# Lean Lean is an open-source programming language and proof assistant for formally verified code. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## A "proof" of Fermat's Last Theorem that fits the margin DevFeed: [A "proof" of Fermat's Last Theorem that fits the margin]() Original publisher: [Read original article]() Author: "Marc Ilunga" Published: 2026-09-09T11:00:00Z Content type: article Language: en Sources: [The Trail of Bits Blog](), [The Trail of Bits Blog]() Topics: [Lean](), [bug](), [Memory safety verification]() Tags: [bug](), [exploits](), [memory-safety](), [open-source](), [vulnerability-disclosure]() ### AI overview A Lean string-slicing bug caused its logical evaluator and compiled native code to disagree, allowing a contradiction that could make an invalid proof appear checked. The issue was fixed after disclosure. ### Source excerpt Fermat famously claimed to have a "truly marvelous proof" of his Last Theorem, but he never wrote it down, insisting the margin of his page was too narrow to contain it. A few centuries later, Anthropic announced a complete formalization of Fermat's Last Theorem using 13 million lines of Lean code (clearly not what Fermat intended). Luckily, we found a wonderfully cursed Lean bug, shown below, that suggests the proof may have fit the margin after all. The issue affects all stable versions of Lean up to 4.33.1, and the patch is incorporated in v4.34.0-rc1. A "checked" proof of Fermat's Last Theorem using Lean 4.33.1 The blue checkmarks in the screenshot above would suggest that Lean considers this proof correct. This seems odd given the amount of work Sir Andrew Wiles put into this problem and the vast size of Claude's proof. So what is going on? The "proof" clearly doesn't make any sense and exploits an issue in Lean. We found the issue while using GPT-5.6 to experiment with a new skill for code review. We want to clarify up front that the issue is not a kernel soundness issue, but it happens to nicely fit any discussion of strings, lengths, and substrings. The issue affects String.Pos.Raw.extract, Lean's low-level string-slicing function. When asked to extract a one-byte slice at an astronomically large position, Lean's logical definition returns the empty string. But the compiled native code returns the entire original string. That disagreement is enough to manufacture a contradiction. Lean's ordinary evaluator "proves" that the tiny slice was empty, while native evaluation "proves" that the very same slice contained "a truly marvelous proof." Put those together, and Lean concludes that the empty string equals a non-empty string. And once you have a contradiction, you can prove anything, including Fermat's Last Theorem. On the bright side, the Lean team was considerably faster than mathematical history. About 90 minutes after we reported the issue, hargoniX opened ## On the Navier-Stokes Millennium Prize Problem DevFeed: [On the Navier-Stokes Millennium Prize Problem]() Original publisher: [Read original article]() Published: 2026-09-08T10:00:00Z Content type: article Language: en Sources: [OpenAI News]() Topics: [Math and Logic](), [Lean]() Tags: [ai](), [gpt](), [model](), [openai](), [research]() ### AI overview OpenAI shares an AI-generated solution to the Navier-Stokes existence and smoothness problem, with a proof writeup and a Lean formalization. ### Source excerpt We're sharing an AI-generated solution to the Navier-Stokes Millennium Prize Problem, including a writeup and a formal proof in Lean. ## Anthropic Formalized Fermat's Last Theorem in Lean, Shifting the Verification Challenge DevFeed: [Anthropic Formalized Fermat's Last Theorem in Lean, Shifting the Verification Challenge]() Original publisher: [Read original article]() Published: 2026-09-06T00:00:00Z Content type: opinion Language: en Sources: [Alex Korbonits]() Topics: [Lean](), [anthropic](), [Math and Logic]() Tags: [anthropic](), [compiler](), [formalized](), [research](), [statement](), [trust]() ### AI overview The article argues that Anthropic's machine-generated Lean proof of Fermat's Last Theorem changes the challenge from formalizing the theorem's statement to checking a very large proof artifact. It describes public build checks and an independent Rust-based Lean kernel re-check, while noting that the author has not read the patches used to complete that re-check. ### Source excerpt Anthropic formalized Fermat's Last Theorem in Lean in eleven days. It is the frontier I said in May was untouched, and the first result in this series where nobody had to trust the statement. The problem that replaced it is that 13 million lines is more than anyone can read. ## Raising machine-checked security benchmarks to advance hash-based SNARKs through agentic collaboration DevFeed: [Raising machine-checked security benchmarks to advance hash-based SNARKs through agentic collaboration]() Original publisher: [Read original article]() Author: Ethereum Foundation Formal Verification team Published: 2026-08-20T00:00:00Z Content type: article Language: en Sources: [Ethereum Foundation Blog]() Topics: [Formal verification](), [Lean](), [Ethereum](), [AI research agents](), [AI Models](), [Library](), [Security]() Tags: [agentic](), [ai-agents](), [collaboration](), [ethereum](), [formal-verification](), [leaderboard](), [paper](), [research](), [research-development](), [security](), [verification]() ### AI overview The Ethereum Foundation's Formal Verification team launched better.codes, an open autoresearch challenge focused on raising the machine-checked soundness bound of the Lean-formalized koalaIRS12 Reed-Solomon proximity problem toward a fixed 128-bit target. Submissions are checked by the Lean kernel and promoted proofs are shared publicly. ### Source excerpt better.codes, an open autoresearch challenge built by the Ethereum Foundation Formal Verification team in collaboration with Yukon and zkSecurity, is now live. better.codes takes a self-contained problem from the Proximity Prize research, formalized in Lean, and puts its soundness bound on a public leaderboard that anyone can push forward.... ## Leonardo de Moura on Lean, Formal Verification, and the Future of Mathematics DevFeed: [Leonardo de Moura on Lean, Formal Verification, and the Future of Mathematics]() Original publisher: [Read original article]() Author: Ryan Peterman Published: 2026-08-10T13:03:04Z Content type: article Language: en Sources: [The Developing Dev]() Topics: [Lean](), [Formal verification](), [math](), [Large Language Model]() Tags: [code](), [formal-verification](), [google](), [language](), [llms](), [math](), [podcasts](), [programming](), [programming-language](), [software](), [verification]() ### AI overview An interview with Leonardo de Moura, creator of Lean, about using the programming language for machine-checkable proofs, software verification, and mathematical reasoning. The discussion also covers how LLMs can work with Lean to generate and verify proofs. ### Source excerpt In 2024, AlphaProof from Google Deepmind broke through in competition math achieving a silver-medal in Interational Mathematical Olympiad (IMO). ## OpenAI's Ten Mathematical Results Tested Through Lean Certificates DevFeed: [OpenAI's Ten Mathematical Results Tested Through Lean Certificates]() Original publisher: [Read original article]() Published: 2026-08-01T00:00:00Z Content type: article Language: en Sources: [Alex Korbonits]() Topics: [Lean](), [OpenAI](), [certificates](), [trust](), [Artificial Intelligence]() Tags: [ai](), [certificates](), [openai](), [paper](), [trust]() ### AI overview The article examines OpenAI's release of ten results on long-standing mathematical problems and reports independently building and checking the accompanying Lean certificates. It says all 38 headline theorems passed with no errors or non-standard axioms, while raising concerns about trusting definitions written by the same system that produced the proofs. ### Source excerpt OpenAI shipped ten open problems with Lean certificates. I built all 550,000 lines and checked what they rest on. Everything passed -- and the only thing left to trust is 1,700 lines of definitions written by the same system that wrote the proofs. ## Dependent Types and the Challenge of Automating Proofs DevFeed: [Dependent Types and the Challenge of Automating Proofs]() Original publisher: [Read original article]() Author: Adam Langley Published: 2026-07-26T00:00:00Z Content type: opinion Language: en Sources: [ImperialViolet]() Topics: [Programming language](), [Lean](), [Programming](), [Coq]() Tags: [interactive](), [language](), [machine](), [programming](), [programming-language]() ### AI overview The article discusses dependently typed languages such as Coq, Rocq, and Lean, which can encode subtle invariants in a type system. It explains that writing and checking proofs can require substantial effort, contributing to the niche status of these languages and motivating attempts to automate proof obligations. ### Source excerpt I've long had a soft spot for dependently-typed languages like Coq Rocq and Lean. They offer the possibility of a type system capable of encoding and enforcing arbitrarily subtle invariants. The sort of thing that, in regular languages, ends up (at best) as a comment, and which quickly gets lost as the size of the team grows. Then you get subtle misunderstandings and components that don't quite fit together. It's often the case that those components have grown to a sufficient size that, when the problem is noticed, aligning either of them is a wearying prospect. Perhaps, say dependent types seductively, you could write those invariants formally and have a machine check them. (p.s. Coq changed its name! I remember many years ago at a Coq conference in Princeton, I tried suggesting that, in an English-speaking world, having a programming language called Coq was an impediment. I don't think the audience agreed at the time. I also joked that many of the talks there sounded like a speech by Tyrion Lannister, there being so many Coqs and Hoares. A joke that was hilarious and timely, even though it fell completely flat, coming as it did before the final season of that show and our collective memory-holing of it.) The problem has always been that with great type-system power comes great proof effort. I can certainly attest to entire days spent proving really quite simple things. Doing proofs is actually quite fun: it's challenging, interactive, and there's a clear goal. But gosh, does it take a lot of time, especially if, like me, you don't know what you're doing. There's also the periodic, galling experience, at the end of many hours of effort, where you realise that the goal that you're trying to prove is, in fact, false. The classic result here is the retrospective from the seL4 effort that found that, even though the project was large enough for the engineers to develop considerable experience, they spent about 10 times as much time proving as they did designing and imp ## Verifying Rust cryptography in SymCrypt, from standards to code DevFeed: [Verifying Rust cryptography in SymCrypt, from standards to code]() Original publisher: [Read original article]() Author: Son Ho, Cédric Fournet, Antoine Delignat-Lavaud, Samuel Lee, Jason Fisher, Jessica Krynitsky Published: 2026-07-13T16:00:00Z Content type: article Language: en Sources: [Microsoft Research]() Topics: [Rust](), [Rust formal verification](), [Cryptography](), [Formal verification](), [Post-quantum cryptography](), [Lean](), [toolchain](), [Microsoft]() Tags: [cryptography](), [formal-verification](), [memory-safety](), [microsoft](), [post-quantum](), [research](), [research-blog](), [rust](), [security]() ### AI overview Microsoft Research describes how SymCrypt uses safe Rust, Lean, and the Aeneas toolchain to formally verify production cryptographic implementations. The approach combines Rust's memory-safety guarantees with machine-checked proofs of functional correctness, with initial verified code for SHA-3 and ML-KEM and support from independently verifiable proof-writing agents. ### Source excerpt Cryptographic code supports vital protections in modern computing systems. Learn how a new method helps verify code as developers write it while preserving speed and adaptability as it gets implemented and evolves. The post Verifying Rust cryptography in SymCrypt, from standards to code appeared first on Microsoft Research. ## Leanstral 1.5: Proof Abundance for All DevFeed: [Leanstral 1.5: Proof Abundance for All]() Original publisher: [Read original article]() Published: 2026-07-02T13:55:54Z Content type: release Language: en Sources: [Mistral AI Blog]() Topics: [Lean](), [Formal methods](), [Artificial Intelligence](), [Open Source](), [hugging face](), [API](), [Code]() Tags: [apache](), [api](), [code](), [developer](), [formal-methods](), [formal-verification](), [hugging-face](), [launch](), [models](), [open-source](), [reinforcement-learning](), [training]() ### AI overview Mistral releases Leanstral 1.5, an Apache-2.0 licensed model for formal verification in Lean 4. The 6B-active-parameter model reports strong miniF2F, PutnamBench, FATE-H, and FATE-X results, and identifies previously unknown bugs in open-source repositories. ### Source excerpt The most powerful AI platform for enterprises. Customize, fine-tune, and deploy AI assistants, autonomous agents, and multimodal AI with open models. ## Who Verifies the Verifier DevFeed: [Who Verifies the Verifier]() Original publisher: [Read original article]() Published: 2026-05-28T00:00:00Z Content type: opinion Language: en Sources: [Alex Korbonits]() Topics: [Artificial Intelligence](), [Formal verification](), [Compiler](), [Lean](), [Math and Logic](), [Google](), [Inference](), [Language models]() Tags: [ai](), [compiler](), [formal-verification](), [google](), [inference](), [model](), [paper](), [research]() ### AI overview The article examines whether formal verification can make AI-generated mathematical proofs scalable. It contrasts human review of natural-language proofs with Google DeepMind's approach of generating proofs directly in Lean and using the Lean compiler to verify them, while noting that the system's ability to read existing mathematics remains limited. ### Source excerpt An AI built the machine I said mathematics needed -- a compiler that verifies proofs for cents instead of expert weekends. The catch is what it still can't read. ## Leanstral: Open-Source foundation for trustworthy vibe-coding DevFeed: [Leanstral: Open-Source foundation for trustworthy vibe-coding]() Original publisher: [Read original article]() Published: 2026-03-16T16:00:00Z Content type: release Language: en Sources: [Mistral AI Blog]() Topics: [Lean](), [AI-assisted coding](), [Vibe coding](), [Code generation](), [Math and Logic](), [Open Source](), [Benchmark](), [Model Context Protocol](), [Rust]() Tags: [agents](), [ai](), [benchmark](), [code-generation](), [math](), [mcp](), [models](), [open-source](), [release](), [rust](), [vibe-coding]() ### AI overview Mistral introduces Leanstral, an open-source coding agent for Lean 4 designed to generate formally verified code and proofs in realistic repositories. The article describes its sparse architecture, 6B active parameters, Apache 2.0 release, MCP support, and evaluation against commercial and open-source coding agents. ### Source excerpt The most powerful AI platform for enterprises. Customize, fine-tune, and deploy AI assistants, autonomous agents, and multimodal AI with open models. ## A chat with Byron Cook on automated reasoning and trust in AI systems DevFeed: [A chat with Byron Cook on automated reasoning and trust in AI systems]() Original publisher: [Read original article]() Author: werner@allthingsdistributed.com (Dr. Werner Vogels) Published: 2026-02-17T14:00:00Z Content type: article Language: en Sources: [All Things Distributed]() Topics: [Automated reasoning](), [Artificial Intelligence](), [AI Agent](), [Lean](), [large-language-models](), [Authorization](), [Architecture & Design]() Tags: [agentic-ai](), [ai](), [ai-agent](), [authorization](), [automated-reasoning](), [cryptographic](), [deployment](), [financial](), [generate](), [language-models](), [large-language-models](), [neural-networks](), [posts](), [reasoning](), [regulatory](), [safety](), [security](), [security-vulnerabilities]() ### AI overview An interview with Byron Cook examines how automated reasoning can establish trust in AI systems. It discusses applying formal verification techniques to agentic systems, generated code, authorization, cryptographic implementations, and virtualization, with neurosymbolic AI presented as a way to combine neural networks with mathematically rigorous symbolic procedures. ### Source excerpt Over the past decade, Byron's team has proven the correctness of our authorization engine, our cryptographic implementations, and our virtualization layer. Now they're taking those same techniques and applying them to agentic systems. ## Cedar Joins CNCF as a Sandbox Project DevFeed: [Cedar Joins CNCF as a Sandbox Project]() Original publisher: [Read original article]() Author: Lara Langdon Published: 2025-12-15T18:21:10Z Content type: article Language: en Sources: [AWS Open Source Blog]() Topics: [Access Control](), [Open Source](), [Authorization](), [Cloud Native Ecosystem](), [SDKs](), [Automated reasoning](), [Lean](), [Rust](), [Testing]() Tags: [authorization](), [automated-reasoning](), [cloud-native](), [cncf](), [open-source](), [rust](), [sdk](), [security-identity-compliance](), [testing](), [verification]() ### AI overview Cedar, an open source authorization policy language and SDK, has joined the Cloud Native Computing Foundation as a Sandbox project. The article explains Cedar's purpose-built approach to fine-grained access control, its support for RBAC, ABAC, and ReBAC, and its focus on performance, analyzability, and safety through formal verification and differential testing. It also describes adoption by organizations including Cloudflare, MongoDB, StrongDM, Cloudinary, and AWS services. ### Source excerpt Cedar, an open source authorization policy language and SDK, has joined the Cloud Native Computing Foundation (CNCF) as a Sandbox project. CNCF provides a neutral home for early stage and developing open source projects. Cedar fulfills the need for a fast, safe, and analyzable authorization policy language in cloud-native environments by allowing developers to define, [...] ## A Lean Syntax Primer DevFeed: [A Lean Syntax Primer]() Original publisher: [Read original article]() Published: 2025-09-02T00:00:00Z Content type: tutorial Language: en Sources: [Dan Abramov]() Topics: [Lean](), [syntax](), [Programming](), [Code]() Tags: [code](), [how-to](), [learn](), [programming](), [syntax](), [types]() ### AI overview An opinionated introduction to Lean syntax covering definitions, assignment and comparison syntax, type inference, explicit type annotations, natural numbers, integers, and running code in the online playground or VS Code. It also introduces the distinction between executing Lean code and proving facts about it. ### Source excerpt Programming with proofs. ## How Lean Propositions Differ from TypeScript Booleans DevFeed: [How Lean Propositions Differ from TypeScript Booleans]() Original publisher: [Read original article]() Published: 2025-08-16T00:00:00Z Content type: tutorial Language: en Sources: [Dan Abramov]() Topics: [Lean](), [Programming](), [Mathematics](), [Code](), [TypeScript]() Tags: [mathematics](), [programming](), [programming-languages](), [types](), [typescript]() ### AI overview This tutorial compares logical expressions in TypeScript with propositions in Lean. It explains that Lean treats propositions as distinct values and types, and that proving a proposition requires supplying a proof rather than simply computing a Boolean result. ### Source excerpt What is the type of 2 + 2 = 4? ## Kimina-Prover-RL DevFeed: [Kimina-Prover-RL]() Original publisher: [Read original article]() Author: Thibaut Barroyer; Jonas Bayer; Marina Vinyes; Mert Unsal; Haiming Wang; Xiaohan Lin; MantasBaksys; Junqi Liu; Marco Dos Santos; Flood Sung; Ying; Zhu Zekai; Lujianqiao; Hugues de Saxcé; Ebony Zhang; B Published: 2025-08-14T12:13:01Z Content type: article Language: en Sources: [Hugging Face - Blog]() Topics: [Lean](), [Open Source](), [grpo](), [Reinforcement learning](), [Large Language Model](), [Benchmark]() Tags: [benchmark](), [code](), [datasets](), [grpo](), [open-source](), [reasoning](), [reinforcement-learning](), [training](), [verification]() ### AI overview Kimina-Prover-RL is an open-source training pipeline for formal theorem proving in Lean 4. It uses a structured reasoning-then-generation approach, GRPO reinforcement learning, format-checking rewards, error-correction turns, and high-throughput proof verification through kimina-lean-server. The article also introduces 1.7B- and 0.6B-parameter models evaluated on the MiniF2F benchmark. ### Source excerpt We are happy to introduce kimina-prover-rl, an open-source training pipeline for formal theorem proving in Lean 4, based on a structured reasoning-then-generation paradigm inspired by DeepSeek-R1. This training pipelinee is a simplified version of the system we used to train Kimina Prover, preserving the key components of the system and offering full compatibility with the open-source Verl framework. ## A Taste of Lean: Formalizing Mathematics as Code DevFeed: [A Taste of Lean: Formalizing Mathematics as Code]() Original publisher: [Read original article]() Published: 2025-07-30T00:00:00Z Content type: tutorial Language: en Sources: [Dan Abramov]() Topics: [Lean](), [math](), [Programming](), [Code]() Tags: [2025](), [code](), [math](), [programming-language](), [syntax]() ### AI overview This tutorial introduces Lean, a programming language designed to formalize mathematics. It explains how Lean represents mathematical structures, theorems, and proofs as code, then uses a small equality theorem to demonstrate tactic states, incomplete proofs, universal proof suppression, and reflexivity. ### Source excerpt A taste of Lean. ## Kimina-Prover: Applying Test-time RL Search on Large Formal Reasoning Models DevFeed: [Kimina-Prover: Applying Test-time RL Search on Large Formal Reasoning Models]() Original publisher: [Read original article]() Author: Haiming Wang; Mert Unsal; Xiaohan Lin; MantasBaksys; Junqi Liu; Marco Dos Santos; Flood Sung; Ying; Zhu Zekai; Lujianqiao; Hugues de Saxcé; Thibaut Barroyer; Ebony Zhang; Bolton Bailey; Frederick Pu; Published: 2025-07-10T12:54:19Z Content type: article Language: en Sources: [Hugging Face - Blog]() Topics: [Lean](), [Reinforcement learning](), [Benchmark](), [Large Language Model](), [Artificial Intelligence]() Tags: [agentic](), [benchmark](), [deepseek](), [large-language-model](), [qwen3](), [reasoning](), [reinforcement-learning](), [rl](), [test](), [training]() ### AI overview The article announces Kimina-Prover-72B, a theorem-proving model for Lean 4, along with distilled 8B and 1.7B variants. It describes test-time reinforcement-learning search, recursive lemma composition, and error-directed proof repair. The model achieves a 92.2% pass rate on the miniF2F benchmark. ### Source excerpt Numina & Kimi Team We're excited to announce the release of Kimina-Prover-72B, our state-of-the-art theorem proving model trained with the Kimi k1.5[1] RL pipeline based on Qwen2.5-72B [2]. Alongside it, we are also releasing two distilled variants: Kimina-Prover-Distill-8B and 1.7B (based on Qwen3-8B and Qwen3-1.7B[3] respectively).