Debates na historiografia da matemática e a história do surgimento do cálculo infinitesimal segundo Carl Boyer

Abstract

In this text we initially presented the discussions between internalists and externalists in the history of the science and the reflexes of this debate in the historiography of the mathematics. We analyzed an article ofresearcher Joan Richards in that she tries to explain the predominance of approaches internalists in the history of the mathematics. We objected, through an analysis of the philosophical debates around the foundations of the mathematics happened in the beginning of the century XX, the main argument of Richards that says that the historians of the mathematics would privilege the history interns for his fundationist posture of theknowledge. In the second chapter, we presented the new historiography of the science appeared in the 60s of the century XX and the impacts of this approaches in the history of the mathematics. In the last chapter, wepresented a history of the appearance of the infinitesimal calculus, elaborated in 1939 by Carl Boyer, and we concluded with a critic to this classic text of the history of the mathematics with base in the historiographical proposals presented in the first two chapters.