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)
Passage: Continuity essence.
Politics: Harmony needed.
Aphorism: Rigor's reward.
Interview: Reflections on career.
Observation: Theorem's power.
Reflection: Journey complete.
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 of science and letters.
A function is continuous if, for every value of the variable, the absolute value of the difference between the function's value at that point and its value at a nearby point can be made arbitrarily small by making the distance between the points sufficiently small.
We say that a variable quantity becomes infinitely small when its numerical value decreases indefinitely in such a way as to converge towards the limit zero.
If a series of functions, each continuous in a given interval, converges uniformly in that interval, then its sum is also a continuous function in that interval.
Every convergent sequence is a Cauchy sequence.
If a function is continuous on a closed interval, then it attains its maximum and minimum values on that interval.
The integral of a continuous function over an interval exists.
The limit of a sum is the sum of the limits, provided these limits exist.
The limit of a product is the product of the limits, provided these limits exist.
The limit of a quotient is the quotient of the limits, provided the limit of the denominator is not zero.
A series is convergent if the sum of its terms approaches a finite limit as the number of terms increases indefinitely.
The general term of a convergent series must tend to zero.
For a series to converge, it is necessary that the absolute value of its general term tends to zero.
The concept of a limit is fundamental to the understanding of calculus.
Contemporaries of Augustin-Louis Cauchy
Other Mathematicss born within 50 years of Augustin-Louis Cauchy (1789–1857).