Shaping the Future of Mathematics in the Age of AI

Artificial intelligence is transforming mathematics at a speed and scale that demand active engagement from the mathematical community. We examine five areas where this transformation is particularly pressing: values, practice, teaching, technology, and ethics. We offer recommendations on safeguarding our intellectual autonomy, rethinking our practice, broadening curricula, building academically oriented infrastructure, and developing shared ethical principles - with the aim of ensuring that the future of mathematics is shaped by the community itself.

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 Lean tactics.