Research in History and Philosophy of Mathematics

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This volume features thirteen papers from the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics, held at Ryerson University in Toronto. It presents rigorously reviewed scholarship on a diverse range of topics in the history and philosophy of mathematics, spanning from Ancient Greece to the twentieth century. Several chapters focus on the eighteenth century, exploring John Marsh’s techniques for computing decimal fractions, Euler’s work on the surface area of scalene cones, John Playfair’s lesser-known contributions to practical mathematics, and Monge’s application of descriptive geometry. After a brief exploration of the culture of research mathematics in 1860s Prussia, the discussion shifts to the twentieth century, examining the historical context of the Axiom of Choice and Anatoly Vlasov’s adaptation of the Boltzmann equation for ionized gases. Additional chapters delve into the philosophy of twentieth-century mathematics, addressing topics such as finitism and its limitations, a reexamination of Mary Leng’s defenses of mathematical fictionalism through an anti-realist lens, and the motivations behind mathematicians' problem selection. Authored by leading scholars, these papers are accessible to mathematicians, students of the history and philosophy of mathematics, and anyone with a general interest in the subject.