Augustin Louis Cauchy

Augustin Louis Cauchy

The greatest French Mathematician who has been described as the first revolution of rigour in mathematics is undoubtedly Augustin Louis Cauchy. He contributed in a major way to almost every branch of mathematics. It is humorously said—Cauchy did not so much master mathematics, mathematics mastered Cauchy.

Augustin Louis Cauchy was born in Paris on August 21, 1789. He was christened Augustin because he was born in August and Louis after his father’s name Louis Francois. His father Louis Francois was a parliamentary lawyer and a lieutenant of police in Paris. His mother Marie- Madeleine came from a very reputed Parisian family. Cauchy’s childhood fell in the bloodiest period of the revolution. In 1794, the Cauchy family fled to Arcueil to escape the terror. Louis Francois could hardly manage to feed his family and as a consequence Cauchy grew up delicate and underdeveloped physically.

Two years later the Cauchy family returned to Paris where Louis Francois began to rebuild his carrier under the new regime and was appointed as secretary general to the newly constituted Senate of which Laplace was chancellor. Louis had a great friendship with Lagrange’s and Laplace and they used to visit Cauchy’s house every now and then. Lagrange was impressed by the ability of Augustin and on his advice he was enrolled at the Ecole Centrale de Pantheon to study humanities. Pointing to Louis, Lagrange once said--- he will supplement all of us so far as we are mathematicians. Don’t let him touch a mathematical book till he is 17.

At the age of 13, Augustin Cauchy entered the Central school of Pantheon. He won the grand prize for the best student instituted by Napoleon. On leaving the school in 1804, Cauchy won the sweepstakes and a special prize in mathematics. For the next ten months he studied mathematics intensively with a good tutor and at the age of 16, he entered the Ecole Polytechnic. By 1810, he was a qualified Junior Engineer.

In March 1810, he left Paris to work on the construction of a naval base at Cherbourg, the Port Napoleon.  Cauchy took 4 books with him to Cherbourg-- The Mecanique celeste of Laplace, The Traite des fonctions analytiques of Lagrange, The Imitation of Christ by Thomas a Kempls and the work of Virgil. He remained there for 3 years where he used to do some mathematical research in part time.

In December 1810, he had begun to go over again all branches of mathematics, beginning with Arithmetic and finishing with Astronomy. Some of his discoveries were sufficiently significant to attract the attention of learned society in Paris particularly the memoir on polyhedral and that on symmetric functions, which included the germs of the fundamental ideas that eventually blossomed into Group Theory. He also extended the formula of Euler connecting the numbers(E), faces(F) and vertices(V) of a polyhedron given as E+2 =F+V

He also developed the theory of determinants but he got his due recognition as a brilliant mathematician when he submitted a work on Calculation of Definite Integrals to the Academy in 1814. In 1815, Cauchy created a sensation by proving one of the great theorems which Fermat has bequeathed to a baffled posteiry.

Every positive integers is a sum of three triangles, four squares, five pentagons, six hexagons and so on---

In 1816, he received the Grand Prize offered by the Academy for a theory of the propagation of waves on the surface of a heavy fluid of indefinite depth. In 1816 itself he was elected a member of the Paris Academy. This success made him the enemies of those great mathematician likes Monge and Carnot who were displaced from Academy. In the same year, he was appointed Assosiate Professor of Analysis at the Ecole Polytechnic.

The discovery with which Cauchy’s name is most firmly associated is his fundamental theorems in Complex Analysis. The first pivotal theorem proved by Cauchy, now known as Cauchy's integral theorem, was the following:

Where  f(z) is a complex-valued function holomorphic on and within the non-self-intersecting closed curve C (contour) lying in the complex plane. The contour integral is taken along the contour C.

 He is therefore known as the father of Complex Analysis.  In 1818, Cauchy married with Aloise de Bure. She was a close relative of the publisher who published most of Cauchy's works. They had two daughters Marie Francoise Alicia and Marie Mathilde born in 1819 and 1823 respectively. Encouraged by Laplace, Cauchy in 1821 wrote up for publication of his lecture on Analysis given in Ecole Polytechnic. This book contains the definition of limits and continuity and convergence of infinite series which we still read in the book of Calculus.

In 1825, Cauchy started his own monthly journal Exercises de mathemaliques. Its pages were exclusively filled by Cauchy himself. Cauchy's writings covered notable topics including: the theory of series, where he developed the notion of convergence and discovered many of the basic formulas for q-series. The theory of numbers and complex quantities; he was the first to define complex numbers as pairs of real numbers. 

The turmoil in 1830 in Paris had a great impact on the mind of Cauchy. Cauchy lost most of his positions at the institutes because he refused to take the oath of allegiance to the new king, Louis-Philippe.  He left for Switzerland and remain there in self imposed exile for eight years where he was offered the Post of Professor in Mahematical Physics by Charles Albert, the King of Sardinia.  He taught in Turin during 1832-1833. In 1831, he had been elected a foreign member of the Royal Swedish Academy of Sciences. In 1833, Cauchy was appointed tutor of Charles’ grandson.

Cauchy went back to Paris in 1838 when he finished his work with Charles X in Prague, and resumed his involvement with the Academy. At the time, because Cauchy was a mathematician, he was exempted from the oath of allegiance. After the establishment of the Second Republique in 1848, Cauchy resumed his position at the Sorbonne. Cauchy continued with his writings and publications through the remainder of his life. The long hour of work made him ill. On medical advice he left for Paris on May 12, 1857 but his health suddenly detorieted and he died on 23 rd May 1857 at the age of 67. His name is one of the 72 names inscribed on the Eiffel Tower.

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