Mathematical Conquerors, Unguru Polarity, and the Task of History

Journal of Humanistic Mathematics

article

Katz, Mikhail¹ 

[1] Bar-Ilan University

关键词: history of mathematics;    Weil;    Unguru;   

DOI  :  10.5642/jhummath.202001.27

学科分类：社会科学、人文和艺术（综合）

来源: Claremont Center for the Mathematical Sciences

【 摘 要 】

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.

【 授权许可】

CC BY-NC-ND