Large-Scale Formal Proof for the Working Mathematician

Irrationality Criteria for Series by Erdős and Straus

Author(s): Angeliki Koutsoukou-Argyraki, Wenda Li
Published in: Archive of Formal Proofs, 2020
Publisher: Technical University of Munich

Undirected Graph Theory

Author(s): Chelsea Edmonds
Published in: Archive of Formal Proofs, 2022
Publisher: TUM

Szemerédi's Regularity Lemma

Author(s): Chelsea Edmonds, Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
Published in: Archive of Formal Proofs, 2021, ISSN 2150-914x
Publisher: TUM

The Nash-Williams Partition Theorem

Author(s): Lawrence C. Paulson
Published in: Archive of Formal Proofs, 2020, ISSN 2150-914x
Publisher: TUM

Grothendieck's Schemes in Algebraic Geometry

Author(s): Anthony Bordg, Lawrence Paulson, Wenda Li
Published in: Archive of Formal Proofs, 2021, ISSN 2150-914x
Publisher: TUM

Strict Omega Categories

Author(s): Anthony Bordg, Adrián Doña Mateo
Published in: Archive of Formal Proofs, 2023
Publisher: Technical University of Munich

Irrational numbers from THE BOOK

Author(s): Lawrence C Paulson
Published in: Archive of Formal Proofs, 2022, ISSN 2150-914x
Publisher: TUM

The Balog–Szemerédi–Gowers Theorem

Author(s): Angeliki Koutsoukou-Argyraki, Mantas Bakšys, Chelsea Edmonds
Published in: Archive of Formal Proofs, 2022
Publisher: TUM

Amicable Numbers

Author(s): Angeliki Koutsoukou-Argyraki
Published in: Archive of Formal Proofs, 2020, ISSN 2150-914x
Publisher: TUM

General Probabilistic Techniques for Combinatorics and the Lovasz Local Lemma

Author(s): Chelsea Edmonds
Published in: Archive of Formal Proofs, 2023
Publisher: TU Munich

Khovanskii's Theorem

Author(s): Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
Published in: Archive of Formal Proofs, 2022
Publisher: TUM

Isabelle Marries Dirac: a Library for Quantum Computation and Quantum Information

Author(s): Anthony Bordg, Hanna Lachnitt and Yijun He
Published in: Archive of Formal Proofs, 2020, ISSN 2150-914x
Publisher: TUM

Hypergraphs

Author(s): Chelsea Edmonds
Published in: Archive of Formal Proofs, 2023
Publisher: TU Munich

Wetzel's Problem and the Continuum Hypothesis

Author(s): Lawrence C Paulson
Published in: Archive of Formal Proofs, 2022, ISSN 2150-914x
Publisher: TUM

Euler's Polyhedron Formula

Author(s): Lawrence C Paulson
Published in: Archive of Formal Proofs, 2023
Publisher: TU Munich

Young's Inequality for Increasing Functions

Author(s): Lawrence C Paulson
Published in: Archive of Formal Proofs, 2022, ISSN 2150-914x
Publisher: TUM

The Plünnecke-Ruzsa Inequality

Author(s): Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
Published in: Archive of Formal Proofs, 2022, ISSN 2150-914x
Publisher: TUM

Ordinal Partitions

Author(s): Lawrence C. Paulson
Published in: Archive of Formal Proofs, 2020, ISSN 2150-914x
Publisher: TUM

Aristotle's Assertoric Syllogistic

Author(s): Angeliki Koutsoukou-Argyraki
Published in: Archive of Formal Proofs, 2020, ISSN 2150-914x
Publisher: TUM

The Transcendence of Certain Infinite Series

Author(s): Angeliki Koutsoukou-Argyraki, Wenda Li
Published in: Archive of Formal Proofs, 2019, ISSN 2150-914x
Publisher: TUM

The Prime Number Theorem

Author(s): Manuel Eberl; Lawrence C. Paulson
Published in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Publisher: TUM

Octonions

Author(s): Angeliki Koutsoukou-Argyraki
Published in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Publisher: TUM

Irrational Rapidly Convergent Series

Author(s): Angeliki Koutsoukou-Argyraki; Wenda Li
Published in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Publisher: TUM

Zermelo Fraenkel Set Theory in Higher-Order Logic

Author(s): Lawrence C. Paulson
Published in: Archive of Formal Proofs, 2019, ISSN 2150-914x
Publisher: TUM

Fourier Series

Author(s): Lawrence C. Paulson
Published in: Archive of Formal Proofs, 2019, ISSN 2150-914x
Publisher: TUM

Quaternions

Author(s): Lawrence C. Paulson
Published in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Publisher: TUM

An Isabelle/HOL formalisation of Green's Theorem

Author(s): Mohammad Abdulaziz and Lawrence C. Paulson
Published in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Publisher: TUM

The Budan-Fourier Theorem and Counting Real Roots with Multiplicity

Author(s): Wenda Li
Published in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Publisher: TUM

Evaluate Winding Numbers through Cauchy Indices

Author(s): Wenda Li
Published in: Archive of Formal Proofs, 2017, ISSN 2150-914x
Publisher: TUM

Count the Number of Complex Roots

Author(s): Wenda Li
Published in: Archive of Formal Proofs, 2017, ISSN 2150-914x
Publisher: TUM

Projective Geometry

Author(s): Anthony Bordg
Published in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Publisher: TUM

The Localization of a Commutative Ring

Author(s): Anthony Bordg
Published in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Publisher: TUM

The Theorem of Three Circles

Author(s): Fox Thomson, Wenda Li
Published in: Archive of Formal Proofs, 2021, ISSN 2150-914x
Publisher: TUM

Hypergraph Colouring Bounds

Author(s): Chelsea Edmonds, Lawrence Paulson
Published in: Archive of Formal Proofs, 2023
Publisher: TU Munich

Kneser's Theorem and the Cauchy–Davenport Theorem

Author(s): Mantas Bakšys, Angeliki Koutsoukou-Argyraki
Published in: Archive of Formal Proofs, 2022
Publisher: Technical University of Munich

Fisher's Inequality: Linear Algebraic Proof Techniques for Combinatorics

Author(s): Chelsea Edmonds, Lawrence C. Paulson
Published in: Archive of Formal Proofs, 2022, ISSN 2150-914x
Publisher: TUM

Roth's Theorem on Arithmetic Progressions

Author(s): Chelsea Edmonds, Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
Published in: Archive of Formal Proofs, 2021, ISSN 2150-914x
Publisher: TUM

Polygonal Number Theorem

Author(s): Kevin Lee, Zhengkun Ye, Angeliki Koutsoukou-Argyraki
Published in: Archive of Formal Proofs, 2023
Publisher: Technical University of Munich

The Interpretation Lifting Theorem for C-Systems

Author(s): Anthony Bordg
Published in: Theory and Applications of Categories, 2022, ISSN 1201-561X
Publisher: R. Rosebrugh

Simple Type Theory is not too Simple: Grothendieck’s Schemes Without Dependent Types

Author(s): Anthony Bordg, Lawrence Paulson, Wenda Li
Published in: Experimental Mathematics, 2022, ISSN 1058-6458
Publisher: A K Peters Ltd.
DOI: 10.1080/10586458.2022.2062073

Formalising Szemerédi’s Regularity Lemma and Roth’s Theorem on Arithmetic Progressions in Isabelle/HOL

Author(s): Chelsea Edmonds, Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
Published in: Journal of Automated Reasoning, 2023, ISSN 0168-7433
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10817-022-09650-2

Formalising Mathematics – in Praxis; A Mathematician’s First Experiences with Isabelle/HOL and the Why and How of Getting Started

Author(s): Angeliki Koutsoukou-Argyraki
Published in: Jahresbericht der Deutschen Mathematiker-Vereinigung, 2020, ISSN 0012-0456
Publisher: Springer Verlag
DOI: 10.1365/s13291-020-00221-1

A Replication Crisis in Mathematics?

Author(s): Anthony Bordg
Published in: The Mathematical Intelligencer, 2021, ISSN 0343-6993
Publisher: Springer Verlag
DOI: 10.1007/s00283-020-10037-7

An Isabelle/HOL Formalisation of Green’s Theorem

Author(s): Mohammad Abdulaziz, Lawrence C. Paulson
Published in: Journal of Automated Reasoning, 2018, ISSN 0168-7433
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10817-018-9495-z

Deciding Univariate Polynomial Problems Using Untrusted Certificates in Isabelle/HOL

Author(s): Wenda Li, Grant Olney Passmore, Lawrence C. Paulson
Published in: Journal of Automated Reasoning, Issue 62/1, 2019, Page(s) 69-91, ISSN 0168-7433
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10817-017-9424-6

Evaluating Winding Numbers and Counting Complex Roots Through Cauchy Indices in Isabelle/HOL

Author(s): Wenda Li, Lawrence C. Paulson
Published in: Journal of Automated Reasoning, 2019, ISSN 0168-7433
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10817-019-09521-3

Certified Quantum Computation in Isabelle/HOL

Author(s): Anthony Bordg, Hanna Lachnitt, Yijun He
Published in: Journal of Automated Reasoning, 2020, ISSN 0168-7433
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10817-020-09584-7

A formalised theorem in the partition calculus

Author(s): Lawrence C. Paulson
Published in: Annals of Pure and Applied Logic, 2023, ISSN 0168-0072
Publisher: Elsevier BV
DOI: 10.1016/j.apal.2023.103246

Formalizing Ordinal Partition Relations Using Isabelle/HOL

Author(s): Mirna Džamonja, Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
Published in: Experimental Mathematics, 2021, ISSN 1058-6458
Publisher: A K Peters Ltd.
DOI: 10.1080/10586458.2021.1980464

Irrationality and Transcendence Criteria for Infinite Series in Isabelle/HOL

Author(s): Angeliki Koutsoukou-Argyraki; Wenda Li; Lawrence C. Paulson
Published in: Experimental Mathematics, 2021, ISSN 1058-6458
Publisher: A K Peters Ltd.
DOI: 10.1080/10586458.2021.1980465

Ackermann’s Function in Iterative Form: A Proof Assistant Experiment

Author(s): Lawrence C. Paulson
Published in: The Bulletin of Symbolic Logic, 2021, Page(s) 1-10, ISSN 1079-8986
Publisher: Association for Symbolic Logic
DOI: 10.1017/bsl.2021.47

Formalising Fisher’s Inequality: Formal Linear Algebraic Proof Techniques in Combinatorics

Author(s): Chelsea Edmonds, Lawrence C. Paulson
Published in: 13th International Conference on Interactive Theorem Proving (ITP 2022), 2022, Page(s) 11:1-11:19
Publisher: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.itp.2022.11

LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning

Author(s): Yuhuai Wu, Markus Rabe, Wenda Li, Jimmy Ba, Roger Grosse, Christian Szegedy
Published in: ICML 2021 (International Conference on Machine Learning), 2021
Publisher: Proceedings of Machine Learning Research

Encoding Dependently-Typed Constructions into Simple Type Theory

Author(s): Anthony Bordg, Adrián Doña Mateo
Published in: Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs, 2023
Publisher: ACM
DOI: 10.1145/3573105.3575679

Thor: Wielding Hammers to Integrate Language Models and Automated Theorem Provers

Author(s): Albert Q. Jiang, Wenda Li, Szymon Tworkowski, Konrad Czechowski, Tomasz Odrzygóźdź, Piotr Miłoś, Yuhuai Wu, Mateja Jamnik
Published in: Thirty-sixth Conference on Neural Information Processing Systems (NeurIPS 2022), 2022
Publisher: Curran Associates

Formal Probabilistic Methods for Combinatorial Structures using the Lovász Local Lemma

Author(s): Chelsea Edmonds, Lawrence C. Paulson
Published in: 2024
Publisher: ACM
DOI: 10.1145/3636501.3636946

Nine Chapters of Analytic Number Theory in Isabelle/HOL

Author(s): Manuel Eberl
Published in: 10th International Conference on Interactive Theorem Proving (ITP 2019), 2019
Publisher: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
DOI: 10.4230/lipics.itp.2019.16

A Parallel Corpus of Natural Language and Isabelle Artefacts

Author(s): Anthony Bordg, Yiannos Stathopoulos, Lawrence Paulson
Published in: Conference on Artificial Intelligence and Theorem Proving AITP 2022, 2022
Publisher: AITP

IsarStep: a Benchmark for High-level Mathematical Reasoning

Author(s): Wenda Li, Lei Yu, Yuhuai Wu, Lawrence C. Paulson
Published in: International Conference on Learning Representations, 2021
Publisher: International Conference on Representation Learning

On Preserving the Computational Content of Mathematical Proofs: Toy Examples for a Formalising Strategy

Author(s): Angeliki Koutsoukou-Argyraki
Published in: Connecting with Computability, 2021, ISBN 978-3-030-80048-2
Publisher: Springer
DOI: 10.1007/978-3-030-80049-9_26

A Formalisation of the Balog–Szemerédi–Gowers Theorem in Isabelle/HOL

Author(s): Angeliki Koutsoukou-Argyraki, Mantas Bakšys, Chelsea Edmonds
Published in: Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs, 2023
Publisher: ACM
DOI: 10.1145/3573105.3575680

Counting polynomial roots in Isabelle/HOL: a formal proof of the Budan-Fourier theorem

Author(s): Wenda Li, Lawrence C. Paulson
Published in: Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2019, Issue annual, 2019, Page(s) 52-64, ISBN 9781-450362221
Publisher: ACM Press
DOI: 10.1145/3293880.3294092

Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs

Author(s): Albert Qiaochu Jiang, Sean Welleck, Jin Peng Zhou, Timothee Lacroix, Jiacheng Liu, Wenda Li, Mateja Jamnik, Guillaume Lample, Yuhuai Wu
Published in: The Eleventh International Conference on Learning Representations (ICLR 2023), 2023
Publisher: International Conference on Learning Representations

Elements of Differential Geometry in Lean: A Report for Mathematicians

Author(s): Anthony Bordg, Nicolò Cavalleri
Published in: FMM 2021 – Fifth Workshop on Formal Mathematics for Mathematicians, 2021
Publisher: Cornell University
DOI: 10.48550/arxiv.2108.00484

Algebraically Closed Fields in Isabelle/HOL

Author(s): Paulo Emílio de Vilhena, Lawrence C. Paulson
Published in: Automated Reasoning - 10th International Joint Conference, IJCAR 2020, Paris, France, July 1–4, 2020, Proceedings, Part II, Issue 12167, 2020, Page(s) 204-220, ISBN 978-3-030-51053-4
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-51054-1_12

Bayesian Ranking for Strategy Scheduling in Automated Theorem Provers

Author(s): Chaitanya Mangla, Sean Holden, Lawrence C. Paulson
Published in: Automated Reasoning. IJCAR 2022, 2022
Publisher: Springer
DOI: 10.1007/978-3-031-10769-6_33

A Modular First Formalisation of Combinatorial Design Theory

Author(s): Chelsea Edmonds, Lawrence C. Paulson
Published in: Intelligent Computer Mathematics - 14th International Conference, CICM 2021, Timisoara, Romania, July 26–31, 2021, Proceedings, Issue 12833, 2021, Page(s) 3-18, ISBN 978-3-030-81096-2
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-81097-9_1

Univalent Foundations and the UniMath Library

Author(s): Anthony Bordg
Published in: Reflections on the Foundations of Mathematics - Univalent Foundations, Set Theory and General Thoughts, 2018
Publisher: Springer

Formalising Mathematics In Simple Type Theory

Author(s): Lawrence C. Paulson
Published in: Reflections on the Foundations of Mathematics - Univalent Foundations, Set Theory and General Thoughts, 2018
Publisher: Springer

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