History and Philosophy of Mathematics at the 1924 International Mathematical Congress in Toronto

Abstract

When the University of Toronto hosted the International Mathematical Congress (IMC) in August 1924, the prime organizer, University of Toronto mathematician John Charles Fields (1863–1932) insisted the papers cover a wide range of mathematical topics: algebra, analysis, astronomy, engineering, statistics, and history and philosophy of mathematics. Section VI of the Congress covered History, Philosophy and Didactics of Mathematics. There were in total 13 papers in the published proceedings: seven full Communications and six Abstracts. Five were historical, six philosophical and only two pedagogical. In Section VI the American algebraist G. A. Miller looked at “The History of Several Mathematical Concepts” including “the unknown” and “permutations”, going back to the ancient Egyptians and Greeks. Miller also presented in Toronto on algebra, looking at commutativity in Abelian subgroups. The great Italian logician Giuseppe Peano, who had also presented in Zurich in 1897 at the IMC and then in Cambridge in 1912, spoke in simplified Latin “De Aequalitate”, On Equality. The Swiss educator Henri Fehr contributed to the pedagogical programmes at four other IMCs (1904, 1908, 1912 and 1932), focusing in Toronto on the university’s preparation of high school mathematics teachers. Florian Cajori, the great American historian of mathematics, discussed mathematical notation in two different papers: its history in geometry and a programme for its improvement. This paper examines the role of both History and Philosophy of Mathematics at the Toronto IMC.