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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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II.5 The Development of Rigor in Mathematical Analysis

Tom Archibald

1 Background

This article is about how rigor came to be introduced into mathematical analysis. This is a complicated topic, since mathematical practice has changed considerably, especially in the period between the founding of the calculus (shortly before 1700) and the early twentieth century. In a sense, the basic criteria for what constitutes a correct and logical argument have not altered, but the circumstances under which one would require such an argument, and even to some degree the purpose of the argument, have altered with time. The voluminous and successful mathematical analysis of the 1700s, associated with names such as Johann and Daniel BERNOULLI [VI.18], EULER ...

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