Baron Augustin-Louis Cauchy was a French mathematician and physicist who made pioneering contributions to analysis. He was one of the greatest of modern mathematicians.
Background
Cauchy was born on August 21, 1789, in Paris, France, the son of Louis François Cauchy and Marie-Madeleine Desestre. He had two brothers, Alexandre Laurent Cauchy, who became a president of a division of the court of appeal in 1847, and a judge of the court of cassation in 1849; and Eugene François Cauchy, a publicist who also wrote several mathematical works.
Education
Having received his early education from his father, who held several minor public appointments and counted Lagrange and Laplace among his friends, Cauchy entered École Centrale du Panthéon (now Lycée Henri-IV) in 1802. But upon choosing an engineering career, and proceeded to the École Polytechnique in 1805, and to the École des Ponts et Chaussées in 1807. He graduated in civil engineering, with the highest honors.
In 1809 Cauchy became an engineer, first at the works of the Ourcq Canal, then the Saint-Cloud bridge, and then, in 1810, at the harbor of Cherbourg, where Napoleon had started building a naval base for his intended operations against England. When he departed for Cherbourg, Cauchy carried in his baggage Laplace’s Mécanique céleste, Lagrange’s Traité des fonctions analytiques, Vergil, and Thomas à Kempis’ Imitatio. Cauchy returned to Paris in 1813, allegedly for reasons of health, although nothing is known about any illness he suffered during his life.
Cauchy had started his mathematical career in 1811 by solving a problem set to him by Lagrange: whether the angles of a convex polyhedron are determined by its faces. His solution, which surprised his contemporaries, is still considered a clever and beautiful piece of work and a classic of mathematics. In 1812 he solved Fermat’s classic problem on polygonal numbers: whether any number is a sum of n ngonal numbers. He also proved a theorem in what later was called Galois theory, generalizing a theorem of Ruffini’s. In 1814 he submitted to the French Academy the treatise on definite integrals that was to become the basis of the theory of complex functions. In 1816 he won a prize contest of the French Academy on the propagation of waves at the surface of a liquid; his results are now classics in hydrodynamics. He invented the method of characteristics, which is crucial for the theory of partial differential equations, in 1819; and in 1822 he accomplished what to the heterodox opinion of the author is his greatest achievement and would suffice to assure him a place among the greatest scientists: the founding of elasticity theory.
When in 1816 the republican and Bonapartist Gaspard Monge and the “regicide” Lazare Carnot were expelled from the Académie des Sciences, Cauchy was appointed (not elected) a member. Meanwhile, Cauchy had been appointed répétiteur, adjoint professor (1815), and full professor (1816) at the École Polytechnique; at some time before 1830 he must also have been appointed to chairs at the Faculté des Sciences and at the Collège de France. His famous textbooks, which date from this period, display an exactness unheard of until then and contain his fundamental work in analysis, which has become a classic. These works have been translated several times. Cauchy’s quiet life was suddenly changed by the July Revolution of 1830, which replaced the Bourbon king, Charles X, with the Orléans king of the bourgeoisie, Louis-Philippe. Cauchy refused to take the oath of allegiance, which meant that he would lose his chairs. But this was not enough: he exiled himself. It is not clear why he did so: whether he feared a-new Terror and new religious persecutions, whether he meant it as a demonstration of his feelings against the new authority, or whether he simply thought he could not live honestly under a usurper. Leaving his family, Cauchy went first to Fribourg, where he lived with the Jesuits. They recommended him to the king of Sardinia, who offered him a chair at the University of Turin. Cauchy accepted. In 1833, however, he was called to Prague, where Charles X had settled, to assist in the education of the crown prince (later the duke of Chambord). Cauchy accepted the offer with the aim of emulating Bossuet and Fénelon as princely educators. In due time it pleased the ex-king to make him a baron.
The life at court and journeys with the court took much of Cauchy’s time, and the steady flow of his publications slowed a bit. In 1838 his work in Prague was finished, and he went back to Paris. He resumed his activity at the Academy, which meant attending the Monday meeting and presenting one or more communications to be printed in the weekly Comptes rendus; it is said that soon the Academy had to put a restriction on the size of such publications. In the course of less than twenty years, the Comptes rendus published 589 notes by Cauchy - and many more were submitted but not printed. As an academician Cauchy was exempted from the oath of allegiance. An effort to procure him a chair at the Collège de France foundered on his intransigence, however. In 1839 a vacancy opened at the Bureau des Longitudes which legally completed itself by cooption. Cauchy was unanimously elected a member, but the government tied the confirmation to conditions that he again refused to accept.
When the February Revolution of 1848 established the Second Republic, one of the first measures of the government was the repeal of the act requiring the oath of allegiance. Cauchy resumed his chair at the Sorbonne (the only one that was vacant). He retained this chair even when Napoleon III reestablished the oath in 1852, for Napoleon generously exempted the republican Arago and the royalist Cauchy. A steady stream of mathematical papers traces Cauchy’s life. He also produced French and Latin poetry, which, however, is better forgotten. Cauchy remained a professor at the University until his death at the age of 67. He received the Last Rites and died of a bronchial condition at 4 a.m. on May 23, 1857.
Cauchy was a staunch Catholic and a member of the Society of Saint Vincent de Paul. He also had links to the Society of Jesus and defended them at the Academy when it was politically unwise to do so. His zeal for his faith may have led to his caring for Charles Hermite during his illness and leading Hermite to become a faithful Catholic. It also inspired Cauchy to plead on behalf of the Irish during the Potato Famine.
Cauchy also took a leading part in such charities as that of François Régis for unwed mothers, aid for starving Ireland, rescue work for criminals, aid to the Petit Savoyards, and important activity in the Society of Saint Vincent de Paul. Cauchy was one of the founders of the Institut Catholique, an institution of higher education; he served on a committee to promote the observance of the sabbath; and he supported works to benefit schools in the Levant.
Politics
Cauchy grew up in the house of a staunch royalist. This made his father flee with the family to Arcueil during the French Revolution. Cauchy also inherited his father's staunch royalism and hence refused to take oaths to any government after the overthrow of Charles X.
Views
Quotations:
"I am a Christian, that is, I believe in the divinity of Christ, as did Tycho Brahe, Copernicus, Descartes, Newton, Fermat, Leibniz, Pascal, Grimaldi, Euler, Guldin; Boscovich, Gerdil, as did all the great astronomers, physicist and geometricians of past ages."
Membership
Royal Swedish Academy of Sciences
,
Sweden
1831
American Academy of Arts and Sciences
,
United States
1832
Connections
Cauchy married Aloise de Bure in 1818. She was a close relative of the publisher who published most of Cauchy's works. They had two daughters, Marie Françoise Alicia (1819) and Marie Mathilde (1823).