Research in History and Philosophy of Mathematics: The CSHPM 2017 Annual Meeting in Toronto, Ontario (Proceedings of the Canadian Society for History and ... et de philosophie des mathématiques)

This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. A series of chapters all set in the eighteenth century consider topics such as John Marsh’s techniques for the computation of decimal fractions, Euler’s efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge’s use of descriptive geometry. After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov’s adaptation of the Boltzmann equation to ionized gases. The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng’s defenses of mathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue. Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics. This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d'Histoire et de Philosophie des Mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. A series of chapters all set in the eighteenth century consider topics such as John Marsh's techniques for the computation of decimal fractions, Euler's efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge's use of descriptive geometry. After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov's adaptation of the Boltzmann equation to ionized gases. The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng's defenses of mathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue. Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.-- Provided by publisher Front Matter ....Pages i-xiii The Definitions and Theorems of the Spherics of Theodosios (R. S. D. Thomas)....Pages 1-21 John Marsh and the Curious World of Decimal Arithmetic (Duncan J. Melville)....Pages 23-42 Euler’s Discovery and Resolution of D’Alembert’s Paradox (William W. Hackborn)....Pages 43-57 Euler’s Work on the Surface Area of Scalene Cones (Daniel J. Curtin)....Pages 59-67 What Mathematics Rittenhouse Knew (Marion W. Alexander)....Pages 69-89 John Playfair’s Approach to “the Practical Parts of the Mathematics” (Amy Ackerberg-Hastings)....Pages 91-107 Monge’s Descriptive Geometry in Three Examples (Christopher Baltus)....Pages 109-120 The Culture of Research Mathematics in 1860s Prussia: Adolph Mayer and the Theory of the Second Variation in the Calculus of Variations (Craig Fraser)....Pages 121-140 The Axiom of Choice as Paradigm Shift: The Case for the Distinction Between the Ontological and the Methodological Crisis in the Foundations of Mathematics (Valérie Lynn Therrien)....Pages 141-155 Boltzmann et Vlasov (Roger Godard)....Pages 157-166 Takeuti’s Well-Ordering Proof: Finitistically Fine? (Eamon Darnell, Aaron Thomas-Bolduc)....Pages 167-180 A Non-error Theory Approach to Mathematical Fictionalism (Phil Bériault)....Pages 181-189 Mathematical Problem Choice and the Contact of Minds (Zoe Ashton)....Pages 191-203