Lean

Aristotle is now on @leanprover 4.28 Happy vibe proving!

I'm at this DARPA expMath (AI for math) program kickoff and the lineup is legendary. Like, at the level of a truly historical meeting, held at a historical time. Makes me feel way more important than I actually am lol

Yesterday, John Morgan and I completed our “Covering Spaces Project”, whose goal was to formally (in Lean @leanprover, of course) prove the Fundamental Theorem of Algebra (that polynomials have complex roots) using only continuity: covering spaces, trivializations, and winding numbers, instead of the Mathlib proof that goes through complex analysis / Liouville. We started the morning about 30% through the proof, and tried playing with the Codex VS code extension (running GPT-5.4, extra high reasoning). We had already written a complete natural language blueprint (last June, at the Simons @SimonsFdn Lean workshop) and were meeting for about an hour a month, leisurely working through the details by hand (John wanted to learn the process). We’d used AI before (mostly Claude) to help move things along, but this was the first time that we met after I turned on Codex. I started by asking for Codex to give me just the formal *statement* corresponding to our next unfinished leaf in the dependency graph. It thought for 5 mins, and gave what looked like a reasonable statement. So I said, ok, can you now give a formal proof? It thought for 10 mins, and came back with a full proof, including helper lemmas. I asked it to add natural language around the helper lemmas so we’d see what they’re doing in the blueprint. It thought for 5 mins, and did it. We went on to the next statement, then the next proof, and it got those too. It continued like this for an hour or so, and we jumped to about 60% done with the project, amazing progress! I had to run to get on a train to DC (for the DARPA meeting). Once in my seat, I decided on a whim to just tell Codex to keep working on the whole file and get as far as it could, stopping to ask me for help if it got stuck. I left VS Code running in the background, while working on other things. After an hour, I remembered to check back on what progress Codex had made. It was done. And so was the project! Now I’m having Codex go through the whole proof all over again, remove all our bespoke definitions and statements, and make it clean and Mathlib-ready. Many more hours of iteration later, and it’s ready to go as a PR. Wild wild times we’re living in!

This is a huge upgrade -- Aristotle can handle much larger and more complex projects than before. Stay tuned for what's coming next! 🚢🚢🚢

@KSHartnett @leanprover @KirkusReviews Congratulations Kevin! Can't wait to read your book.

🦾Meet Aristotle Agent, the world’s first autonomous mathematician — live and currently free of charge. We designed Aristotle Agent to solve and formalize the world’s most challenging mathematical research problems. It is now: ☑️#1 in Formal Math: We’re the #1 formal math model according to ProofBench, by @ValsAI, ahead of the closest competitor by 15%. Aristotle Agent can autonomously prove/formalize for up to 24 hrs without human intervention. ☑️Fully Agentic: Give it an English problem and it will prove/formalize from scratch, or it can work and edit files directly inside your Lean project / repository. ☑️Github-ready: Aristotle agent produces repo-quality code; project leads are increasingly merging Aristotle-drafted PRs with no modifications. Now live across both web, CLI, and API. 🔥

"The Proof in the Code" received its first trade review and it's a good one. Thank you @KirkusReviews for this kind read. "Proofs, personalities, and machines collide—intriguingly—at the uneasy intersection of mathematics and computer science." Pre-orders: quantabooks.org/books/the-proo… Full review: kirkusreviews.com/book-reviews/k…

ZK proofs are headed for real-world deployment — but writing correct ZK statements is tricky. Our new post introduces zkLean, a Lean library that defines a domain specific language for specifying and formally verifying ZK statements. Read more: galois.com/articles/zklea…

Axiom Math founder @carinalhong on why math is the path to general superintelligence: “Math is the sandbox for reality. You very quickly see verifiable rewards because in math, there’s an absolute right or wrong.” “And especially when you have Lean, you can check the proof or solution step by step. You’ll be able to apply reinforcement learning in a much more efficient way.” “We have currently scaled from winning a Putnam perfect score to solving a batch of research problems that professional mathematicians find really challenging. And we also see this transfer to code verification.”

Prover correctness is becoming a central question as AI enters mathematics and software verification. New essay on why Lean's architecture is designed to survive AI pressure. leodemoura.github.io/blog/2026-3-16…

Announcing our fully open source code agent to support development in @leanprover. This has been a labor of love by our team at @MistralAI and we look forward to seeing what the #LeanProver community does with it!

mistral.ai/news/leanstral Excited to share what the formal team @MistralAI has been building for the last couple of months: an Apache 2 Lean code agent with 6B active parameters. Outperforms open models like Qwen3.5, GLM5, Kimi-K2.5, and very competitive against Claude 4.6. Use for free in Mistral-Vibe: ``` $ uv tool install mistral-vibe --upgrade $ vibe / leanstall ``` enjoy the lean mode via shift+tab!

Very interesting new challenge launched by @SAIRfoundation. Looks like a great way for researches and enthusiasts alike to contribute to the field. Happy Pi day!

Mahalo to Micky Iwamasa! 🌺 Thrilled to see him prove Knuth's Claude's cycle in Lean 4. Huge thanks for using Axle, Axiom's free Lean toolkit, to help make it happen. Seeing our tools tackle beautiful math is exactly why we build them! @leanprover @axiommathai Check it out: @mikito3/how-i-build-a-proof-on-the-prof-donald-knuths-claud-s-cycle-with-opus-4-6-and-lean4-skills-62b99a982f67" target="_blank" rel="nofollow noopener">medium.com/@mikito3/how-i…

"Autoformalized within hours of the solution being discovered." Exciting to see how fast this space is moving! 🚀

Thanks to @SAIRfoundation for hosting this great interview with Leo in celebration of Pi day!

Great job by @CarinaLHong on @CNBC at the 18 minute point onward in this episode: AI’s new power brokers: Ramp’s chief economist and the 24-yr-old taking ... youtube.com/live/hf_UlPABr… via @YouTube

@fede_intern AMO-Lean is so cool 🤯 blog.lambdaclass.com/amo-lean-towar…

Lean in the NYT this week: with a report on how startups like Axiom are using Lean to verify code "in much the same way that mathematicians prove elaborate math problems." 📰 nytimes.com/2026/03/12/tec… #leanlang #leanprover #formalverification

The hardest part of AI-generated code is no longer how to build it, but when to trust it. That's the problem @CarinaLHong set out to solve when she founded @AxiomMathAI. Her insight was that the path to verified AI reasoning runs through mathematics, specifically through formal proofs, when you need to trust the output's correctness. Train a model on that foundation, and you leverage the speed and knowledge of non-deterministic models with the confidence of formal verification. You get a system that can prove whether an answer is right, not just whether it sounds right. Last December, Axiom's system achieved a perfect score on the Putnam Exam. More recently, it demonstrated that the same reasoning transfers to code verification, catching bugs in AI-generated software with a level of rigor that manual review can't consistently match. That's the unlock: as AI writes more of the world's code, the ability to formally verify that code becomes a critical layer in how modern software gets built. Carina is one of the most technically deep founders I've worked with, and the team she's assembled around her reflects the same standard in mathematics, AI, and programming. Today's $200M raise was covered in the New York Times, and I had the pleasure of interviewing Carina on stage to a packed house at @MontySummit yesterday, both fitting backdrops for innovation that will change the world. Congratulations to her and the whole Axiom team. Read more Axiom's Series A here: ordnl.link/uGBJndu