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 theory of determinants is useful for solving systems of linear equations.
The concept of a matrix is a generalization of the concept of a determinant.
The theory of eigenvalues and eigenvectors is important for understanding linear transformations.
The study of infinite series requires careful attention to the conditions of convergence.
The concept of uniform convergence is crucial for interchanging limits and integrals or derivatives.
The theory of functions of a real variable is the foundation for the theory of functions of a complex variable.
The use of rigorous definitions and proofs is paramount in mathematics.
The concept of a limit is not merely an approximation, but a precise mathematical definition.
The properties of continuous functions are not always intuitive and require careful demonstration.
The theory of permutations is a powerful tool for solving problems in algebra and number theory.
The concept of a group is a fundamental abstraction in mathematics.
The study of complex numbers extends the realm of analysis and provides new insights.
The geometric interpretation of complex numbers is a valuable aid to understanding.
The theory of functions of a complex variable has applications in physics and engineering.
The concept of a residue is a powerful tool for evaluating integrals that are difficult to compute by other means.
The development of rigorous foundations for calculus was a necessary step for its continued progress.
You see that little changes in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible.
Algebra is generous; she often gives more than is asked of her.
I am a Christian, that is to say, I believe in the divinity of Jesus Christ, and I profess the religion of the Gospel.
Give me the continuity of a function, and I will give you its integral.
Contemporaries of Augustin-Louis Cauchy
Other Mathematicss born within 50 years of Augustin-Louis Cauchy (1789–1857).