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.

中文翻译：

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数学征服者，Unguru极性和历史任务

我们比较了Blasjo，Fraser-Schroter，Fried等人最近提出的几种数学历史方法。我们认为，数学和历史学工具对于有意义的学科历史必不可少。在有关几何代数概念的Unguru-Weil争议的扩展中，Michael Fried提出了反对“特权观察者” Andre Weil和“数学征服者” Pierre de Fermat的案子。我们分析了弗里德（Fried）对昂古鲁（Unguru）所谓的历史学家和数学家历史之间极性的看法。我们确定了弗里迪安史学思想的一些公理，并提出了一个思想实验来衡量其相关性。安古鲁（Unguru）和他的门徒科里（Corry），弗里德（Fried）和罗（Rowe）描述了弗洛伊登塔尔（Freudenthal），范德瓦尔登（van der Waerden），韦尔（Weil）是柏拉图主义者，但没有提供任何证据；我们提供相反的证据。在包括费马，莱布尼兹，欧拉和考奇在内的数学分析先驱的研究中，我们分析了各种史学方法是如何发挥作用的。