Abstract / Synopsis
I compare several approaches to the history of mathematics recently proposed by Blåsjö, Fraser–Schroter, Fried, and others. I 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 Andr ́e Weil the “privileged observer” and Pierre de Fermat the “mathematical conqueror.” Here I analyze Fried’s version of Unguru’s alleged polarity between a historian’s and a mathematician’s history. I 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; here I provide evidence to the contrary I also analyze how the various historiographic approaches play themselves out in the study of the pioneers of mathematical analysis including Fermat, Leibniz, Euler, and Cauchy.
Katz, M. "Mathematical Conquerors, Unguru Polarity, and the Task of History," Journal of Humanistic Mathematics, Volume 10 Issue 1 (January 2020), pages 475-515. DOI: 10.5642/jhummath.202001.27 . Available at: https://scholarship.claremont.edu/jhm/vol10/iss1/27