Research in History and Philosophy of Mathematics: The CSHPM 2022 Volume (Annals of the Canadian Society for History and Philosophy of Mathematics/ ... et de philosophie des mathmatiques)

This volume contains 8 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. Some of the topics explored include: A way to rethink how logic is taught to philosophy students by using a rejuvenated version of the Aristotelian idea of an argument schema A quantitative approach using data from Wikipedia to study collaboration between nineteenth-century British mathematicians The depiction and perception of Émilie Du Châtelet’s scientific contributions as viewed through the frontispieces designed for books written by or connected to her A study of the Cambridge Women’s Research Club, a place where British women were able to participate in scholarly scientific discourse in the middle of the twentieth century An examination of the research and writing process of mathematicians by looking at their drafts and other preparatory notes A global history of al-Khwārāzmī’s Kitāb al-jabr wa-l-muqābala as obtained by tracing its reception through numerous translations and commentaries 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 Logical Methodology and the Structure of Logic Syllabi 1 The Constitutive Promise of Logic 2 The Promise of Logic in the Liberal Arts Tradition 3 Premature Attempts at Rigour in Logic 4 Revisiting the Traditional Methodology of Formal Logic References Ancient Greek Mathematical Proofs and Metareasoning 1 Introduction 2 Hippocrates of Chios' Proof of the Quadrature of a Lune 3 Mathematical Proofs as a Form of (Guided) Intentional Reasoning 4 Two Euclidean Proofs 5 Conclusion References Wikipedia and the Portrayal of Collaborative Networks of Nineteenth-Century British Mathematicians 1 Introduction 2 Motivation 2.1 Nineteenth Century 2.2 Wikipedia 2.3 Comparison Groups 3 Method 4 Results 4.1 Average Number of Mentions per 1000 Characters Across Categories 4.2 Length of Articles 4.3 Commonly Linked Mathematicians 4.3.1 Performance of Methods 5 Conclusion References Mathematical and Philosophical Imagery in Original Sources Related to Émilie du Châtelet 1 Introduction 2 Émilie du Châtelet 3 Algarotti 4 Voltaire 5 Institutions de Physique 6 Translating Newton's Principia 7 Conclusion References Cambridge Women's Research Club 1 Background 2 Foundations 3 Lectures 4 Operations 5 Decline 6 Conclusion References Going to the Source(s) of Sources in Mathematicians' Drafts 1 Introduction 2 Written Tools and Artefacts for Research 2.1 Cartan's Notational Changes 2.2 A Very Cursory Glimpse in Leibniz's Drafts 2.3 Computations and Experimentations 3 Processes of Redaction 3.1 Dedekind's Terminological Fine-Tuning in Was sind und was sollen die Zahlen? 3.1.1 In 1872–1877 3.1.2 In 1887 3.2 Some Additional Examples 4 Concluding Remarks References Two Textbooks on Vector Analysis: Gibbs and Runge 1 Introduction 2 Brief Biographical Sketch of Gibbs 3 Brief Biographical Sketch of Runge 4 The Scientific Styles of Gibbs-Wilson and of Runge 5 Scalars and Vectors 5.1 Chapters I and II of Gibbs-Wilson 5.2 Runge and the Exterior Product 6 The Vector Operators 6.1 Chapter III of Gibbs-Wilson 6.2 The Gibbs and Wilson Integral Calculus of Vectors 6.3 Runge: The Differentiation and Integration of Vectors 7 Tensor Analysis: Runge 8 Conclusion References The Legacy of Al-Khwārazmī in History of Algebra 1 Introduction 2 Life and Works 3 The Scope and Limits of Arabic Algebra 4 Diophantus and Abū Kāmil 5 Oral Traditions, Books, and al-Khwārazmī's Innovations 6 Al-Khwārazmī's Influence on Arabic Algebra 7 A New Beginning: Al-Khwārazmī and Abū Kāmil in Latin 8 Al-Khwārazmī's Influence on Medieval Italian Algebra 9 Al-Khwārazmī and Abū Kāmil in Hebrew 10 Latin Manuscripts in Germany 11 Printed Latin and Vernacular Algebra in the Sixteenth Century 12 Censuring the Middle Ages 13 Al-Khwārazmī's Swan Song: Adriaan van Roomen's Commentary 14 The Last Echoes from the Textbook Tradition and the Beginning of the Historical al-Khwārazmī 15 Summary Bibliography