Research in History and Philosophy of Mathematics: The CSHPM 2021 Volume

Description

This volume contains eighteen papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics, as well as the teaching of the history of mathematics.   Some of the topics explored include Arabic editions of Euclid’s Elements from the thirteenth century and their role in the assimilation of Euclidean geometry into the Islamic intellectual traditionPortuguese sixteenth century recreational mathematics as found in the Tratado de Prática Darysmetica A Cambridge correspondence course in arithmetic for women in England in the late nineteenth centuryThe mathematical interests of the famous Egyptologist Thomas Eric (T. E.) Peet The history of Zentralblatt für Mathematik and Mathematical Reviews and their role in creating a publishing infrastructure for a global mathematical literatureThe use of Latin squares for agricultural crop experiments at the Rothamsted Experimental StationThe many contributions of women to the advancement of computing techniques at the Cavendish Laboratory at the University of Cambridge in the 1960s The volume concludes with two short plays, one set in Ancient Mesopotamia and the other in Ancient Egypt, that are well suited for use in the mathematics classroom. Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics. Preface Editorial Board Contents Contributors A Tenth-Century Mathematical Glossary 1 Introduction 2 On Ratios and Definitions: A Title 3 Memorable Introduction to the Art of Arithmetic: Another Title 4 On What Should Be Memorized Before the Arithmetic Book: The Original Title 5 Terms and Definitions 5.1 Number per se (Definitions 1–12) 5.2 Plane and Solid Numbers (Definitions 13–25) 5.3 Number Relations (Definitions 26–36) 5.4 Proportion (37–58) 6 The Book of Arithmetic 7 Conclusion A.1 Appendix: English Translation of Text and Original Text References Euclid in Marāgha: The Age of the Taḥrīr 1 Introduction 2 Essential Background: Transmission of the Elements from Greek to Arabic 3 The Taḥrīr of Naṣīr al-Dīn al-Ṭūsī 3.1 The Author 3.2 General Characteristics of al-Ṭūsī's Taḥrīr 3.3 Historical Influence 3.3.1 Foundation of the Persian Transmission of the Elements 3.3.2 Calcutta School Book Society Edition of Euclid 3.3.3 The Commentary on Book I by Muḥamad Barakat 4 The Taḥrīr of Muḥya al-Dīn al-Maghribī 4.1 The Author 4.2 General Characteristics of the Taḥrīr 4.3 Influence 5 The Pseudo-Ṭūsī Taḥrīr 5.1 The Author 5.2 General Characteristics of the Taḥrīr 5.3 Influence 6 Concluding Thoughts 6.1 Internal Cross-Referencing and Mathematical Pedagogy 6.2 Printing Euclidean Geometry and Ottoman Madrasa Education 6.3 Geometrical Compilations and Mathematical Pedagogy Manuscripts Consulted References The Recreational Problems of Tratado de Prática Darysmetica by Gaspar Nicolas, 1519 1 The Tratado in Its Context 2 The Organisation of the Tratado 3 A Few Selected Problems 3.1 A Man and Three Saints 3.2 Generating Squares 4 A Broken Weight 5 Equal Sales 5.1 Interrupted Game 5.2 Bags 6 Conclusion References The Mathematics of Polemic in John Napier's Plaine Discovery 1 Introduction 2 Context 3 Mathematics of Prophecy 4 Seals, Trumpets and Vials 5 Jubilees and the End Times 6 Notes on Table 2 7 Critical Observations 8 Napier's Legacy in Scholarship 9 Closing Remarks References Euler's Series for Sine and Cosine. An Interpretation in Nonstandard Analysis 1 Introduction 2 Forerunners 2.1 Ptolemy 2.2 Newton 2.3 Ptolemy–Newton–Euler 3 Setting the Stage: Trigonometry 4 The Crucial Move 4.1 From Finite to Infinite 4.2 Infinite and Infinitesimal Numbers 4.3 Infinite Series vs Hyperfinite Sums 4.4 Extending Trigonometric Functions 4.5 The Revised Proof 5 Nonstandard Analysis 5.1 The Basics of Ordered Field Theory 5.2 Archimedean Axiom 5.3 Real Numbers 5.4 Hyperreals 5.5 Infinitesimals, Infinite Numbers, and Finite Numbers 5.6 Binomial Coefficients 5.7 *Maps 5.8 Hyperfinite Sums 6 Infinitesimals and Infinite Numbers in Institutiones calculi differentialis 6.1 Three Kinds of Quantities: Infinite Numbers 6.2 Infinitesimals 6.3 Two Ways of Comparing Zeros 6.4 Arithmetic of Infinitesimals 6.5 Infinitesimals and Infinite Numbers 6.6 Assignable Numbers and ΩΨ Products 7 Summary References Agnesi vs. Colson: Did Location Matter? 1 Introduction 2 Maria Gaetana Agnesi 3 The Reverend John Colson 4 The Witch of Agnesi 5 The Calculus Controversy 6 Comparison of the Italian and English Versions 7 Conclusion References The Limits of Understanding and the Understanding of Limits: David Hume's Mathematical Sources 1 The `Paradoxes' 2 The Port Royal Logic 3 Leibniz 4 Malézieu 5 Hume References Analysis and Synthesis in Robert Simson's The Elements of Euclid 1 Introduction 2 Robert Simson and The Elements of Euclid 3 Analysis and Synthesis as Methods of Proof 4 Analysis and Synthesis as Mathematical Styles 5 Analysis and Synthesis as Pedagogical Approaches 6 Conclusion References Thomas Archer Hirst: Mathematician Xtravagant 1 Introduction 2 Yorkshire 3 Marburg, Germany 4 Göttingen and Berlin 5 Queenwood College, Hampshire 6 France and Italy 7 Return to London References A Cambridge Correspondence Course in Arithmetic for Women 1 Introduction 2 Correspondence Courses for Women 3 Hudson's Correspondence Course in Arithmetic 4 Conclusion Appendix References T. E. Peet, a Mathematician Among Egyptologists? 1 Introduction 2 Thomas Eric Peet 3 Peet the Mathematician 4 Correspondence with Mathematicians 5 Ancient Egyptian Mathematicians? 6 Concluding Remarks Archival Sources References Placing a Global Mathematical Literature 1 The Entire World Literature of Mathematics 2 What Literatures Do 3 Placing Review Journals 4 Moving Review Journals 5 Indexing Reviewers 6 Instructing Reviewers 7 Conclusion: Situating Reviews References *12ptArchives *12ptPublished Sources Latin Squares at Rothamsted in the Time of Fisher and Yates 1 Fisher and Yates at Rothamsted 1.1 People and Place 1.2 Basics of Design of Experiments 2 Latin Squares 2.1 What Is a Latin Square? 2.2 Orthogonal Latin Squares 2.3 Mutually Orthogonal Latin Squares 2.4 A Catalogue of Sets of Mutually Orthogonal Latin Squares 2.5 Randomization 3 Statistical Tables 3.1 The Need for Tables 3.2 What Do the Tables Cover? 3.3 A Catalogue of Latin Squares 3.4 A Catalogue of Complete Sets of Mutually Orthogonal Latin Squares 4 Technical Communication 35 4.1 Brief Overview 4.2 Explanation of Mutually Orthogonal Latin Squares 5 Some Later Developments 5.1 Inequivalent Complete Sets 5.2 Explanation Using Abelian Groups References Les équations différentielles ordinaires « raides » et les méthodes robustes : une approche historique 1 Introduction 2 Les premières méthodes numériques à un seul pas : Euler et Cauchy 3 Le triomphe des méthodes à un seul pas et celles à pas multiples 4 La théorie des erreurs de troncature locales et globales 4.1 Le début 4.2 Cauchy et Lipschitz sur la théorie des erreurs locales et globales 5 Existence and unicité 6 Richardson et le contrôle du pas 7 Stabilité, problèmes bien posés, et condition 8 Les équations différentielles « raides » et les méthodes robustes : les outils mathématiques Références The Cavendish Computors: The Women Working in Scientific Computing for Radio Astronomy 1 Introduction 2 The Women in Radio Astronomy Computing 3 The First Forays into Scientific Computing 4 Earth Rotation Aperture Synthesis and the Steady State Hypothesis 4.1 The Steady State Hypothesis 5 A Radio Survey of the North Polar Region 6 Discussion 7 Conclusion References The Algebra Project, Feature Talk, and the History of Mathematics 1 Algebra as a Civil Rights Issue 2 The Algebra Project as a Curricular Process 3 Feature Talk and the History of Mathematics References Corrupt Land Inspectors: Solving Equations with Picture-Language in Ancient Mesopotamia—A Dialogue 1 Introduction and Programme Notes 2 The Play: Solving Equations with Picture-Language Curtain Rises References Entrance into All Obscure Secrets: A Workshop on Bringing Episodes in the History of Mathematics to Life in the Classroom by Means of Theatre, Incorporating a Short Play Set in an Ancient Egyptian Scribal School 1 Introduction 2 Why a Mathematical-Historical Play? 3 Welcome and Synopsis 4 The Play SLIDE 1 SLIDE 2 SLIDE 3 SLIDE 4 Part 2 SLIDE 5 SLIDE 6 SLIDE 7 SLIDE 8 SLIDE 9 SLIDE 10 5 Discussion 6 Concluding Remarks References