Augustin-Louis Cauchy Brandon Lukas Cauchy's life On August 21, 1789, Augustin-Louis Cauchy was born in Paris. He was born just one month after the beginning of the French Revolution. His father, Francois Cauchy, was a senior French government officer who feared for his life in Paris and lost his job due to France's political turmoil during the Reign of Terror. As a result, his father moved the family to the village of Arcueil, a commune in the southern suburbs of Paris, and homeschooled Cauchy and his two brothers, Alexandre Laurent Cauchy and Eugene Francois Cauchy. Arcueil is where Cauchy first met mathematician Laplace and chemist Berthollet. Cauchy and his family returned to Paris when the atmosphere had calmed down following the guillotine of Robespierre in 1794. His father worked in Napoleon Bonaparte's bureaucracy as Secretary-General of the Senate with Laplace. Another mathematician, Lagrange, was a friend of the family. Laplace and Lagrange often visited Cauchy's home. Intrigued with Cauchy's mathematical education, Lagrange suggested that Cauchy be educated in classical languages before seriously studying mathematics. And so, Lagrange helped Cauchy pursue an education at the Ecole Centrale du Pantheon, arguably the best secondary school of Paris, in 1802. Cauchy excelled in his studies of mathematics and classical languages as demonstrated by winning multiple prizes in Latin and Humanities. Despite his talent with humanities, Cauchy's passion was with engineering. Cauchy finished his secondary education in 1804 and immediately began preparing for the entrance exam to enter the elite French institute of higher education and research, the Ecole Polytechnique in Palaiseau. The Ecole Polytechnique was a very prestigious military engineering school taught by some of the world's greatest mathematicians. Cauchy took the entrance exam (he was examined by mathematician Biot) and not only passed, but impressively placed second out of 293 applicants. At the Ecole Polytechnique, Cauchy took engineering courses by Lacroix, de Prony, and Hachette. At the same time, Ampere was his analysis tutor and the two had a close relationship with each other. Cauchy graduated Ecole Polytechnique and continued his education at the Ecole des Ponts et Chaussees (School for Bridges and Roads). For his practical, Cauchy worked on the Ourcq Canal project under Pierre Girard. He also worked on the Saint-Cloud bridge. In 1810, Cauchy began his three year long work in Cherbourg on the harbors and fortifications for Napoleon's English invasion fleet. Despite having an extremely busy managerial job, Cauchy undertook heavy research in mathematics on the side. He prepared several important mathematical papers. One paper contained the solution to a Lagrange problem which established that the faces determine the angles of a convex polyhedron. Another paper solved Fermat's problem on polygonal numbers. In another paper, Cauchy gave determinants its current definition. Cauchy submitted three mathematical papers to the Premiere Classes (First Class) of the Institut de France. Two of them about polyhedra were accepted but the third about conic sections was not. Cauchy fell ill with severe depression from being overworked and losing interest with his engineering job and wanted to move back to Paris where he could devote himself to mathematics in 1813. Cauchy's payroll was transferred from the Ministry of the Marines to the Ministry of the Interior and for three years, Cauchy was on unpaid sick leave. He worked on symmetric functions and symmetric groups as well as the theory of higher- order algebraic equations. He also set the basis of the theory of complex functions after publishing a memoir on definite integrals. Meanwhile, Cauchy wanted to pursue an academic career. Cauchy applied to several posts, positions, and chairs in the Bureau des Longitudes, the Institute, and the Ecole Polytechnique but was continually denied until Napoleon was defeated at Waterloo in 1815 and the new Bourbon king Louis XVIII removed Monge, considerably the greatest mathematician of France at the time, from the Academie des Sciences for political reasons and appointed Cauchy assistant professor of a second year course in analysis at the Academy after Cauchy lost a mechanics chair to mathematician Binet. A membership in the academy is one of the highest honors a scientist could receive. Cauchy's unreserved acceptance of the membership earned him many enemies within the mathematic and scientific community. Nonetheless, Cauchy continued his work and by the next year, he won the Grand Prix of the French Academy of Sciences for a paper on wave propagation used in hydrodynamics. In the fall of 1815, mathematician and professor Louis Poinsot left his position at the Ecole Polytechnique for health issues. Cauchy fully quit his engineering job and took over for him. His mathematical ability qualified him for the position but it was his loyalty to the Bourbons that guaranteed his spot. He received a one-year contract, and when several professors were fired for being too liberal in the Bonapartist school, Cauchy was promoted to full professor in 1816. 2 Single and still living with his parents, Cauchy was encouraged to marry at age 28 by his father. His father found him a suitable bride named Aloise de Bure whose family were printers and booksellers. In fact, the de Bure family published most of Cauchy's works, helping him become the one of the most published mathematician in the world. The couple was married with in the Roman Catholic church Saint-Sulpice in 1818. One year later, the couple's first daughter, Marie Francoise Alicia was born. Following in 1823, the couple's second daughter, Marie Mathilde was born. During the 1820s, Cauchy's production was at an all time high and he received cross appointments at the College de France and the Faculte des sciences de Paris. After the French July Revolution of 1830, the oath of allegiance was required by the new king, Louis-Philippe. However, Cauchy remained loyal to the old political regime, so he refused to accept the oath and thereby lost most of his positions at the institutes. With practically no positions in Paris anymore, Cauchy decided to leave France and his family behind and went into exile. He moved to Turin, a city in northern Italy, to teach mathematical and theoretical physics after a chair was created by the King of Piedmont for him at the University of Turin. He was a brilliant and eccentric professor, but many of his students could not grasp his teachings. In 1833, he received and invitation from the dethroned Charles X to tutor his grandson, the Duke of Bordeaux in Prague. So Cauchy traveled to Prague to tutor his grandson. One year later, in 1834, his wife and daughters joined him in Prague. Even though Cauchy was a brilliant mathematician, he was not a very good tutor (or even professor in some cases). He was known to expect too much from his students and assumed that his students understood him. Additionally, Cauchy was unorganized, he rambled on, and he tried to crunch too much information into a small period. Moreover, the Duke was far from interested in mathematics. The Duke and Cauchy were a perfect mismatch and they often got frustrated with each other. Cauchy's mathematic output was slow during the five years he tutored the Duke because he hardly done any research. Meanwhile, the Duke acquired a lifelong disliked of mathematics. However, Cauchy was promoted to the title Baron and finished tutoring the Duke when the Duke turned 18. Near the end of the 1830s, Cauchy moved back to Paris. He wanted to return to his teaching positions, but because he persistently refused to swear an oath of allegiance, Cauchy was denied his formal position in Parisian science. He was, however, able to have an informal position at the Academy of Sciences. Cauchy tried to apply for the Bureau des Longitudes when a position became available. The Bureau was an organization that aimed to solve the problem of determining position on sea, and it resembled the academy but was less strict in a sense that the members do not have to take the oath of allegiance so seriously. Cauchy was elected to the Bureau, but was surprised and disappointed when he realized that the oath was still required. He still refused to take the oath, and so the king could not approve his election. In essence, Cauchy was in the position of being elected but not approved. He was able to be part of the Bureau, but as a nonmember, he could not participate, receive payment, or submit papers. Even though Cauchy could not do much with his involvement within the Bureau, he still focused on his studies and research, exploring the topic of celestial mechanics. Although he wasn't able to submit papers, Cauchy was able to present papers, and in fact, he presented dozens of papers on the matter of celestial mechanics in 1840 to the Academy. Cauchy's time at the Bureau ended when he was replaced by Poinsot at the end of 1843. After leaving the Bureau, Cauchy worked with the Catholic Church to help establish its own branch of edu- cation. As a very religious man, Cauchy willingly helped the Catholic Ecole Normale Ecclesiastique train the teachers for their colleges. Furthermore, he helped the Catholic Chuch with his help establishing the Institut Catholique. Even though Cauchy was doing these actions out of the goodness in his heart, his colleagues were offended because they went against the Enlightenment ideals of the French Revolution and so Cauchy was further ostracized from the intellectual community and became harder, almost impossible, for him to be approved for chairs. For example, Cauchy applied for a chair of mathematics at the College de France but 3 only got three out of the 45 votes casted despite his impressive mathematical prowess.