Augustin-Louis Cauchy - Collected Quotes

"As for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra." (Augustin-Louis Cauchy, "Cours d'analyse", 1821)

"Thus, let us be persuaded that there are other truths than those of algebra, realities other than sensible objects. Let us cultivate ardently the mathematical sciences, without trying to extend them beyond their domain; and let us not imagine that one can tackle history with formulae, or use theorems of algebra or of differential calculus as an assent to morals.16 (Augustin-Louis Cauchy, "Cours d’analyse de l’École Royale Polytechnique", 1821)

"When variable quantities are so tied to each other that, given the values of some of them, we can deduce the values of all the others, we usually conceive these various quantities expressed in terms of one of them, which then bears the name independent variable; and the other quantities expressed in terms of the independent variable are what we call functions of that variable." (Augustin-Louis Cauchy, "Cours d’analyse de l’École Royale Polytechnique", 1821)

"When variable quantities are so tied to each other that, given the values of some of them, we can deduce the values of all the others, we usually conceive these various quantities expressed in terms of several of them, which then bear the name independent variables; and the remaining quantities expressed in terms of the independent variables, are what we call functions of these same variables." (Augustin-Louis Cauchy, "Cours d’analyse de l’École Royale Polytechnique", 1821)

"[…] a function of the variable x will be continuous between two limits a and b of this variable if between two limits the function has always a value which is unique and finite, in such a way that an infinitely small increment of this variable always produces an infinnitely small increment of the function itself." (Augustin-Louis Cauchy, "Mémoire sur les fonctions continues" ["Memoir on continuous functions"], 1844)

"We completely repudiate the symbol √-1, abandoning it without regret because we do not know what this alleged symbolism signifies nor what meaning to give to it." (Augustin-Louis Cauchy, 1847)

"[...] very often the laws derived by physicists from a large number of observations are not rigorous, but approximate." (Augustin-Louis Cauchy, "Sept leçons de physique" ["Seven lessons of Physics"], Bureau du Journal Les Mondes, 1868)