Semantic Search over 9 Million Mathematical Theorems
Searching for mathematical results remains difficult: most existing tools retrieve entire papers, while mathematicians and theorem-proving agents often seek a specific theorem, lemma, or proposition that answers a query. While semantic search has seen rapid progress, its behavior on large, highly technical corpora such as research-level mathematical theorems remains poorly understood. In this work, we introduce and study semantic theorem retrieval at scale over a unified corpus of 9.2 million theorem statements extracted from arXiv and seven other sources, representing the largest publicly available corpus of human-authored, research-level theorems. We represent each theorem with a short natural-language description as a retrieval representation and systematically analyze how representation context, language model choice, embedding model, and prompting strategy affect retrieval quality. On a curated evaluation set of theorem-search queries written by professional mathematicians, our approach substantially improves both theorem-level and paper-level retrieval compared to existing baselines, demonstrating that semantic theorem search is feasible and effective at web scale. The theorem search tool is available at https://huggingface.co/spaces/uw-math-ai/theorem-search{this link}, and the dataset is available at https://huggingface.co/datasets/uw-math-ai/TheoremSearch{this link}.
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Luke Alexander
69854f5b4ad556f294b7eaee
Eric Leonen
69854f5b4ad556f294b7eaef
Sophie Szeto
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2026-02-11T11:20:16.502Z
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Sophie Szeto
slszeto
user
slszeto
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Artemii Remizov
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Ignacio Tejeda
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Giovanni Inchiostro
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Vasily Ilin
claimed_verified
2026-02-12T20:28:51.647Z
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Vasily Ilin
Vilin97
user
Vilin97
Semantic Search over 9 Million Mathematical Theorems
Searching for mathematical results remains difficult: most existing tools retrieve entire papers, while mathematicians and theorem-proving agents often seek a specific theorem, lemma, or proposition that answers a query. While semantic search has seen rapid progress, its behavior on large, highly technical corpora such as research-level mathematical theorems remains poorly understood. In this work, we introduce and study semantic theorem retrieval at scale over a unified corpus of 9.2 million theorem statements extracted from arXiv and seven other sources, representing the largest publicly available corpus of human-authored, research-level theorems. We represent each theorem with a short natural-language description as a retrieval representation and systematically analyze how representation context, language model choice, embedding model, and prompting strategy affect retrieval quality. On a curated evaluation set of theorem-search queries written by professional mathematicians, our approach substantially improves both theorem-level and paper-level retrieval compared to existing baselines, demonstrating that semantic theorem search is feasible and effective at web scale. The theorem search tool is available at https://huggingface.co/spaces/uw-math-ai/theorem-search{this link}, and the dataset is available at https://huggingface.co/datasets/uw-math-ai/TheoremSearch{this link}.
Large-scale semantic theorem retrieval system demonstrates superior performance over existing baselines using a 9.2 million theorem corpus with systematic analysis of representation context, language model choice, and embedding strategies.
semantic search theorem retrieval natural-language description retrieval representation language model choice embedding model prompting strategy theorem-level retrieval paper-level retrieval