Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta

Description

This volume contains fourteen papers that were presented at the 2016 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held at the University of Calgary in Alberta, Canada. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics, this meeting also honored the life and work of the logician and philosopher of mathematics Aldo Antonelli (1962-2015). The first four papers in this book are part of that remembrance and have a philosophical focus. Included in these are a discussion of Bolzano’s objections to Kant’s philosophy of mathematics and an examination of the influence of rhetorical and poetic aesthetics on the development of symbols in the 16th and 17th Centuries. The remaining papers deal with the history of mathematics and cover such subjects as Early schemes for polar ordinates in the work of L’Hôpital, based on lessons given to him by Bernoulli A method devised by Euler for determining if a number is a sum of two squares Playfair’s Axiom and what it reveals about the history of 19th-Century mathematics education The modern library classification system for mathematical subjects An exploration of various examples of sundials throughout Paris 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. Front Matter ....Pages i-xiii Bolzano Against Kant’s Pure Intuition (Paul Anh McEldowney)....Pages 1-17 Poincaré on the Foundation of Geometry in the Understanding (Jeremy Shipley)....Pages 19-37 Natural Deduction for Diagonal Operators (Fabio Lampert)....Pages 39-51 What is a Symbol? (Valerie Allen)....Pages 53-66 Polar Ordinates in Bernoulli and L’Hôpital (Robert E. Bradley)....Pages 67-80 Magic Squares of Subtraction of Adam Adamandy Kochański (Henryk Fukś)....Pages 81-95 Euler’s E228: Primality Testing and Factoring via Sums of Squares (V. Rickey)....Pages 97-116 “A Most Elegant Property”: On the Early History of Lexell’s Theorem (Eisso J. Atzema)....Pages 117-132 The Misnamings of Playfair’s Axiom (Amy Ackerberg-Hastings)....Pages 133-147 Napier, Torporley, Menelaus, and Ptolemy: Delambre and De Morgan’s Observations on Seventeenth-Century Restructuring of Spherical Trigonometry (Joel S. Silverberg)....Pages 149-168 The Reception of American Mathematics Education in Soviet Pedagogical Journals of the 1960s and 1970s (Mariya Boyko)....Pages 169-179 Mathematics in Library Subject Classification Systems (Craig Fraser)....Pages 181-197 The Convolution as a Mathematical Object (Roger Godard)....Pages 199-212 Sundials–Une Promenade Parisienne (A Math Walk in Paris) (George Heine)....Pages 213-218