Mathlib
Mathlib is a large open-source mathematical formalization library based on the Lean theorem prover, covering formal proofs and definitions across multiple mathematical branches including algebra, topology, number theory, and analysis. The project is collaboratively maintained by the mathematics and computer science community, providing unified mathematical infrastructure that enables users to construct and verify rigorous mathematical proofs within the Lean environment. It includes a standardized code style guide to ensure consistency and maintainability.
Core Facts
Mathlib is a core mathematics library maintained by the Lean community; it currently contains approximately 2.5 million lines of code and includes a large number of formalized definitions and theorems spanning group theory, topology, and measure theory.
Lean's mathematics library Mathlib has accumulated more than one million lines of machine-verified mathematical theorems.
Timeline (last 90 days)
NanoLean takes approximately 11.85 seconds to check Mathlib, 17.13 seconds to verify OpenAI's Navier-Stokes formalization, and only 3.66 seconds to verify content related to the Kepler conjecture; the relevant code has been open-sourced on GitHub.
Lean 4 has gained widespread attention through the Mathlib project (a large-scale formalized mathematics library), which has formalized a large number of theorems in fields such as algebraic geometry and number theory.
Astra produced a complete formal proof written in Lean that can be compiled by machine, with the repository pinning the versions of Lean and Mathlib, passing an axiom audit, and containing no sorry placeholders.
OpenAI's Navier-Stokes proof repository is licensed under Apache 2.0, built on Lean 4.34 with the Mathlib mathematics library, and has zero sorry statements and zero errors.
Around 2022, the Mathlib project promoted by mathematicians including Kevin Buzzard incorporated a large number of modern mathematical theorems into Lean's formalization library.
This achievement builds on three centuries of accumulated mathematical work and the contributions of hundreds of Lean and Mathlib community contributors.
Lean 4 has an active community and a continuously expanding mathematics library, Mathlib, and has been used by mathematicians to formalize modern mathematical theorems.
The field of stochastic processes has long been underrepresented in Mathlib.
The Lean 4 language and its mathematics library Mathlib have formalized over 150,000 mathematical theorems and definitions, with more than 400 contributors.
Lean was developed by Leonardo de Moura at Microsoft Research, and its mathematics community Mathlib has formalized more than 150,000 mathematical theorems and lemmas.
10 more timeline events
All Facts (20)
Mathlib is a core mathematics library maintained by the Lean community; it currently contains approximately 2.5 million lines of code and includes a large number of formalized definitions and theorems spanning group theory, topology, and measure theory.
80%VerifiedLean's mathematics library Mathlib has accumulated more than one million lines of machine-verified mathematical theorems.
75%UnverifiedMathlib的设计哲学是Bourbaki风格——在最大程度的一般性上定义概念，然后再特化到常见用例
90%UnverifiedLean拥有名为Mathlib的庞大数学库，涵盖数论、代数、拓扑等众多分支
70%UnverifiedAround 2022, the Mathlib project promoted by mathematicians including Kevin Buzzard incorporated a large number of modern mathematical theorems into Lean's formalization library.
60%UnverifiedLean 4 has an active community and a continuously expanding mathematics library, Mathlib, and has been used by mathematicians to formalize modern mathematical theorems.
60%UnverifiedNanoLean takes approximately 11.85 seconds to check Mathlib, 17.13 seconds to verify OpenAI's Navier-Stokes formalization, and only 3.66 seconds to verify content related to the Kepler conjecture; the relevant code has been open-sourced on GitHub.
50%UnverifiedLean 4 has gained widespread attention through the Mathlib project (a large-scale formalized mathematics library), which has formalized a large number of theorems in fields such as algebraic geometry and number theory.
50%UnverifiedAstra produced a complete formal proof written in Lean that can be compiled by machine, with the repository pinning the versions of Lean and Mathlib, passing an axiom audit, and containing no sorry placeholders.
50%UnverifiedOpenAI's Navier-Stokes proof repository is licensed under Apache 2.0, built on Lean 4.34 with the Mathlib mathematics library, and has zero sorry statements and zero errors.
50%UnverifiedThis achievement builds on three centuries of accumulated mathematical work and the contributions of hundreds of Lean and Mathlib community contributors.
50%UnverifiedThe field of stochastic processes has long been underrepresented in Mathlib.
50%UnverifiedThe Lean 4 language and its mathematics library Mathlib have formalized over 150,000 mathematical theorems and definitions, with more than 400 contributors.
50%UnverifiedLean was developed by Leonardo de Moura at Microsoft Research, and its mathematics community Mathlib has formalized more than 150,000 mathematical theorems and lemmas.
50%UnverifiedThe Mathlib project initiated by Kevin Buzzard in 2017 built a formalized mathematics library on Lean.
50%UnverifiedLean's mathematical library Mathlib currently contains more than 150,000 theorems and definitions.
50%UnverifiedThe Fermat's Last Theorem proof project was led by Tianyi Peng, an assistant professor at Columbia University; the AI autonomously completed more than 30,000 intermediate theorems, generated approximately 13 million lines of Lean 4 code, a volume five times that of the Mathlib core library.
50%UnverifiedThe formalization of Fermat's Last Theorem relies heavily on modules in Mathlib such as elliptic curve theory and Galois representation theory.
50%UnverifiedRetrieval-Augmented Generation (RAG) can retrieve known lemmas and proof techniques most relevant to the current proof goal from mathematical literature databases such as arXiv and Mathlib.
50%UnverifiedAs of 2024, Lean's Mathlib library has formalized more than 170,000 mathematical theorems.
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