Lean

A new type of "high-level programming language" that seems really worth trying to make, is a language that gets compiled to Lean (or HOL, or...) that is specifically about making it as friendly as possible for a human to read definitions and theorems. Not the proofs - as all that matters with proofs is that the proofs are correct - just the definitions and theorems. The intended use case is that AI outputs a blob of proofs, and you're trying to make it as easy as possible for anyone reading the output to understand what the actual precise claims are that have been proven

𝘛𝘩𝘦 𝘗𝘳𝘰𝘰𝘧 𝘪𝘯 𝘵𝘩𝘦 𝘊𝘰𝘥𝘦, @KSHartnett 's book on the development of Lean and Mathlib, is out across the EU this week. For readers picking it up, the two launch panels he moderated are still available to watch: 𝐓𝐡𝐞 𝐁𝐮𝐢𝐥𝐝𝐞𝐫𝐬, with Leonardo de Moura, Sebastian Ullrich, and Jeremy Avigad, on Lean from the inside: its origins, design, and where it's headed. 𝐓𝐡𝐞 𝐌𝐚𝐭𝐡𝐞𝐦𝐚𝐭𝐢𝐜𝐢𝐚𝐧𝐬, with Johan Commelin, Kevin Buzzard, and Alex Kontorovich, on what it means to formalize mathematics in Lean. Watch both: youtube.com/watch?v=uZUzcs… #LeanLang #LeanProver #Mathlib #FormalMathematics #SoftwareVerification

Tau Ceti is released! This is the brainchild of Kim Morrison at the Lean FRO @leanprover, a “Mathlib for AIs”; move fast and break things, and get a whole lot more formalized math than can be done at the scale of human review.

Site: github.com/TauCetiProject…

Excited to share the launch of Tau Ceti, a new library of AI-formalized mathematics in Lean, with human-curated roadmaps and adversarial review against open rubrics. Tau Ceti: github.com/TauCetiProject… Review rubrics: github.com/TauCetiProject… Roadmaps: github.com/TauCetiProject… Zulip discussion: #narrow/channel/610393-Tau-Ceti/topic/Welcome.20to.20Tau.20Ceti.21/near/603228923" target="_blank" rel="nofollow noopener">leanprover.zulipchat.com/#narrow/channe… Tau Ceti sits downstream of Mathlib, the gold standard for human-curated mathematics in Lean. It aims for reusable code others can build on, not the "perfection of knowledge" role Mathlib plays. Mathematicians contribute roadmaps; AIs implement the formal mathematics and review each other's work against evolving rubrics. Contributors can use the project's tools or their own. We're glad to co-incubate Tau Ceti alongside Kim Morrison and the Mathlib Initiative. New roadmaps, roadmap review, and AI contributors are all welcome. #LeanLang #LeanProver #Mathlib #AI #Mathematics

1/3 Thrilled to sit down with Fields Medalist Terry Tao on Aug 8th to discuss the intersection of AI & Math! Since joining @axiommathai in December, exploring these frontiers through formalization has been my focus. An absolute honor to moderate. @leanprover

13 years ago today, the first commit landed in the Lean repository: a handful of C++ files for debugging and exception handling. Since then: 40,000+ commits, 250+ contributors, and four major versions of Lean. Try it live: live.lean-lang.org More on Lean's history in @KSHartnett's new book, The Proof in the Code: quantabooks.org/books/the-proo… #LeanLang #LeanProver #OpenSource

Thank you to @theNASciences and @DARPA for having Axiom represent at this important convention in Washington DC on the frontier of AI for formal mathematics. Our Founder & CEO @CarinaLHong and Founding Mathematician @KenOno691 will discuss in keynote and panel the mathematical discoveries we are able to make thanks to formal languages like @leanprover, report on internal efforts kickstarting large-scale formalization projects, and share research progress on high quality library-building.

Lean's role here: proving that SymCrypt's Rust code for ML-KEM and SHA3 matches the NIST/IETF standards it's meant to implement, with Lean proofs ensuring correctness stays intact as the code evolves. Proof artifacts: github.com/microsoft/SymC… More about Aeneas: lean-lang.org/use-cases/aene…

Lean 4.32.0 is out with 102 changes, including: The new do elaborator, which has been opt-in since 4.29, is now the default. The legacy elaborator is still available via backward.do.legacy if you need it. A new module linter framework (checks that run once per module instead of after every command), a round of fixes to mvcgen' and grind for combining verification and proof automation, and a fix that cuts Mathlib import time by roughly 10%. Full release notes: lean-lang.org/doc/reference/… #LeanLang #LeanProver #FormalVerification

"SNARKs are an ideal use-case for formal verification." A new Lean use case from @dhsorens of @ethereumfndn on ArkLib: formally verified arguments of knowledge in Lean, anchoring a growing ecosystem of @ethereum projects (VCV-io, CompPoly, Clean) for verifying these cryptographic proofs. 🔗See the ArkLib use case: lean-lang.org/use-cases/arkl…

Lean gets a mention in three articles of the @SimonsFdn 2025 annual report, released today. In the report's opening letter, Simons Foundation president David Spergel describes Lean as "a proof assistant that brings rigorous machine-verified structure for testing theorems." The report also recounts how 57 early-career researchers from around the world formalized the prime number theorem in Lean during a two-week Simons Foundation workshop in June 2025, led by @AlexKontorovich, Antoine Chambert-Loir and Heather MacBeth. 🔗 simonsfoundation.org/series/2025-an…

JUST IN: Aristotle claims the top spot in lean-eval, the Lean AI formalization leaderboard! Aristotle is getting stronger and more capable by the day, try it out for your formalization needs.

The negation of Erdos unit distance conjecture, now formalized by Aristotle You can try it for free at aristotle.harmonic.fun

Lean 4.31.0 is live. 305 changes. A consolidation-heavy release, with notable additions across the language, tools, and verification story: * while conditions in do blocks now accept any form already allowed by if, including pattern-matching variants. Existing repeat/while loops are now verifiable without source changes. * mvcgen' is a from-scratch reimplementation of mvcgen on the SymM framework, outperforming mvcgen by 100x+ on some benchmarks. It's also usable as a step inside interactive sym => proofs. * lake lint is now built in, shipping with environment linters upstreamed from Batteries and Mathlib. * Tactic configuration evaluation now runs in 6.2% of the time it previously required. Release notes: lean-lang.org/doc/reference/… #LeanLang #LeanProver #FormalVerification

Scratch-like environment for Lean 4 is coming! This is another game level😉 for learning Lean 4 youtu.be/Um_2x5wHi20?t=… #LeanLang #LeanProver #Scratch #Play #Education #Proofs #Mathematics

This week, @QuantaBks released "The Proof in the Code" by journalist Kevin Hartnett, which tells the story of the birth and rise of Lean, a proof assistant that’s shifting the way mathematicians seek truth: bit.ly/43msryr #math #science

"AI may have the answers, but mathematics has the questions." With all the recent excitement around AI for math, many start to wonder: can mathematics be automated? And what does it mean to learn and understand math? For EP5, we're thrilled to talk with Prof. Jeremy Avigad, philosopher & mathematician @CarnegieMellon and one of the early forces behind 3w. This episode features rich technical discussions on AI & mathematics, as well as many touching moments where Jeremy shares his vision for the future of mathematicians, math education, and mathematics itself. Outline: 0:00 - Teaser 1:04 - Monologue 2:50 - The Historical Landscape of AI for Mathematics 7:28 - Formalization and Computer-Aided Proof 11:56 - The Birth of the Lean Project 21:21 - Lean Blueprint, Model Training with Lean, Using Lean in Agentic Systems 29:48 - Making AI Actually Useful for Mathematicians 32:46 - How AI is Changing Mathematics 36:29 - "It's Our Mathematics, and Us Doing Mathematics" 43:04 - The Verification Gap in Human-AI Collaboration 47:46 - The Future of Math Education 52:23 - Capital, Startups, and the Mathematicians' Ecosystem 1:01:08 - Predictions