TheoremGraph: Search 18M+ Mathematical Dependencies (www.theoremsearch.com)

TheoremGraph has launched a comprehensive unified graph that encapsulates over 18 million mathematical dependencies, bridging informal and formal mathematics. This vast structure includes 11.7 million statements from arXiv, facilitating a shared embedding space that aligns formal proofs with informal mathematical discourse. The significance of this development lies in its potential to enhance attribution and novelty detection in mathematical research, allowing mathematicians to accurately trace the foundations of their proofs and identify previously established results. A recent study indicated that 2.4% of withdrawn arXiv submissions were non-novel, underscoring the necessity for improved dependency tracking. The technical implementation involves parsing informal statements from arXiv to extract 18.3 million directed dependency edges, while LeanGraph consolidates 388,105 nodes and 11.3 million typed edges from various Lean projects. Utilizing advanced AI models, informal and formal statements are summarized and embedded into a shared semantic space, allowing for efficient cross-referencing through a REST API. This architecture empowers AI agents with enhanced navigational capabilities, enabling them to perform sophisticated searches and deductions within vast mathematical contexts, ultimately streamlining the process of formalization and theorem proving in the AI/ML community.