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 4 has an active community and a continuously expanding mathematics library, Mathlib, and has been used by mathematicians to formalize modern mathematical theorems.
Lean is both a programming language and an interactive theorem prover, in which users write mathematical propositions in a formal language and have them verified step by step by the machine.
Timeline (last 90 days)
Mathlib is developed collaboratively by volunteers worldwide, using continuous integration and code review to ensure quality.
Lean 4 and its accompanying mathematics library Mathlib have become the de facto standard for formalized mathematics, and benchmarks such as arXivLean and PutnamBench are built on top of them.
The dependency graph of LeanGraphSearch comes from Mathlib itself, requires no additional annotation, and its propagation and re-ranking are relatively lightweight, so it has scalability potential.
LeanGraphSearch is a graph retrieval method for Lean 4 formal theorem proving that, by constructing a graph from Mathlib's forward dependencies, first performs semantic matching to locate anchor points, then uses a graph ranking algorithm to propagate relevance along dependency edges, and finally re-ranks the candidate set.
Lean was initiated by Microsoft Research and in recent years has become a mainstream choice thanks to the rapid expansion of the Mathlib mathematics library; Coq has a long history and is widely used in the field of formal verification.
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.
15 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 4 has an active community and a continuously expanding mathematics library, Mathlib, and has been used by mathematicians to formalize modern mathematical theorems.
75%VerifiedLean is both a programming language and an interactive theorem prover, in which users write mathematical propositions in a formal language and have them verified step by step by the machine.
75%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%UnverifiedMathlib is developed collaboratively by volunteers worldwide, using continuous integration and code review to ensure quality.
50%UnverifiedLean 4 and its accompanying mathematics library Mathlib have become the de facto standard for formalized mathematics, and benchmarks such as arXivLean and PutnamBench are built on top of them.
50%UnverifiedLeanGraphSearch is a graph retrieval method for Lean 4 formal theorem proving that, by constructing a graph from Mathlib's forward dependencies, first performs semantic matching to locate anchor points, then uses a graph ranking algorithm to propagate relevance along dependency edges, and finally re-ranks the candidate set.
50%UnverifiedThe dependency graph of LeanGraphSearch comes from Mathlib itself, requires no additional annotation, and its propagation and re-ranking are relatively lightweight, so it has scalability potential.
50%UnverifiedLean was initiated by Microsoft Research and in recent years has become a mainstream choice thanks to the rapid expansion of the Mathlib mathematics library; Coq has a long history and is widely used in the field of formal verification.
50%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.
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