August 21, 2010 <Back to Index>
|
Baron Augustin-Louis Cauchy (21 August 1789 – 23 May 1857) was a French mathematician who was an early pioneer of analysis. He started the project of formulating and proving the theorems of infinitesimal calculus in a rigorous manner. He also gave several important theorems in complex analysis and initiated the study of permutation groups in abstract algebra.
A profound mathematician, Cauchy exercised a great influence over his
contemporaries and successors. His writings cover the entire range of
mathematics and mathematical physics. Cauchy
was a prolific writer; he wrote approximately eight hundred research articles and five complete textbooks. He was a devout Roman Catholic, strict (Bourbon) royalist, and a close associate of the Jesuit order. Cauchy's father (Louis François Cauchy) was a high official in the Parisian Police of the Old Régime. He lost his position because of the French Revolution (July 14, 1789) that broke out one month before Augustin-Louis was born. The Cauchy family survived the revolution and the following Reign of Terror (1794) by escaping to Arcueil, where Cauchy received his first education, from his father. After the death of Robespierre (1794),
it was safe for the family to return to Paris. There
Louis-François Cauchy found himself a new bureaucratic job, and
quickly moved up the ranks. When Napoleon Bonaparte came
to power (1799), Louis-François Cauchy was further promoted, and
became Secretary-General of the Senate, working directly under Laplace (who is now better known for his work on mathematical physics). The famous mathematician Lagrange was also no stranger in the Cauchy family. On Lagrange's advice, Augustin-Louis was enrolled in the École Centrale du Panthéon,
the best secondary school of Paris at that time, in the fall of 1802.
Most of the curriculum consisted of classical languages; the young and
ambitious Cauchy, being a brilliant student, won many prizes in Latin
and Humanities. In spite of these successes, Augustin-Louis chose an
engineering career, and prepared himself for the entrance examination
to the École Polytechnique. In
1805 he placed second out of 293 applicants on this exam, and he was
admitted. One of the main purposes of this school was to give future
civil and military engineers a high-level scientific and mathematical
education. The school functioned under military discipline, which
caused the young and pious Cauchy some problems in adapting.
Nevertheless, he finished the Polytechnique in 1807, at the age of 18,
and went on to the École des Ponts et Chaussées (School for Bridges and Highways). He graduated in civil engineering, with the highest honors. After
finishing school in 1810, Cauchy accepted a job as a junior engineer in
Cherbourg, where Napoleon intended to build a naval base. Here
Augustin-Louis stayed for three years, and although he had an extremely
busy managerial job, he still found time to prepare three mathematical
manuscripts, which he submitted to the Première Classe (First Class) of the Institut de France. Cauchy's first two manuscripts (on polyhedra) were accepted; the third one (on directrices of conic sections) was rejected. In
September 1812, now 23 years old, after becoming ill from overwork,
Cauchy returned to Paris. Another reason for his return to the capital
was that he was losing his interest in his engineering job, being more
and more attracted to the abstract beauty of mathematics; in Paris he would
have a much better chance to find a mathematics related position.
Although he formally kept his engineering position, he was transferred
from the payroll of the Ministry of the Marine to the Ministry of the
Interior. The next three years Augustin-Louis was mainly on unpaid sick
leave, and spent his time quite fruitfully, working on mathematics (on
the related topics of symmetric functions, the symmetric group and
the theory of higher-order algebraic equations). He attempted admission
to the First Class of the Institut de France, but failed on three
different occasions between 1813 and 1815. In 1815 Napoleon was
defeated at Waterloo, and the newly installed Bourbon king Louis XVIII (a brother of the beheaded Louis XVI) took the restoration in hand. The Académie des Sciences was re-established in March 1816; Lazare Carnot and Gaspard Monge were removed from this Academy for political reasons, and the king appointed
Cauchy to take the place of one of them. The reaction by Cauchy's peers
was harsh; they considered his acceptance of membership of the Academy
an outrage, and Cauchy thereby created many enemies in scientific
circles. In November 1815, Louis Poinsot,
who was an associate professor at the École Polytechnique, asked
to be exempted from his teaching duties because of health reasons.
Cauchy was by then a rising mathematical star, who certainly merited a
professorship. One of his great successes at that time was the proof of Fermat's polygonal number theorem.
However, the fact that Cauchy was known to be very loyal to the
Bourbons, doubtless also helped him in becoming the successor of
Poinsot. He finally quit his engineering job, and received a one-year
contract for teaching mathematics to second-year students of the
École Polytechnique. In 1816, this Bonapartist, non-religious
school was reorganized, and several liberal professors were fired; the
reactionary Cauchy was promoted to full professor. When
Cauchy was 28 years old, he was still living with his parents. His
father found it high time for his son to marry; he found him a suitable
bride, Aloïse de Bure, five years his junior. She was a close
relative of the publisher who published most of Cauchy's works. They
were married on April 4, 1818, with great Roman Catholic pomp and
ceremony, in the Church of Saint-Sulpice. In 1819 the couple's first
daughter, Marie Françoise Alicia, was born, and in 1823 the
second and last daughter, Marie Mathilde. It
appears that Cauchy did not give an important place to his family in
his life, as his work had higher priority. Cauchy 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 Eugène François Cauchy, a publicist who also wrote
several mathematical works. The
oppressive political climate that lasted until 1830 suited Cauchy
perfectly. In 1824 Louis XVIII died, and was succeeded by his even more
reactionary brother Charles X.
During these years Cauchy was highly productive, and published one
important mathematical treatise after another. He received cross
appointments at the Collège de France,
and the Faculté des Sciences of the University. In July 1830
France underwent another revolution. Charles X fled the country, and
was succeeded by the non-Bourbon king Louis-Philippe (of the House of Orléans).
Riots, in which uniformed students of the École Polytechnique
took an active part, raged close to Cauchy's home in Paris. These
events marked a turning point in Cauchy's life, and a break in his
mathematical productivity. Cauchy, shaken by the fall of the
government, and moved by a deep hatred of the liberals who were taking
power, left Paris to go abroad, leaving his family behind. He spent a
short time at Fribourg in
Switzerland, where he had to decide whether he would swear a required
oath of allegiance to the new regime. He refused to do this, and
consequently lost all his positions in Paris, except his membership of
the Academy, for which an oath was not required. In 1831 Cauchy went to
the Italian city of Turin, and after some time there, he accepted an
offer from the King of Sardinia (who
ruled Turin and the surrounding Piedmont region) for a chair of
theoretical physics, which was created especially for him. He taught in
Turin during 1832-1833. In 1831, he had been elected a foreign member of the Royal Swedish Academy of Sciences. In August 1833 Cauchy left Turin for Prague, to become the science tutor of the thirteen year old Duke of Bordeaux Henri d' Artois (1820-1883),
the exiled Crown Prince and grandson of Charles X. As a professor of
the École Polytechnique, Cauchy had been a notoriously bad
lecturer, assuming levels of understanding that only a few of his best
students could reach, and cramming his allotted time with much too much
material. The young Duke had neither taste nor talent for either
mathematics or science, so student and teacher were a perfect mismatch.
Although Cauchy took his mission very seriously, he did this with great
clumsiness, and with surprising lack of authority over the Duke. During
his civil engineering days, Cauchy once had been briefly in charge of
repairing a few of the Parisian sewers, and he made the mistake of
telling his pupil this; with great malice, the young Duke went about
saying that Mister Cauchy started his career in the sewers of Paris.
His role as tutor lasted until the Duke became eighteen years old, in
September 1838. Cauchy did hardly any research during those five years,
while the Duke acquired a life-long dislike of mathematics. The only
good that came out of this episode was Cauchy's promotion to Baron,
a title that Cauchy set great store by. In 1834, his wife and two
daughters moved to Prague, and Cauchy was finally reunited with his
family, after four years of exile. Cauchy
returned to Paris and his position at the Academy of Sciences late in
1838. He could not regain his teaching positions, because he still
refused to swear an oath of allegiance. However, he desperately wanted
to regain a formal position in Parisian science. In August 1839 a vacancy appeared in the Bureau des Longitudes.
This Bureau had some resemblance to the Academy; for instance, it had
the right to co-opt its members. Further, it was believed that members
of the Bureau could "forget" about the oath of allegiance, although
formally, unlike the Academicians, they were obliged to take it. The
Bureau des Longitudes was an organization founded in 1795 to solve the
problem of determining position on sea - mainly the longitudinal coordinate, since latitude is
easily determined from the position of the sun. Since it was thought
that position on sea was best determined by astronomical observations,
the Bureau had developed into an organization resembling an academy of
astronomical sciences. In
November 1839 Cauchy was elected to the Bureau, and discovered
immediately that the matter of the oath was not so easily dispensed
with. Without his oath, the king refused to approve his election. For
four years Cauchy was in the absurd position of being elected, but not
being approved; hence, he was not a formal member of the Bureau, did
not receive payment, could not participate in meetings, and could not
submit papers. Still Cauchy refused to take any oaths; however, he did feel loyal enough to direct his research to celestial mechanics.
In 1840, he presented a dozen papers on this topic to the Academy. The
absurd membership of the Bureau lasted until the end of 1843, when
Cauchy was finally replaced by Poinsot. All
through the nineteenth century the French educational system struggled
with the separation of Church and State. The Catholic Church strived
for freedom of education (that is, the right to establish Catholic
schools); the Church found in Cauchy a staunch and illustrious ally in
this struggle. He lent his prestige and knowledge to the École Normale Écclésiastique, a school in Paris run by Jesuits, for training teachers for their colleges. He also took part in the founding of the Institut Catholique.
The purpose of this institute was to counter the effects of the absence
of Catholic university education in France. These activities did not
make Cauchy popular with his colleagues who, on the whole, supported the Enlightenment ideals
of the French Revolution. When a chair of mathematics became vacant at
the Collège de France in 1843, Cauchy applied for it, but got
just three out of 45 votes. The
year 1848 was the year of revolution all over Europe; revolutions broke
out in numerous countries, beginning in France. King Louis-Philippe,
fearful of sharing the fate of Louis XVI, fled to England. The oath of
allegiance was abolished, and the road to an academic appointment was
finally clear for Cauchy. On March 1, 1849, he was reinstated at the
Faculté de Sciences, as a professor of mathematical astronomy.
After political turmoil all through 1848, France chose to become a
Republic, under the Presidency of Louis Napoleon Bonaparte,
nephew of Napoleon Bonaparte, and son of Napoleon's brother, who had
been installed as the first king of Holland. Soon (early 1852) the
President became the Emperor of France, and took the name Napoleon III.
Not
unexpectedly, the idea came up in bureaucratic circles that it would be
useful to require a loyalty oath from all state functionaries,
including university professors. Not always does history repeat itself,
however, because this time a cabinet minister was able to convince the
Emperor to exempt Cauchy from the oath. Cauchy remained a professor at
the University until his death at the age of 67. He received the Last Sacraments and died at 4 a.m. during the night of May 23, 1857. |