[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"project-82215":3},{"id":4,"name":5,"fullName":6,"owner":7,"repo":5,"description":8,"homepage":9,"htmlUrl":9,"language":10,"languages":9,"totalLinesOfCode":9,"stars":11,"forks":12,"watchers":13,"openIssues":14,"contributorsCount":15,"subscribersCount":15,"size":15,"stars1d":14,"stars7d":16,"stars30d":17,"stars90d":15,"forks30d":15,"starsTrendScore":18,"compositeScore":19,"rankGlobal":9,"rankLanguage":9,"license":20,"archived":21,"fork":21,"defaultBranch":22,"hasWiki":21,"hasPages":21,"topics":23,"createdAt":9,"pushedAt":9,"updatedAt":24,"readmeContent":25,"aiSummary":26,"trendingCount":15,"starSnapshotCount":15,"syncStatus":27,"lastSyncTime":28,"discoverSource":29},82215,"atlas-lean","facebookresearch\u002Fatlas-lean","facebookresearch","ATLAS Autoformalized Textbook Library At Scale",null,"Lean",228,24,4,1,0,23,65,6,4.19,"Other",false,"main",[],"2026-06-12 02:04:24","\u003Cp align=\"center\">\n  \u003Cimg src=\"assets\u002Flogo.svg\" alt=\"ATLAS Logo\" width=\"800\"\u002F>\n\u003C\u002Fp>\n\n# ATLAS - Autoformalized Textbook Library At Scale\n\nATLAS is a Lean 4 library of textbook mathematics autoformalized by LLMs:\ninformal statements and proofs translated into Lean code. It draws from\nundergraduate and graduate textbooks across analysis, algebra, geometry,\ntopology, combinatorics, probability, statistics, PDEs, number theory, and\ntheoretical computer science.\n\nThe goal of ATLAS is to provide reusable formal building blocks for future\nhuman- and machine-driven Lean formalization. This is an active effort: we are\ncontinuing to scale to more sources, curate the generated material, improve\ncoverage and maintainability, and move the library closer to Mathlib\nconventions.\n\nATLAS was generated with\n[AutoformBot](https:\u002F\u002Fgithub.com\u002Ffacebookresearch\u002Fautoform-bot), our\nautoformalization pipeline.\n\n## Links\n\n- Companion paper: [Formalizing Mathematics at Scale](https:\u002F\u002Farxiv.org\u002Fabs\u002F2605.29955)\n- Formalization harness: \u003Chttps:\u002F\u002Fgithub.com\u002Ffacebookresearch\u002Fautoform-bot>\n- Earlier related work: [Formalization of Algebraic Combinatorics](https:\u002F\u002Fgithub.com\u002Ffaabian\u002Falgebraic-combinatorics)\n\n## Library Data\n\nEach book directory under `Atlas\u002F` contains:\n\n- Lean source files for the generated definitions, statements, and proofs.\n- `targets.yaml`, listing the textbook statements selected for\n  formalization.\n- `report.json`, containing automated evaluation results for matched Lean\n  declarations, including faithfulness, proof-integrity, and code-quality\n  scores.\n\n## Visualizer\n\nA visualizer is provided at https:\u002F\u002Frammalahmad.github.io\u002Fatlas\u002F. It allows\nusers to browse ATLAS, compare informal\nstatements with their Lean formalizations, inspect logical dependency graphs\nbetween results, and extract the Lean code needed to state a selected theorem.\n\n![ATLAS visualizer](assets\u002Fvisualizer.png)\n\n## Status and Contributions\n\nATLAS is an ongoing, machine-generated extension effort rather than a finished\nproduct. We are actively working on scaling the corpus, curating\nthe generated code, formalizing remaining statements, and improving idiomatic\nMathlib reuse. External contributions are welcome!\n\nTo build the full library with the pinned Lean and Mathlib versions, run:\n\n```bash\nlake build\n```\n\n## Statistics (May 2026)\n**26** books · **630,999** lines of code · **483,917** lines of Lean code (excl. comments\u002Fblanks) · **46,203** declarations · **42,837** proved (92.7%) · **2,855** \u002F **4,007** statements formalized (71.3%) · **183,157M** tokens\n\n| Book | Target Statements | Formalized | % Formalized | Lines of Code | Lines of Lean | Declarations | Proved | % Proved | Tokens (M) |\n|------|------------------:|-----------:|-------------:|--------------:|--------------:|-------------:|-------:|---------:|-----------:|\n| [AlgebraNotes](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002Fres-18-011-algebra-i-student-notes-fall-2021\u002F) | 176 | 151 | 85.8% | 5,037 | 4,409 | 274 | 261 | 95.3% | 1,962.99 |\n| [AlgebraicCombinatorics](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-318-topics-in-algebraic-combinatorics-spring-2006\u002F) | 39 | 37 | 94.9% | 10,695 | 9,343 | 737 | 734 | 99.6% | 1,440.73 |\n| [AlgebraicGeometryI](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-725-algebraic-geometry-fall-2015\u002F) | 186 | 112 | 60.2% | 40,678 | 27,393 | 4,499 | 4,210 | 93.6% | 7,629.26 |\n| [AlgebraicTopologyI](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-905-algebraic-topology-i-fall-2016\u002F) | 171 | 110 | 64.3% | 29,154 | 20,142 | 2,416 | 2,063 | 85.4% | 10,323.27 |\n| [AnAlgorithmistsToolkit](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-409-topics-in-theoretical-computer-science-an-algorithmists-toolkit-fall-2009\u002F) | 158 | 131 | 82.9% | 9,656 | 8,234 | 712 | 668 | 93.8% | 2,004.00 |\n| [ArithmeticGeometry](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-782-introduction-to-arithmetic-geometry-fall-2013\u002F) | 335 | 266 | 79.4% | 39,257 | 29,573 | 3,047 | 2,861 | 93.9% | 11,100.62 |\n| [BooleanFunctions](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-218-topics-in-combinatorics-analysis-of-boolean-functions-spring-2021\u002F) | 108 | 44 | 40.7% | 9,516 | 7,949 | 667 | 614 | 92.1% | 2,327.49 |\n| [Buildings](https:\u002F\u002Fwww-users.cse.umn.edu\u002F~garrett\u002Fm\u002Fbuildings\u002Fbook.pdf) | 74 | 44 | 59.5% | 64,383 | 48,809 | 4,345 | 4,247 | 97.7% | 20,442.93 |\n| [CombinatorialOptimization](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-433-combinatorial-optimization-fall-2003\u002F) | 36 | 22 | 61.1% | 8,908 | 7,934 | 428 | 414 | 96.7% | 2,475.65 |\n| [ComplexVariables](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-112-functions-of-a-complex-variable-fall-2008\u002F) | 38 | 37 | 97.4% | 7,231 | 6,225 | 285 | 280 | 98.2% | 1,250.91 |\n| [DifferentialAnalysis](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-155-differential-analysis-fall-2004\u002F) | 113 | 88 | 77.9% | 31,302 | 23,713 | 1,634 | 1,506 | 92.2% | 11,743.27 |\n| [DifferentialGeometry](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-950-differential-geometry-fall-2008\u002F) | 147 | 112 | 76.2% | 10,592 | 8,942 | 888 | 781 | 88.0% | 1,933.97 |\n| [EllipticCurves](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-783-elliptic-curves-spring-2021\u002F) | 360 | 212 | 58.9% | 32,819 | 22,316 | 3,483 | 2,981 | 85.6% | 11,058.00 |\n| [FourierAnalysis](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-103-fourier-analysis-fall-2013\u002F) | 38 | 34 | 89.5% | 7,943 | 6,671 | 373 | 359 | 96.2% | 1,185.90 |\n| [GeometryOfManifolds](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-966-geometry-of-manifolds-spring-2007\u002F) | 72 | 40 | 55.6% | 22,686 | 16,408 | 3,251 | 3,098 | 95.3% | 6,864.93 |\n| [HighDimensionalStatistics](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-s997-high-dimensional-statistics-spring-2015\u002F) | 73 | 65 | 89.0% | 39,656 | 31,715 | 1,564 | 1,518 | 97.1% | 975.36 |\n| [IntroductionToFunctionalAnalysis](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-102-introduction-to-functional-analysis-spring-2021\u002F) | 72 | 68 | 94.4% | 2,709 | 2,006 | 113 | 109 | 96.5% | 553.64 |\n| [IntroductionToPartialDifferentialEquations](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-152-introduction-to-partial-differential-equations-fall-2011\u002F) | 105 | 86 | 81.9% | 27,666 | 20,740 | 1,585 | 1,414 | 89.2% | 2,972.23 |\n| [LieGroups](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-757-representations-of-lie-groups-fall-2023\u002F) | 185 | 74 | 40.0% | 60,285 | 50,594 | 4,219 | 3,814 | 90.4% | 45,384.33 |\n| [NumberTheoryI](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-785-number-theory-i-fall-2021\u002F) | 576 | 460 | 79.9% | 64,958 | 54,760 | 3,764 | 3,591 | 95.4% | 15,424.36 |\n| [ProbabilisticMethodsInCombinatorics](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-226-probabilistic-methods-in-combinatorics-fall-2022\u002F) | 210 | 109 | 51.9% | 20,555 | 15,604 | 1,272 | 1,089 | 85.6% | 2,720.15 |\n| [ProjectionTheory](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-156-projection-theory-spring-2025\u002F) | 111 | 73 | 65.8% | 13,357 | 9,672 | 979 | 871 | 89.0% | 2,678.00 |\n| [RealAnalysis](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-100a-real-analysis-fall-2020\u002F) | 177 | 175 | 98.9% | 2,886 | 2,224 | 149 | 147 | 98.7% | 585.64 |\n| [TensorCategories](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-769-topics-in-lie-theory-tensor-categories-spring-2009\u002F) | 229 | 137 | 59.8% | 42,812 | 29,729 | 3,373 | 3,176 | 94.2% | 11,338.45 |\n| [TheoryOfComputation](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-404j-theory-of-computation-fall-2020\u002F) | 118 | 84 | 71.2% | 15,094 | 10,581 | 1,553 | 1,482 | 95.4% | 3,580.36 |\n| [TheoryOfProbability](https:\u002F\u002Focw.mit.edu\u002Fcourses\u002F18-175-theory-of-probability-spring-2014\u002F) | 100 | 84 | 84.0% | 11,164 | 8,231 | 593 | 549 | 92.6% | 3,200.61 |\n| **Total** | **4,007** | **2,855** | **71.3%** | **630,999** | **483,917** | **46,203** | **42,837** | **92.7%** | **183,157** |\n\n## Contributors\n\nThe initial ATLAS effort was led by Ahmad Rammal, Niket Patel, Fabian Gloeckle, Amaury Hayat, Julia Kempe, Remi Munos, Charles Arnal, and Vivien Cabannes.\n\n## Citation\n\nIf you find this work useful, please cite our paper:\n\n```bibtex\n@misc{rammal2026formalizingmathematicsscale,\n      title={Formalizing Mathematics at Scale}, \n      author={Ahmad Rammal and Niket Patel and Fabian Gloeckle and Amaury Hayat and Julia Kempe and Remi Munos and Charles Arnal and Vivien Cabannes},\n      year={2026},\n      eprint={2605.29955},\n      archivePrefix={arXiv},\n      primaryClass={cs.AI},\n      url={https:\u002F\u002Farxiv.org\u002Fabs\u002F2605.29955}, \n}\n```\n","ATLAS 是一个由大型语言模型自动形式化的数学教科书库，涵盖了分析、代数、几何、拓扑、组合数学、概率论、统计学、偏微分方程、数论和理论计算机科学等领域的本科及研究生教材内容。该项目使用 Lean 4 语言将非正式的数学陈述和证明转化为可复用的形式化代码，旨在为未来的自动化与人工形式化工作提供基础构件。ATLAS 适合于需要高精度数学形式化验证的研究场景，如数学定理证明、算法正确性验证以及教育领域中对复杂数学概念的理解与教学。此外，项目还提供了一个可视化工具，便于用户浏览库中的内容，并比较非正式文本与其对应的 Lean 形式化版本。",2,"2026-06-11 04:08:05","CREATED_QUERY"]