Mathematician:Augustin Louis Cauchy

Mathematician
French Engineer and mathematician, from a suburb of Paris, which at the time was home to many leading mathematicians.

Wrote seven books and more than 700 papers in various fields of mathematics.

Made significant contributions in number theory, the theory of determinants, eigenvalues, ordinary and partial differential equations, permutation groups, and the foundation of calculus.

Famous for founding the theory of functions of a complex variable.

Argued by some as the founder of group theory.

A devout Roman Catholic, also strongly devoted to the Bourbon kings who ruled France after Napoleon's defeat. When Charles X was exiled in $1830$, Cauchy willingly followed the former king into exile in Prague.

Some make much of what are perceived as his personal shortcomings with respect to his religious beliefs, political leanings and moral attitudes, but it is at least as equally often suggested that they are ultimately unimportant in comparison with to his legacy.

Nationality
French

History

 * Born: 21 Aug 1789, Paris, France
 * 1805: Entered the École Polytechnique
 * 1807: Graduated from the École Polytechnique, entered the École des Ponts et Chaussées
 * 1810: Moved to Cherbourg: worked on port facilities for Napoleon's English invasion fleet
 * 1811: Proved that the angles of a convex polyhedron are determined by its faces
 * September 1812: Returned to Paris suffering from depression
 * 1815: Appointed assistant professor of analysis at the École Polytechnique
 * 1816: Won the Grand Prix of the French Academy of Sciences for a work on waves
 * 1817: Replaced at the Collège de France
 * September 1830: Left Paris after the July revolution, and spent a short time in Switzerland where he helped to set up the Académie Helvétique
 * 1831: Went to Turin, accepted an offer from the King of Piedmont of a chair of theoretical physics, where he taught from 1832
 * 1833: To Prague, in order to follow Charles X and to tutor his grandson (with not much success)
 * 1838: Returned to Paris and regained his position at the Academy, but not his teaching positions because he had refused to take an oath of allegiance
 * 1848: Regained his university positions on overthrow of Louis Philippe
 * Died: 23 May 1857, Sceaux (near Paris), France

Theorems and Definitions

 * Cauchy Criterion
 * Cauchy Determinant
 * Cauchy Distribution
 * Cauchy Equivalent
 * Cauchy-Euler Equation (with )
 * Cauchy Form of Remainder of Taylor Series
 * Cauchy Horizon
 * Cauchy Matrix
 * Cauchy Principal Value
 * Cauchy Product
 * Cauchy Sequence
 * Cauchy Surface


 * Cauchy-Green Tensor (with )
 * Cauchy-Riemann Equations (with )
 * Navier-Cauchy Equations (with )


 * Cauchy Argument Principle
 * Cauchy Boundary Condition
 * Cauchy Condensation Test
 * Cauchy's Convergence Criterion
 * Cauchy's Convergence Test
 * Cauchy's Equation
 * Cauchy Formula for Repeated Integration
 * Cauchy Functional Equation
 * Cauchy's Lemma (Group Theory) (on groups with elements of prime order)
 * Cauchy's Lemma (Number Theory) (on representation of integers as sums of $4$ integers or squares)
 * Cauchy's Inequality
 * Cauchy's Integral Formula
 * Cauchy Integral Test
 * Cauchy's Mean Theorem (also known as Cauchy's Formula)
 * Cauchy Mean Value Theorem
 * Cauchy Momentum Equation
 * Cauchy Problem
 * Cauchy's Radical Test
 * Cauchy Ratio Test (also known as D'Alembert's Test, for, or just the Ratio Test)
 * Cauchy's Test (also known as the Nth Root Test or just the Root Test)
 * Cauchy's Theorem (Geometry)


 * An elegant proof of what is now called the Nyquist Stability Criterion.


 * Binet-Cauchy Identity (with ) (also known as Binet's Formula)
 * Cauchy-Bunyakovsky-Schwarz Inequality (with and )
 * Cauchy-Binet Formula (with ) (also known, confusingly, as the Binet-Cauchy Identity)
 * Cauchy-Frobenius Lemma (with )
 * Cauchy-Goursat Theorem (with ) (also known as the Cauchy Integral Theorem)
 * Cauchy-Hadamard Theorem (with )
 * Cauchy-Kovalevsky Theorem (with )
 * Cauchy-Lipschitz Theorem (with )
 * Cauchy-Peano Theorem (with )
 * Maclaurin-Cauchy Test (with )

Publications



 * 1821: Cours d'analyse (Course in Analysis)
 * 1823: Le Calcul infinitésimal
 * 1826: Sur un nouveau genre de calcul analogue au calcul infinitésimal
 * 1829: Leçons sur le Calcul Différentiel
 * 1840-47: Exercices d'analyse et de physique mathématique



Critical View

 * His scientific production was enormous. For long periods he appeared before the Academy once a week to present a new paper, so that the Academy, largely on his account, was obliged to introduce a rule restricting the number of articles a member could request to be published a year.

Also known as
Some sources render his name as Augustin-Louis Cauchy.