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)
The notion of an infinitely small quantity is not a fiction, but a rigorous mathematical concept.
We must distinguish between the convergence of a series and its uniform convergence.
The existence of a derivative does not guarantee the continuity of the derivative itself.
The theory of permutations is fundamental to the study of algebraic equations.
Every permutation can be decomposed into a product of disjoint cycles.
The order of a group is divisible by the order of any of its subgroups.
The concept of a limit is the cornerstone of modern analysis.
Mathematical rigor is essential for the progress of science.
The use of geometric intuition, while helpful, must always be supported by rigorous analytical proofs.
The notion of a function must be defined with precision, independent of any particular representation.
The theory of series is one of the most delicate parts of analysis.
We must be careful not to extend to infinite series results that are only valid for finite sums.
The concept of a definite integral is a generalization of the concept of area.
The properties of continuous functions are fundamental to the study of calculus.
The theory of residues provides a powerful tool for evaluating definite integrals.
The concept of a derivative is a measure of the rate of change of a function.
The fundamental theorem of calculus establishes the connection between differentiation and integration.
The theory of differential equations is essential for understanding physical phenomena.
The existence and uniqueness of solutions to differential equations are important questions.
The method of variation of parameters is a powerful technique for solving non-homogeneous differential equations.
Contemporaries of Augustin-Louis Cauchy
Other Mathematicss born within 50 years of Augustin-Louis Cauchy (1789–1857).