Augustin-Louis Cauchy was, in many respects, the father of modern mathematical analysis - an idea I discussed in some detail when I

noded my homework under

Augustin-Louis Cauchy and the Rigorisation of Analysis. However, it is not this alone for which he is famous, and I've been commissioned by

the powers that be to furnish a potted biography that's more comprehensive than that essay.

Augustin-Louis Cauchy was born on

August 21, 1789, in

Paris, at the dawn of

the French Revolution. His father, Louis-François Cauchy, was a city police chief, and before the child was more than a few weeks old, the family had had to flee to more rural areas to escape retribution from the revolutionary mob. The astronomer

Bailly was among those directing the

Storming of the Bastille shortly afterwards, and the Cauchys were well out of it. In

1794, when the

Reign of Terror was over, they returned to Paris, and Cauchy Sr got a new job.

Napoleon Bonaparte's arrival in the

Brumaire coup of

1799 further advanced the family's fortunes, and young Augustin-Louis was offered academic advancement by Count

Pierre Laplace, and in

1805 he entered the École Polytechnique.

*(Literally 'Polytechnic School - actually one of the principal universities.)*
After graduation, Cauchy went to work on the

Ourcq Canal project, but returned to the École as a teacher when political changes in

1815 left many vacancies. While there, he made himself unpopular with staff and students alike, but succeeded in producing his crucial textbook

Cours d'Analyse de l'École Royale Polytechnique: Première Partie: Analyse Algébrique (Analysis Course of the Royal École Polytechnique: First Part: Algebraic Analysis), which lays down the theory of

limits as now understood, and represented a tremendous advance from the

infinitesimal theory which had prevailed beforehand.

Cauchy did not make friends easily. One of his students, the great

Niels Henrik Abel, said:

Cauchy is mad and there is nothing that can be done about him, although, right now, he is the only one who knows how mathematics should be done.

Abel died, at home in

Norway, in 1829, some three years after making this assertion. Cauchy had still not returned Abel's work to him, and when the work finally did get marked, the comments Cauchy made reflected neither his own talents nor those of Abel. Shortly afterwards, Cauchy's conservatism and awkwardness exiled him from his native

France. In July

1830 the

Orleanist claimant

Louis Philippe became

king, and the

Bourbon loyalist Cauchy moved to

Switzerland, teaching for a time at the

Académie Helvétique, before moving on to

Turin. At about this time Cauchy was considered to have failed to swear an

oath of allegiance to the new French régime, and lost all standing in Paris. Critical opinion of the courses he taught in Turin was poor, and he seemed to be suffering a

depression or

mania of some kind. In

1833 he headed on to

Prague, where he acted as tutor to the grandson of the emperor

Charles X. Here also, Cauchy's disjointed teaching style and short temper failed to win him friends.

Whilst in

Prague, Cauchy met with

Bernard Bolzano, a

Czech priest who was working on the question of

continuity. Their encounter is not closely documented, but it seems clear that both learned from it. In

1838 Cauchy returned to Paris, but although he regained hism post at the École and a new one at the

Bureau des Longitudes, his continued failure to swear

allegiance meant that he could not teach or earn money in these positions. He subsequently failed (in

1843) to gain the

mathematics chair at the

Collège de France, due to the unpopularity of his ultra-

Catholic, pro-

Jesuit views and his reactionary political stance. During this time, although his work was less intense than whilst at the École, he produced important results on

differential equations,

mathematical physics and

astronomy.

The downfall of Louis Philippe in

1848 allowed Cauchy to regain his full standing in the mathematical community, but he never did achieve the post at the Collège, this going to

Liouville in

1850 following the flight of

Libri, who had defeated Liouville and Cauchy but was suspected (correctly) o theft. Cauchy died in an appropriately pious and Catholic manner, calling on

Jesus,

Mary and

Joseph before he passed on, on

May 23, 1857.

His many achievements are summed up in Professor

Bruno Belhoste's 'Cauchy 1789-1857', translated into

English as

Augustin-Louis Cauchy: A Biography, like this:

Cauchy's creative genius found broad expression not only in his work on the foundations of real and complex analysis, areas to which his name is inextricably linked, but also in many other fields. Specifically, in this connection, we should mention his major contributions to the development of mathematical physics and to theoretical mechanics... his two theories of elasticity and his investigations on the theory of light, research which required that he develop whole new mathematical techniques such as Fourier transforms, diagonalisation of matrices, and the calculus of residues.

Cauchy discoveries include:

Sources:

My own essay cited above, and its sources listed there; Belhoste's book; and assorted websites, in order to remind me what Professor Belhoste's excellent biography had to say. I snagged the node-list from

pax music's node

Augustin Cauchy.