com/mcp`.

---

## Citation

```bibtex
@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}
}

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