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)
Every symmetric function of the roots of an equation can be expressed rationally in terms of the coefficients.
The difficulty in analysis often lies not in the formulas but in the conditions under which they are valid.
It is the glory of science to be of no use... and it is precisely because it has no use that it is so sublime.
The theory of probability is, at bottom, only common sense reduced to calculation.
Go on, faith will follow.
The imagination in mathematics is not less necessary than in poetry.
A sequence that converges has a limit; this is the fundamental concept of analysis.
The integral of a continuous function over a closed interval exists.
In the sciences, there is no authority; the only authority is truth.
The calculus of probabilities, when reduced to its simplest elements, is nothing but common sense.
The progress of the integral calculus is tied to the progress of our knowledge of functions.
The concept of a limit is the true foundation of the differential and integral calculus.
Every function which remains continuous for all real values of the variable within given limits can be expanded into a convergent series ordered according to the ascending powers of the variable.
The derivative of a function is the limit of the ratio of the increments.
I have sought to establish the calculus on a method which is independent of any diagram.
The beauty of analysis lies in its generality and its rigor.
A divergent series has no sum; to speak of the sum of a divergent series is an abuse of language.
The principles of the calculus, however fertile, must be founded on exact reasoning.
It is to the clarity of geometric ideas that we owe the certainty of mathematical truths.
The method of induction, so fruitful in the natural sciences, is not admissible in the mathematical sciences except as a means of discovery.
Contemporaries of Augustin-Louis Cauchy
Other Mathematicss born within 50 years of Augustin-Louis Cauchy (1789–1857).