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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.
OpenAI announces ten results on long-standing open problems in mathematics and theoretical computer science, achieved by an internal version of its next model Astra, with proofs formalized in Lean.
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.
A research paper introducing a failure-triggered cascade approach to safely integrate machine learning into Lean 4's grind tactic, achieving improved efficiency and solving previously unsolvable proofs without regressions.
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.
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.
This position paper argues for theory-level autoformalization, which formalizes entire theories including axioms, definitions, and lemmas as coherent libraries, rather than isolated statements. It discusses the significance, alternative views, open challenges, and proposes paths forward for this shift in formalization research.
OpenProver is an open-source system for LLM-driven automated theorem proving using Lean 4, featuring a Planner-Worker-Verifier architecture and both autonomous and interactive modes. It enables reproducible evaluation and human-AI synergy in mathematical proof search.
This position paper reviews the current state of LLM-driven formal mathematics, identifies key limitations in applying these systems to open-ended research mathematics, and proposes a strategic roadmap for developing AI agents capable of advancing mathematical frontiers.
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.
This paper presents a benchmark and evaluation protocol for faithful natural-language-to-Lean statement formalization, revealing a 29-point gap between compile-pass and consensus-faithfulness, and decomposing the effects of expert drafting, context search, and elaboration feedback.
Mistral AI releases Leanstral 1.5, an updated Lean 4 formal proof engineering model optimized for automated theorem proving and autoformalization, with 119B total parameters and 6.5B active parameters.
A detailed blog post presenting a fully commented proof of the Fundamental Theorem of Arithmetic in Agda, intended for intermediate learners of the proof assistant.
This paper audits five widely used Lean theorem-proving benchmarks, uncovering 398 mechanically certified issues such as counterexamples, vacuous theorems, and unsound axioms. It proposes a fault taxonomy, automated checkers, and release standards to improve evaluation reliability and trustworthiness.
Introduces LCS-Bench, a theory-scale benchmark for auto-formalization of logics for computer science, covering 327 textbook items over 4,076 Lean declarations. Evaluation on 14 models shows the benchmark is challenging, with SOTA models achieving only 20.1% on auto-formalization tasks.
This paper presents Process-Verified Reinforcement Learning, using the Lean proof assistant as a process oracle to provide fine-grained tactic-level feedback during training, improving theorem proving performance.
This paper presents improvements to IsabeLLM, an automated theorem proving tool built on Isabelle, by integrating a retrieval-augmented generation framework, error tracing, and counterexample generation. The improved tool is evaluated on the formal verification of Bitcoin's Proof of Work consensus protocol.
This paper presents an agent pipeline for formalizing a numerical analysis textbook in Lean 4 and introduces a quality audit framework that evaluates semantic correctness and library reuse beyond kernel acceptance, revealing common unfaithful formalization patterns.
This paper presents a case study of using a large language model (Claude Code) to formalize Grothendieck's vanishing theorem in the Lean theorem prover. It finds that while agents can produce verified code, they struggle with definitions and API design, emphasizing the need for expert review beyond mere compilation.
MA-ProofBench is a new formal benchmark for evaluating LLMs on theorem proving in mathematical analysis, containing 200 problems across two difficulty levels. The best model, GPT-5.5, achieves only 16% on Level I and 5% on Level II, highlighting a significant gap between informal and formal reasoning.