ai-in-mathematics
Latest stories covering ai-in-mathematics, 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.
Why Erdős Problems Are Falling to AI
news
16 min read
OpenAI's internal AI model discovered a counterexample to the "unit distance" problem, a conjecture proposed by Paul Erdős in 1946. This marks a significant achievement in the application of AI to solve longstanding mathematical questions.
The Fall of the Theorem Economy
opinion
53 min read
The theorem economy is facing challenges as AI technologies evolve, potentially diminishing the role of traditional mathematical proofs. Bill Thurston emphasizes that the essence of mathematics lies in clarity and understanding rather than merely accumulating theorems.
AI in mathematics is forcing big questions
opinion
15 min read
Researchers are exploring the implications of AI in mathematics, focusing on the changing motivations and purposes within the field. The discussion includes how AI's ability to perform complex calculations may redefine the role and future of mathematicians.
Leiden Declaration on Artificial Intelligence and Mathematics
research
14 min read
The Leiden Declaration on Artificial Intelligence and Mathematics acknowledges the transformative impact of AI technologies on mathematical practice. It recognizes both the potential benefits and diverse reactions among researchers regarding the use of AI in mathematics.