Research in History and Philosophy of Mathematics

1. Front Matter

   Pages i-xiii

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2. The Definitions and Theorems of the Spherics of Theodosios

   • R. S. D. Thomas

   Pages 1-21

3. John Marsh and the Curious World of Decimal Arithmetic

   • Duncan J. Melville

   Pages 23-42

4. Euler’s Discovery and Resolution of D’Alembert’s Paradox

   • William W. Hackborn

   Pages 43-57

5. Euler’s Work on the Surface Area of Scalene Cones

   • Daniel J. Curtin

   Pages 59-67

6. What Mathematics Rittenhouse Knew

   • Marion W. Alexander

   Pages 69-89

7. John Playfair’s Approach to “the Practical Parts of the Mathematics”

   • Amy Ackerberg-Hastings

   Pages 91-107

8. Monge’s Descriptive Geometry in Three Examples

   • Christopher Baltus

   Pages 109-120

9. 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

10. 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

11. Boltzmann et Vlasov

    • Roger Godard

    Pages 157-166

12. Takeuti’s Well-Ordering Proof: Finitistically Fine?

    • Eamon Darnell, Aaron Thomas-Bolduc

    Pages 167-180

13. A Non-error Theory Approach to Mathematical Fictionalism

    • Phil Bériault

    Pages 181-189

14. Mathematical Problem Choice and the Contact of Minds

    • Zoe Ashton

    Pages 191-203

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.  

• History of Mathematics
• Philosophy of Mathematics
• Theodosios
• John Marsh
• d'Alembert's Paradox
• Scalene Cone
• David Rittenhouse
• John Playfair
• Gaspard Monge
• Adolph Mayer

     

• Mathematical, Information and Computer Sciences, Point Loma Nazare University, San Diego, USA

  Maria Zack

• Department of Philosophy, McGill University, Montreal, Canada

  Dirk Schlimm

  

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