• DOI:10.1007/BF00357440
• Corpus ID: 120781880

Cauchy's conception of rigour in analysis

@article{Smithies1986CauchysCO,
  title={Cauchy's conception of rigour in analysis},
  author={Frank Smithies},
  journal={Archive for History of Exact Sciences},
  year={1986},
  volume={36},
  pages={41-61}
}

• F. Smithies
• Published 1 March 1986
• Philosophy
• Archive for History of Exact Sciences

This paper is an expanded form of an address given at a meeting of the British Society for the History of Mathematics in September 1983. Augustin Louis Cauchy lived from 1789 to 1857. Between 1814 and 1824 he undertook a thorough reorganisation of the foundations of analysis, aiming, as he put it, to make the treatment of the subject as rigorous as that of geometry. He expounded his new framework in two textbooks, to which we shall refer briefly as the Analyse algebrique [1821a] and the Calcul infinitesimal [1823 a]. We shall also look at some of his earlier papers, from which we may hope to gather some indications of the way in which his ideas developed. Our aim will be to try to uncover the main ideas that guided Cauchy in his enterprise; our attention will be focussed not so much on what he did, but rather on what he thought he was doing. In particular, we shall be interested in why he rejected some commonly used types of argument as non-rigorous and accepted other procedures as rigorous; in other words, in what his own conception of rigorous mathematical argument consisted, especially in the context of analysis. Cauchy's private papers and almost all his correspondence seem to have disappeared, so our evidence has to be drawn almost entirely from his publications; we shall discuss in detail only those passages that seem to throw some light on his point of view and his intentions. We shall also look at some of the work of his immediate predecessors and his contemporaries, in order to trace interactions between their ideas and his.