Augustin-Louis Cauchy

augustin-louis-cauchy

Augustin-Louis Couchy was an important French mathematician. His work was used not only by mathematicians during his lifetime but also by mathematicians that followed. Cauchy published around eight hundred articles and five textbooks. There are more concepts and theorem named after Cauchy that after any other mathematician. Augustin-Louis Cauchy is one of the seventy-two names that are inscribed on the Eiffel Tower.

Early Years

Augustin-Louis Cauchy was born on August 21, 1789, in Paris. His father was a police lieutenant and a parliamentary lawyer. Cauchy was born just thirty-eight days before the storming of the Bastille (the beginning of the French Revolution). Since Cauchy’s father was a strong supporter of the royal family, Cauchy’s father decided to take the family to live in Arcueil, where he had a cottage. Life was difficult for the family in Arcueil, and Cauchy’s father wrote in his journal about not having much food to eat.

Cauchy lived in Arcueil for almost eleven years where he was homeschooled. His father taught him the classics and his mother taught him religious studies.

The French Revolution ended in 1799 and by 1800, things had calmed down enough for the family to move back to Paris. Cauchy’s father was given the position of secretary of the senate in the new government under Napoleon. As a result of his position, Cauchy’s father met a number of influential people. One of these people was Joseph Louis Lagrange. Lagrange was a French mathematician and he seemed to recognize Cauchy’s mathematical ability. Lagrange advised Cauchy’s father to first train Cauchy in the classics before allowing Cauchy to begin to study mathematics.

In 1802, Cauchy enrolled in the École Centrale du Panthéon. When he graduated, he had placed first in Latin and Greek verse and second in Latin composition. After graduation, Cauchy spent a year studying mathematics to prepare for the entrance exam for the EcolePolytechnique. Cauchy passed the exam (he placed second) and entered the EcolePolytechnique in 1805 (at the age of sixteen). Cauchy spent two years here and then enrolled in the ÉcoleNationale des Ponts et Chaussées to study engineering.

Cauchy became an engineer and moved to Cherbourge in 1810 but he returned to Paris three years later. When he returned to Paris, he renewed his acquaintance with Lagrange as well as Pierre-Simon Laplace, a mathematical physicist. Both men persuaded Cauchy to leave engineering and focus on a career in mathematics.

Early Career in Math

While in Cherbourge, Cauchy began to work on problems in mathematics. His first published success was in 1811 when he proved a problem that Lagrange had given him. Cauchy was able to prove that the faces of a convex polyhedron determine the angles of that polyhedron. His proof is still considered a classic in mathematics.

Cauchy continued to work on mathematics and in 1812, published papers on polygons and polyhedral as well as a paper on symmetric functions and one on determinants. He also proved a problem on polygonal numbers that was formulated by Fermat. A polygonal number is a number that is represented by dots organized into a specific shape. For example, the number three is a triangular number because the three dots make a triangle.

It was shortly after this that Cauchy returned to Paris claiming illness. There is no record of him actually being ill and some scholars believe that he suffered from depression. Cauchy did not want to return to Cherbourg so he asked to become an associate professor at Ecole des Ponts et Chaussees. His request was refused but he was allowed to work on a different engineering project (the Ourcq Canal) instead of returning to Cherbourg.

Cauchy continued to look for a position in a school but was turned down a number of times. He continued to work on the Ourcq Canal until work was stopped because of the political situation in France. This allowed Cauchy to focus on his mathematics.

Professor

Cauchy was finally given an academic position when he was made the assistant professor of analysis at the EcolePolytechnique in 1815. He became a full professor in 1816. In 1816, Cauchy was awarded the Grand Prix of the French Academy of Sciences for his work on waves that are produced on the surface of a liquid.

Cauchy was made a member of the French Academy of Sciences in 1816 at the age of twenty-seven, which was a fairly young age to be admitted to the academy. Cauchy’s admittance to the academy was accompanied by some controversy. After the overthrow of Napoleon and the return of Louis XVIII to the throne, two members of the academy who were closely associated with the government under Napoleon lost their spots in the academy. Cauchy took over one of the spots that was lost. This created some hard feelings between Cauchy (who was a strong supporter of the royalty) and some of the other members of the academy. This was not the only source of conflict between Cauchy and other scientists. Cauchy had strong religious beliefs, which resulted in him supporting the Jesuits against the Academy. At times, he would also use religion when he was criticizing the academic works of others. For example, in 1824, Cauchy criticized a scientist for reporting that Newton believed that people did not have souls.

Another example of Cauchy’s religious beliefs conflicting with his scientific ability occurred at a meeting at the Academy in 1826. A naturalist gave a presentation and at the end, while the naturalist was receiving his applause, Cauchy stood up and stated that even if the naturalist was correct, it should not be shared with the general public because it would have a negative effect on religion. Most people responded to Cauchy’s comments with laughter, but he did not stop pushing his point.

There is some debate about how good of a teacher Cauchy actually was. According to one biographer (Valson), Cauchy was an excellent teacher who ensured that every student understood the points Cauchy was making and that Cauchy continued teaching a point until there were no more questions to be asked. In response to this portrayal as a wonderful teacher, Joseph Bertrand, who attended lectures given by Cauchy, reports that Cauchy’s lectures would deal with a confusing variety of subjects and cover subjects that Cauchy thought were new but were already known by all the students. Bertrand states that he never returned to hear anymore lectures but he regretted this action because if he had gone back, he would have heard lectures on some of the brilliant discoveries Cauchy had made. This story seems to convey a teacher who was a bit disorganized and would likely lecture on any points that struck him as interesting regardless of the needs of his students.

Cauchy married Aloise de Bure in 1818. De Bure was related to the man who published most of Cauchy’s work. The couple had two daughters.

In the 1820s, Cauchy published a number of major treatises, including a treatise on higher algebra and another one on mathematical physics. He also published his own journal in 1826. The journal, titled Mathematical Exercises, focused on Cauchy’s work and continued to be published until Cauchy died.

For the next decade, Cauchy published numerous works and seemed to touch on every possible subject within mathematics, both theoretical as well as applied. He published so much material that, at times, he was publishing two papers a week.

One of the main areas that Cauchy studied was mathematical analysis. Cauchy wanted to work on the problem of justifying the methods used in differential calculus. This had been a problem for a long time and although Cauchy did not succeed, he did come up with a number of influential new ideas in the field.

Cauchy also developed a new branch of analysis—the theory of functions of a complex variable. This theory is now one of the main tools used in physics.

Cauchy did not just contribute to various fields in mathematics. He also made contributions to the field of astronomy. The work Cauchy is best known for in astronomy is his work on Leverrier’s computations on the inequality that is seen in the mean motion of Pallas. Leverrier’s computations are difficult to work through and Cauchy came up with a much simpler method to compute the same thing.

Voluntary Exile

In 1830, another revolution took place in France replacing the French king Charles X with Louis-Philippe, the Duke of Orleans. When the new king took the throne, people were made to swear an oath of allegiance to the new king. Cauchy refused to do this.

As a result of his refusal, Cauchy lost his position in the French Academy of Sciences. After losing his position, Cauchy decided to leave France. The reasons behind Cauchy’s voluntary exile are not known. He could have left because he feared persecution under the new government or he may have done it as a personal protest against the new government.

Cauchy moved to Fribourg (leaving his family behind) and lived with the Jesuits until they recommended him to the king of Sardinia. The Sardinian king offered Cauchy a position at the University of Turin which Cauchy accepted. He did not remain for long at the university. In 1833, Charles X (the deposed king) asked Cauchy to move to Prague and help educate the deposed king’s son.

Cauchy stayed in Prague until 1838 and then he moved back to Paris where he rejoined the Academy but he was not able to resume his teaching position. Cauchy still refused to take the oath of allegiance and as a result, when he was unanimously elected to the Bureau des Longitudes, the government refused to let Cauchy take the position unless he swore the oath. There was an attempt to find a way around Cauchy’s refusal so that he could still take up the position but Cauchy refused all concessions. One concession was that Cauchy just had to not mention that he never took the oath but he refused even this. Cauchy still worked at the Bureau des Longitudes, but this was basically illegal.

Louis-Philippe was overthrown in 1848 and the demand for the oath was dropped. As a result, Cauchy went back to work at the EcolePolytechnique in his old position. When Napoleon III came to the throne in 1851, the oath of allegiance was reinstated but Napoleon exempted Cauchy as well as Francois Arago from having to take the oath.

Later Life and Death

As Cauchy grew older, he began to focus on charity and religion although he continued to work in the area of mathematics as well. He learned Hebrew so that he could help his father with some research and he donated a major part of his salary to the state so that it could be used for various charitable purposes. Cauchy also worked and supported causes such as famine relief in Ireland, support for unwed mothers, and working with criminals.

In 1857, Cauchy submitted a treatise on a new method to conduct astronomical calculations. A week after submitting the paper, he attended the academy even though he was ill with a cold. His illness became worse and it soon affected his ability to move and the way he looked. A clerk at the academy encouraged Cauchy to slow down but Cauchy had no interest in this. He was determined to continue working.

He continued working right up to his death. On May 23, 1857, he woke up in the middle of the night and then died a half hour later. According to some reports, just before he died, he mentioned Jesus, Mary and Joseph while other reports claim that his last words were “Men pass away, but their deeds abide.” His exact last words will probably never be known but this is not as important as the many mathematical achievements Cauchy made during his lifetime.

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