Saturday, July 26, 2008

Augustin-Louis Cauchy

Augustin-Louis Cauchy was born on August 21, 1789 in Paris. It was the time of the French Revolution. For a bit, Cauchy's father left Paris but later returned.

Cauchy's father was friends with some of the most famous mathematicians of France. Joseph-Louis Lagrange and Pierre-Simon Laplace were visitors to the Cauchy home. Indeed, it is said that Lagrange took an interest in young Cauchy and recommended that Augustin start with the study of classical languages before taking on mathematics.

In 1802, Augustin entered the Ecole Central du Pantheon where he followed Lagrange's advice and focused on the study of languages for the first two years and then switched to mathematics in 1804.

In 1805, he took the entrance exam for the Ecole Polytechnique. He got the second highest score. At the Ecole Polytechnique, he shined in mathematics and was over all, an excellent student. After he graduated from the Polytechnique, he studied engineering and became an engineer.

In 1811, he published his first paper in mathematics on the angles of a convex polyhedron. He showed the angles depended on the faces of the polyhedron. Encouraged by the response to the first paper, in 1812, he submitted a second mathematical paper whose topic was polygons and polyhedra.

In 1812, he moved to Paris in an effort to make more of an impact in mathematics. His next paper was on symmetric functions. He now tried to get an academic post in Paris. He applied for numerous positions but was unable to get them. For two years, he continued with his mathematical researches. He continued to try for different positions. Despite his failure at achieving academic positions, his mathematical output was phenomenal. In 1814, he wrote his very important work on definite integrals which would have a big impact on the theory of complex functions.

Finally, in 1815, he received an assistant professorship at the Ecole Polytechnique. This seemed to indicate that his time had finally come. The next year, his work on waves won the Grand Prix at the French Academy of Sciences. He became even more well known when we he resolved on of Pierre de Fermat's claims about polygonal numbers. He now was admitted to the French Academy of Sciences.

At this time, Cauchy began his very important analysis on the foundations of calculus. It began as preparation for a textbook. He focused on the convergence conditions of an infinite series. He sought a precise definition of the integral. In 1829, he was the first to study complex functions with complex variables.

Cauchy did not have the best reputation with the other mathematicians of his day. He was famous for being arrogant. Niels Abel wrote (see MacTutor reference below):
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.
Jean-Victor Poncelet, when he tried to talk with Cauchy about a paper that Cauchy criticized, reported (see MacTutor reference below):
...without allowing me to say anything else, he abruptly walked off, referring me to the forthcoming publication of his Leçons à 'École Polytechnique where, according to him, 'the question would be very properly explored'.
After the "July Revolution," Cauchy left Paris. At first, it appears he planned to take a break, but when a loyalty oath was required for him to keep his position, he declined. In 1832, he accepted a position in Theoretical Physics at Turin. In 1833, he moved to Prague to tutor the grandson of Charles X. It is said that Cauchy was not a very patient teacher. One person reported (see MacTutor):
As with mathematics, the prince showed very little interest in these subjects. Cauchy became annoyed and screamed and yelled. The queen sometimes said to him, soothingly, smilingly, 'too loud, not so loud'.
Cauchy returned to Paris in 1838. Because he refused to take the loyalty oath, he was limited in the responsibilities he could take. He was not allowed to teach, not allowed to attend scientific meetings, and could not not earn a salary for his work. During this period of time, Cauchy wrote on differential equations, mathematical physics, and mathematical astronomy.

By 1848, Louis Philippe and his government were out. Cauchy was now able to reclaim his position in academia. In 1850, he ran against Joseph Liouville for a top mathematical chair position. The election was close but Liouville won. This led to bad relations between the two top mathematicians.

Cauchy died on May 23, 1857. His daughter wrote the following (see MacTutor reference):

Having remained fully alert, in complete control of his mental powers, until 3.30 a.m.. my father suddenly uttered the blessed names of Jesus, Mary and Joseph. For the first time, he seemed to be aware of the gravity of his condition. At about four o'clock, his soul went to God. He met his death with such calm that made us ashamed of our unhappiness.

Cauchy was one of the most productive mathematicians of all time. The collection of his work spans 27 volumes. In all, he had written 789 mathematical papers. Here is how one historian summarized his life work (see MacTutor reference):
... such an enormous scientific creativity is nothing less than staggering, for it presents research on all the then-known areas of mathematics ... in spite of its vastness and rich multifaceted character, Cauchy's scientific works possess a definite unifying theme, a secret wholeness