Lean @leanprover

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

Alex Kontorovich @AlexKontorovich

a week ago

Oh and Kim Morrison used Claude + Aristotle + Codex to formalize the negation of the Erdos unit distance conjecture: github.com/kim-em/erdos-u… It's nice to see that this was built on top of PNT+; so despite the fact that we haven't been able to upstream it to Mathlib (the Residue

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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

Did you miss the panels marking the launch of The Proof in the Code, @KSHartnett's book on the development of Lean and Mathlib? Both conversations are now up to watch. The Mathematicians, with Johan Commelin, Kevin Buzzard, and @AlexKontorovich . The Builders, with @leodemoura, Sebastian Ullrich (@derKha), and Jeremy Avigad. Watch both: youtube.com/playlist?list=… #LeanLang #LeanProver #FormalMathematics #SoftwareVerification

I've been telling people for 25 years that Jane Street is not interested in formal methods. No more! And we're actively hiring to form a new formal methods team!

Lean is software that allows mathematical proofs to be written and checked as computer code. Mathematician Terence Tao uses it as a part of his collaborative approach to solving complex mathematical problems. quantamagazine.org/how-terry-tao-…

@KSHartnett The Proof in the Code: The Mathematicians panel is going live in 15 minutes!

The first of two panels for the launch of The Proof in the Code, @KSHartnett 's new book on the development of Lean and Mathlib. The Mathematicians. Thursday, June 11, 5pm UTC: Johan Commelin, Director of the Mathlib Initiative and assistant professor at Utrecht University Kevin Buzzard, Professor of Pure Mathematics at Imperial College London, who created the Natural Number Game and leads the effort to formalize Fermat's Last Theorem in Lean @AlexKontorovich , Distinguished Professor of Mathematics at Rutgers University, award-winning mathematical communicator, and maintainer of the PrimeNumberTheoremAnd project They discuss what it means to formalize mathematics in Lean and how computer verification is changing the way mathematicians collaborate, build trust, and decide what counts as proof. Register: forms.gle/w16jkmsMqB2gF8…

Flying now to Jerusalem, to give a mini-workshop on Lean for Mathematicians @leanprover at the Einstein Institute @HebrewU. mathematics.huji.ac.il/event/lean-wor… (Unfortunately the workshop is oversubscribed already, with ~80 participants, so they're not taking more.)

In his new book, "The Proof in the Code: How a Truth Machine Is Transforming Math and AI," Kevin Hartnett (@KSHartnett) tells the definitive story of computer program Lean in an effort to answer a longstanding question: Can computers reveal universal truths? Out today from @QuantaBks: bit.ly/43X5To1 #science #math

To simultaneously prove a theorem while formalizing it a link is needed between definitions, lemmas, propositions, theorems etc. in latex with corresponding declarations in lean. To do this I created a tool called span: github.com/pachterlab/span 2/

Terry Tao has become the foremost proponent of AI and Lean for math research. Today, @QuantaMagazine is running an excerpt from my book, "The Proof in the Code," about a project where Tao made the leap into this new way of working—his unconventional 2024 'equational theories' effort to map relationships between arithmetic laws.

Software like Lean, which allows mathematical proofs to be written and checked as computer code, could usher in a new, more collaborative era of problem solving. One of its most prominent supporters is mathematician Terence Tao. quantamagazine.org/how-terry-tao-…

SAIR Playground for the Modular Arithmetic Challenge: playground.sair.foundation/playground/mod…

The 2nd SAIR Competition is now open: the Modular Arithmetic Challenge. Can a neural network learn to compute (a × b) mod p for large numbers? Easy for standard algorithms, but a hard test of whether neural networks can generalize the computation. Join the SAIR competition: competition.sair.foundation/competitions/m…

The Proof in the Code, @KSHartnett 's new book on the development of Lean and Mathlib, is out today. quantabooks.org/books/the-proo… To mark the launch, a two-part online panel series with the author, both 5pm UTC: The Mathematicians, June 11, with Johan Commelin, Kevin Buzzard, and Alex Kontorovich. Register: forms.gle/w16jkmsMqB2gF8… The Builders, June 12, with Leo de Moura, Sebastian Ullrich, and Jeremy Avigad. Register: forms.gle/PsxPkq3x2pESXQ…

The second of two panels for the launch of The Proof in the Code, Kevin Hartnett's (@KSHartnett) new book on the development of Lean and Mathlib. The Builders. Friday, June 12, 5pm UTC. Joining Kevin Hartnett: Leo de Moura (@leodemoura), creator of Lean, co-founder and Chief Architect at the Lean FRO Sebastian Ullrich (@derKha), co-founder and Head of Engineering at the Lean FRO Jeremy Avigad, Professor of Philosophy and Mathematical Sciences at Carnegie Mellon University, Director of the Hoskinson Center for Formal Mathematics, and Directory of the Institute for Computer-Aided Reasoning in Mathematics They talk about Lean from the inside: its origins, its design, and where it's headed, and the long road from a research project to a system now used across mathematics and AI. Register: forms.gle/PsxPkq3x2pESXQ…