19世紀の解析学における「厳密化革命」とは何か
2007 年 35 巻 1 号 p. 21-28
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2007 年 35 巻 1 号 p. 21-28
Historians of mathematics often mention that Cauchy's Cours d'Analyse (1821) brought a “rigor revolution” to analysis. Since the notion of rigor occasionally appears in the history of mathematics, it is essential to characterize Cauchy's “rigorous” attitude. When Cauchy encountered special examples that didn't satisfy general rules, theories, or formulas, he modified the latter to accommodate the former. This attitude was quite innovative because eighteenth century mathematicians generally neglected such examples and kept the general theories. After Cauchy, nineteenth century mathematicians refined their arguments when they found counterexamples to their theories. The change of treatment of counterexamples is an essential factor of Cauchy's rigor revolution.
