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An interview episode with Leonardo de Moura, creator of Lean and Z3, discussing how Lean works, the role of LLMs in formal verification, and how AI-assisted proofs could transform software development and mathematics.
OpenAI's unreleased model Astra reportedly solved ten major open mathematics problems, with results formalized in Lean certificates, signaling a major leap in AI mathematical reasoning.
OpenAI reports that an internal version of its next major model (Astra) solved 10 long-standing open problems in math and theoretical computer science for roughly $2,000 in tokens, with formal Lean certificates.
This paper introduces a three-stage LLM pipeline for systematically generating and validating major mathematical conjectures, using Lean 4 formal verification and reflective validation to discover problems with high 'problem taste'.
A postmortem of a soundness bug in the Lean kernel that was exploited to produce a 'disproof' of the Collatz conjecture, with the fix and analysis of why independent checkers also initially missed it.
Lawrence Paulson discusses a bogus refutation of the Collatz conjecture caused by a bug in the Lean kernel, reflecting on proof objects and soundness in proof assistants.
An AI-generated formal proof in Lean that claimed to disprove the Collatz conjecture actually exploited two bugs in the Lean kernel, now patched. Lean creator Leo de Moura warns this will keep happening as AIs are good at finding soundness bugs.
A technical blog post argues that Rocq (Coq) is better than Lean for program verification due to Rocq's native support for coinductive types and cofixpoints, contrasting with Lean's less mature, library-based approach.
The article discusses how LLMs can automate proof generation in dependently-typed languages like Lean and Rocq, making formal verification dramatically more practical by leveraging proof irrelevance and reducing the need for manual proof engineering.
LeanFlow is an LLM agent system for translating mathematical papers into formalized Lean projects, evaluated through case studies and benchmarks with Kimi-K2.6 and GPT-5.5, achieving high completion rates within budget constraints.
A new formal theorem, verified in Lean, shows that for thresholds tending to infinity, almost every positive integer falls below the threshold within 436 log N Collatz steps, strengthening Terence Tao's earlier result with explicit bounds and natural density.
PriorProof introduces a method to measure the novelty of proof techniques in formal mathematics by analyzing the dependency footprint of Lean proof terms against a prior built from an earlier snapshot of Mathlib. The method agrees with human raters on 69.7% of pairs and provides interpretable score gaps.
AI systems, including ChatGPT and OpenAI's Sol, have disproved and fully formalized the Erdős Unit Distance conjecture, marking a milestone in AI-assisted mathematics. The article discusses the process and implications for the future of mathematical proof verification.
A tutorial introducing formal verification using the Lean proof assistant, specifically verifying the One-Time Pad protocol. Aimed at cryptographic engineers new to formal verification.
Researchers used 20 parallel Codex accounts to solve 20 Erdős problems, including a formal proof of Erdős problem #123 in number theory using Lean.
Microsoft Research presents a new methodology using Rust, Lean, Aeneas, and AI agents to formally verify cryptographic code, enabling scalable verification for production algorithms like ML-KEM and SHA-3 while preserving performance.
Matt Parker's video explores recent cases where AI, including ChatGPT, helped solve open Erdős problems in mathematics, highlighting a new era of AI-assisted mathematical discovery.
Anima Anandkumar announces four Lean-related papers from their group at ICML workshops, covering verified ML systems, functional program synthesis, proof assistant interoperability, and scientific reasoning, positioning Lean as infrastructure for AI.
LeanstralSafeVerify is a tool to safely verify Lean code against specifications, guarding against exploits and used in several web apps and leaderboards.
Mistral AI releases Leanstral 1.5, a 6B active parameter model for Lean 4 proof engineering, achieving state-of-the-art results on multiple formal verification benchmarks and uncovering real-world bugs, fully open-sourced under Apache-2.0.