2020/02/01 by Mikhail G. Katz · 1 citation
Mathematics · #math.HO #msc:01A20 #msc:01A45 #msc:01A50 #msc:01A55 #msc:01A60 #msc:01A61 #msc:01A85
paper · pdf · doi:10.5642/jhummath.202001.27
published as Journal of Humanistic Mathematics 10 (2020), no. 1, 475-515 · 37 pages, 1 figure
arxiv created 2020/02/01 · arxiv updated 2020/02/05
We compare several approaches to the history of mathematics recently proposed by Blasjo, Fraser--Schroter, Fried, and others. We argue that tools from both mathematics and history are essential for a meaningful history of the discipline. In an extension of the Unguru-Weil controversy over the concept of geometric algebra, Michael Fried presents a case against both Andre Weil the "privileged observer" and Pierre de Fermat the "mathematical conqueror." We analyze Fried's version of Unguru's alleged polarity between a historian's and a mathematician's history. We identify some axioms of Friedian historiographic ideology, and propose a thought experiment to gauge its pertinence. Unguru and his disciples Corry, Fried, and Rowe have described Freudenthal, van der Waerden, and Weil as Platonists but provided no evidence; we provide evidence to the contrary. We analyze how the various historiographic approaches play themselves out in the study of the pioneers of mathematical analysis including Fermat, Leibniz, Euler, and Cauchy.