  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.
