theorem-proving
Latest stories covering theorem-proving, with summaries and links to related coverage.
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How to Formalize All of Mathematics
opinion
12 min read
A group of mathematicians and formalization researchers argues that AI can help formalize most of mathematics within three years, but only if the resulting Lean libraries are reusable, reviewed, documented, and governed by mathematical communities. They warn that rapidly generated code has limited value when nobody can understand, extend, or trust it. The authors cite an AI-generated formalization of Maryna Viazovska’s sphere-packing work that its original team discarded because cleanup was harder than rebuilding it, and say Anthropic’s 13-million-line, 11-day formal verification of Fermat’s Last Theorem is unlikely to replace a more modern formalization. They support coordinated efforts built around Mathlib, an open-source Lean library with 65 reviewers and 950 contributors that received the 2026 Jean-Pierre Demailly Prize for Open Science in Mathematics. Tau Ceti uses AI-written contributions and AI adversarial review under expert-curated roadmaps; it has grown beyond Mathlib’s 3 million lines of code and includes results such as Riemann–Roch and Chebotarev density. Formal Frontier uses AI-agent systems to turn source texts into interconnected libraries, with 41 released libraries totaling about 200,000 lines. The authors call for open-source interoperability, public review, avoidance of duplicated results, links to literature, sustained compatibility with Lean and Mathlib, and mathematician control over infrastructure and resources.
TheoremDB – A public workspace for machine mathematics
research
15 min read
TheoremDB is a public workspace designed for machine mathematics, currently in alpha. It allows live contributions, including Lean proof submissions, and aims to reduce redundancy in research efforts.