SorryDB: Can AI Provers Complete Real-World Lean Theorems?

We present SorryDB, a dynamically-updating benchmark of open Lean tasks drawn from 78 real world formalization projects on GitHub. Unlike existing static benchmarks, often composed of competition problems, hillclimbing the SorryDB benchmark will yield tools that are aligned to the community needs, more usable by mathematicians, and more capable of understanding complex dependencies. Moreover, by providing a continuously updated stream of tasks, SorryDB mitigates test-set contamination and offers a robust metric for an agent's ability to contribute to novel formal mathematics projects. We evaluate a collection of approaches, including generalist large language models, agentic approaches, and specialized symbolic provers, over a selected snapshot of 1000 tasks from SorryDB. We show that current approaches are complementary: even though an agentic approach based on Gemini Flash is the most performant, it is not strictly better than other off-the-shelf large-language models, specialized provers, or even a curated list of tactics.

How do AI systems designed to prove theorems perform in day-to-day use by mathematicians? Currently, these AIs are mostly tested on static competition math puzzles, which don't reflect the complex, evolving nature of real-world research. To bridge this gap, we developed SorryDB, a continuously updating test dataset sourced from 78 active, community-driven mathematics projects on GitHub. We used this realistic benchmark to evaluate a wide range of current AI models, from general-purpose AIs to specialized math models. We found that systems which perform well in a vacuum don't always generalize to practical contexts. Furthermore, no single AI method is perfect: different systems have complementary strengths.