Augustin Louis Cauchy
Overview
Baron
Baron is a title of nobility. The word baron comes from Old French baron, itself from Old High German and Latin baro meaning " man, warrior"; it merged with cognate Old English beorn meaning "nobleman"...
Augustin-Louis Cauchy (21 August 1789 – 23 May 1857; oɡystɛ̃ lwi koʃi) was a French
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who was an early pioneer of analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
. He started the project of formulating and proving the theorems of infinitesimal calculus
Infinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...
in a rigorous manner, rejecting the heuristic principle of the generality of algebra
Generality of algebra
In the history of mathematics, the generality of algebra is phrase used by Augustin-Louis Cauchy to describe a method of argument that was used in the 18th century by mathematicians such as Leonhard Euler and Joseph Lagrange...
exploited by earlier authors. He defined continuity
Continuous function
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
in terms of infinitesimal
Infinitesimal
Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. The word infinitesimal comes from a 17th century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a series.In common speech, an...
s and gave several important theorems in complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
and initiated the study of permutation group
Permutation group
In mathematics, a permutation group is a group G whose elements are permutations of a given set M, and whose group operation is the composition of permutations in G ; the relationship is often written as...
s in abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
.
Quotations
Residues arise ... naturally in several branches of analysis ... . Their consideration provides simple and easy-to-use methods, which are applicable to a large number of diverse questions, and some new results ... .
Sur un nouveau genre de calcul, 1826
... très souvent les lois particulières déduites par les physiciens d'un grand nombre d'observations ne sont pas rigoureuses, mais approchées.
... very often the laws derived by physicists from a large number of observations are not rigorous, but approximate.