Augustin-Louis Cauchy
Rigorized calculus and founded complex analysis
Most quoted
"I am a Christian, that is to say, I believe in the divinity of Jesus Christ, like Bossuet and Pascal, like Corneille and Racine, and like so many other great men who have been illustrious in the sciences and in letters. The more I study nature, the more I am amazed at the works of the Creator. The more I study mathematics, the more I admire the wisdom of God."
"The mean value theorem for derivatives states that if a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point in the open interval where the derivative of the function is equal to the average rate of change of the function over the interval."
— from Cours d'Analyse de l'École Royale Polytechnique, 1821
"A function is continuous if, for every value of the variable between given limits, the numerical value of the difference between two successive values of the function becomes indefinitely small with the numerical value of the difference between the corresponding values of the variable."
— from Cours d'Analyse, 1821
All quotes by Augustin-Louis Cauchy (546)
As for methods, I have sought to give them all the rigor that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra.
A function which does not vanish for a certain value within a given interval, remains of the same sign throughout an infinitely small portion of that interval.
To the ordinary operations of algebra I have added one more, the passage to the limit.
Analysis is, to a certain extent, a practical logic.
The calculus is the greatest aid we have for the investigation of nature.
All the truths of mathematics are linked together, and the means of discovering them are not less so.
I shall devote all my efforts to bring light into the immense obscurity that today reigns in Analysis.
A convergent series has a sum; a divergent series does not.
My principal aim has been to reconcile rigor, which I have made a law unto myself, with simplicity.
It is to the principle of continuity that we owe the creation of the infinitesimal calculus.
The theory of functions of a complex variable is the most beautiful and most perfect of all those created by the human mind.
Every equation involving variable quantities is a conditional equation; it is satisfied only for certain values of these variables.
I am persuaded that the progress of analysis will be of great service to mechanics and physics.
One does not really understand something until one can explain it simply.
The mind must be prepared to follow a long sequence of reasoning without losing the thread.
In the mathematical sciences, the most important discoveries have been made by those who have combined a profound knowledge of analysis with a clear understanding of geometry.
The calculus of residues is a new branch of analysis which promises to be of the greatest utility.
A function is continuous if an infinitely small increment of the variable produces an infinitely small increment of the function itself.
The true method of foreseeing the future of mathematics is to study its history and its present state.
I have been forced to admit that the rules of the calculus are only true within certain limits.
Contemporaries of Augustin-Louis Cauchy
Other Mathematicss born within 50 years of Augustin-Louis Cauchy (1789–1857).