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)
Stress is a measure of the internal forces acting within a deformable body.
Strain is a measure of the deformation of a material.
Hooke's Law describes the linear elastic behavior of materials.
The equations of motion for an elastic body are derived from Newton's second law and the constitutive relations for the material.
The principle of virtual work is a fundamental concept in mechanics.
The study of light and optics involves understanding the propagation and interaction of electromagnetic waves.
The wave nature of light explains phenomena such as diffraction and interference.
The equations governing the propagation of light can be derived from Maxwell's equations.
Mathematics is a science that deals with logical reasoning and quantitative calculations.
Rigor in mathematical proofs is of utmost importance.
The foundations of calculus must be established on solid logical principles.
The use of infinitesimals should be avoided in favor of the concept of limits.
Mathematical concepts should be defined with precision and clarity.
Mathematics is the language of nature.
I am convinced that the truths of religion are as certain as the truths of geometry.
Mathematics is the science of the infinite.
The progress of science is due to the efforts of many individuals, each contributing their part.
I have always sought to combine the rigor of mathematics with the clarity of exposition.
The most beautiful theories are those that are simple and elegant.
One must never be afraid to question established ideas.
Contemporaries of Augustin-Louis Cauchy
Other Mathematicss born within 50 years of Augustin-Louis Cauchy (1789–1857).