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 moment is an opportunity for learning.
God's creation is a testament to His wisdom and power.
Consciousness is the ability to reflect on our own existence.
The pursuit of truth requires courage and perseverance.
Meaning is found in our connections to others and to the world around us.
The universe is a masterpiece of design.
To live is to experience, to learn, and to contribute.
I believe that all analysis must be founded on the theory of limits, and that the theory of limits must be founded on the theory of numbers.
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.
We say that a variable quantity becomes infinitely small when its numerical value decreases indefinitely in such a way as to converge to the limit zero.
The sum of an infinite series is the limit of the sum of its first n terms, as n increases indefinitely.
It is not enough to show that a series converges; one must also show that its sum is independent of the order of its terms.
The general solution of a differential equation of the first order contains an arbitrary constant.
Every continuous function can be represented by a convergent series of powers of the variable.
The integral of a continuous function between two limits is the limit of the sum of an infinite number of infinitely small terms.
A complex number is an expression of the form a + bi, where a and b are real numbers, and i is a symbol subject to the condition i² = -1.
The theory of functions of a complex variable is one of the most beautiful and fruitful branches of analysis.
The value of a definite integral of a function of a complex variable along a closed contour is equal to 2πi times the sum of the residues of the function at its poles inside the contour.
A function is analytic if it is differentiable at every point in its domain.
The convergence of a series of functions does not necessarily imply the continuity of its sum.
Contemporaries of Augustin-Louis Cauchy
Other Mathematicss born within 50 years of Augustin-Louis Cauchy (1789–1857).