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 principal object of this work is to give a complete and rigorous exposition of the principles of the infinitesimal calculus.
A variable quantity approaches a fixed limit when the difference between the variable and the limit can become as small as desired.
In the theory of limits, we must distinguish between the limit itself and the approach to the limit.
The concept of continuity is fundamental to the understanding of functions.
Derivatives represent the instantaneous rate of change.
The integral is the limit of a sum.
Residue theory allows us to evaluate complex integrals efficiently.
The Cauchy-Riemann equations are necessary and sufficient for analyticity.
Elasticity is governed by the principles of continuum mechanics.
The propagation of waves in elastic media follows certain differential equations.
Mathematics must be founded on rigorous proofs, not intuition alone.
Faith and reason are not opposed; they complement each other in the pursuit of truth.
The beauty of mathematics lies in its precision and universality.
I have always sought to establish the foundations of analysis on solid ground.
In my works, I aim to leave no gap in the reasoning.
The theory of determinants is essential for linear algebra.
Group theory emerges from the study of permutations.
Optical phenomena can be explained through wave theory.
My exile from France was painful, but science transcends borders.
The pursuit of mathematical truth is a noble endeavor.
Contemporaries of Augustin-Louis Cauchy
Other Mathematicss born within 50 years of Augustin-Louis Cauchy (1789–1857).