ProofWiki:Mathematicians/Augustin Louis Cauchy
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- 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 contributions in 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.
- Cauchy was 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.
Contents |
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 Biot 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
- Binet-Cauchy Identity (with Jacques Philippe Marie Binet) (also known as Binet's Formula)
- Cauchy Argument Principle
- Cauchy-Binet Formula (with Jacques Philippe Marie Binet)
- Cauchy Boundary Condition
- Cauchy Condensation Test
- Cauchy's Convergence Test
- Cauchy Criterion
- Cauchy Determinant
- Cauchy Distribution
- Cauchy's Equation
- Cauchy Equivalent
- Cauchy-Euler Equation (with Leonhard Paul Euler)
- Cauchy Functional Equation
- Cauchy-Green Tensor (with George Green)
- Cauchy's Group Theorem
- Cauchy Horizon
- Cauchy Integral Theorem
- Cauchy's Integral Formula
- Cauchy Formula for Repeated Integration
- Cauchy-Frobenius Lemma (with Ferdinand Georg Frobenius)
- Cauchy-Hadamard Theorem (with Jacques Salomon Hadamard)
- Cauchy-Kovalevskaya Theorem (with Sofia Kovalevskaya)
- Cauchy-Lipschitz Theorem (with Rudolf Lipschitz)
- Cauchy Matrix
- Cauchy's Mean Theorem (also known as Cauchy's Formula)
- Cauchy Mean Value Theorem
- Cauchy Momentum Equation
- Cauchy-Peano Theorem (with Giuseppe Peano)
- Cauchy Principal Value
- Cauchy Problem
- Cauchy Product
- Cauchy's Radical Test
- Cauchy-Riemann Equations (with Bernhard Riemann)
- Cauchy-Bunyakovsky-Schwarz Inequality (with Viktor Yakovlevich Bunyakovsky and Hermann Amandus Schwarz)
- Cauchy Sequence
- Cauchy Surface
- Cauchy's Theorem (Geometry)
- Maclaurin-Cauchy Test (with Colin Maclaurin)
- An elegant proof of what is now called the Nyquist Stability Criterion.
Books and Papers
- 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
Also see
- John J. O'Connor and Edmund F. Robertson: "Augustin Louis Cauchy": MacTutor History of Mathematics archive
- Eric Temple Bell: Men of Mathematics (1937): Chapter $\text{XV}$
- Richard A. Dean: Elements of Abstract Algebra (1966): $\S 1.1$
- Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): $\S 55$
- George F. Simmons: Calculus Gems (1992): Chapter $\text{A}.26$
