Augustin-Louis Cauchy Brandon Lukas

Cauchy’s life

On August 21, 1789, Augustin-Louis Cauchy was born in . He was born just one month after the beginning of the . His father, Francois Cauchy, was a senior French government officer who feared for his life in Paris and lost his job due to ’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 , 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 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 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.

Fortunately, Cauchy was finally able to hold a position after the oath of allegiance was abolished in 1848. By 1849, he was recruited by the Faculte de Sciences and taught mathematical astronomy. Even though the loyalty oath came back into effect shortly afterwards within the bureaucratic circles and state functionaries, which include university professors, Cauchy was exempt from taking the oath after a cabinet minister convinced the Emperor to specifically exempt Cauchy. Cauchy stayed a professor until he died at age 67 from the common cold.

Cauchy’s mathematical works

Cauchy overwhelmed the mathematical world with the size and greatness of his works. He produced 789 full length papers in his life which is the largest body of work left behind by any mathematician besides Euler. Most of his works were published by his wife’s family who were publishers. Cauchy is best known for pioneering analysis and the theory of substitution groups. His theory of functions of a complex variable, otherwise simply known as Complex analysis, is used in many branches of mathematics and physics today.

Cauchy’s first works came from when he was a junior engineer in Cherbourg. He prepared three manuscripts and submitted them to the Premiere Classe of the Institut de France. Two of the works on polyhedra were accepted. The third one on the directrices of conic sections was rejected. The first of these works came from 1811 when he solved a problem that Lagrange gave to him. His solution established that the angles of a convex polyhedron are determined by its faces. The second of these works came from 1812 when he solved Fermat’s problem on polygonal numbers which became one of his greatest successes. Cauchy also generalized Ruffini’s theorem which is now known as Galois theory.

When Cauchy left his engineering job and went to Paris, he worked on symmetric functions, symmetric groups, and the theory of higher-order algebraic equations. Cauchy set the basis of the theory of complex functions when he submitted his treatise on definite integrals to the French Academy in 1814. Two years later, the French Academy awarded him on the propagation of waves at the surface of a liquid which is used in hydrodynamics. In 1819, he created the method of characteristics which is used in the theory of partial differential equations. In 1822, he founded elasticity theory which is regarded to be his greatest accomplishment.

Cauchy was known to be one of the first to state and prove theorems of calculus as rigorously as possible. He clarified principles of calculus and put it down on a satisfactory basis at the same time developing limits and continuity which are useful for analysis. Cauchy lectured on methods of integration which he discovered but not had not published in 1817 at the College de France when he had to fill in Biot’s post after he left Paris for an expedition to the Shetland Islands in Scotland. Cauchy was the first to work on defining an integral and making the study of conditions for convergence of infinite series. At the Ecole Polytechnique, Cauchy created a text concerning the development of the basic theorems of calculus titled Cours d’analyse de I’Ecole Royale Polytechnique for his students in 1821. He also published other important treatises including Resume des lecons sur le calcul infinitesimal in 1823 and Lecons sur les applications du calcul infinitesimal a la geometrie from 1826 to 1828. In 1826, Cauchy studied the calculus of residues with his text titled Sur un nouveau genre de calcul analogue au calcul infinitesimal. In 1829, Cauchy was the first to define a complex function of a complex variable in Lecons sur le Calcul Differentiel.

Cauchy’s mathematical output slowed down during the 1830s due to political events, exile, and tutoring the Duke; however, he did work on differential equations, applications to mathematical physics, and mathematical astronomy during his time at the Bureau des Longitudes. During his time at the Bureau, he presented the signed-digit representation of numbers. He published his work in a 4-volume text titled Exercices d’analyse et de physique mathematique in the 1840s.

4 Overall, Cauchy’s collected work is published in 27 volumes in Oeuvres completes d’Augustin Cauchy. Many mathematical terms are named after Cauchy; in fact, there are 16 concepts named after him which is more than any other mathematician. In the theory of complex functions, there is the Cauchy integral theorem. For the solution of partial differential equations, there is the Cauchy-Kovalevskaya existence theorem. Finally, there are the Cauchy-Riemann equations and Cauchy sequences. Cauchy contributed to the theory of numbers, published three papers on error theory, and attempted to create a mathematical basis in the study of optics.

Collaboration with other scholars

While Cauchy didn’t collaborate with many other scholars or mathematicians due to his unpopularity and seemingly offensive nature, he interacted and met with many intellectuals that definitely influenced his work.

When Cauchy was still young, mathematicians Laplace and Lagrange were friends of the family and commonly visited the Cauchy household. Lagrange was especially interested in Cauchy’s mathematical education and influenced Cauchy’s education by convincing his dad to enroll Cauchy in the Ecole Centrale du Pantheon. Their influence followed Cauchy even after he graduated his formal education which was demonstrated when Cauchy took a copy of Mecanique Celeste by Laplace and Theorie des Fonctions by Lagrange with him to his first job in Cherbourg.

When Cauchy took his entrance exam for the Ecole Polytechnique, he was examined by mathematician Jean- Baptiste Biot who also worked in astronomy and elasticity like Cauchy would in the future. At the Ecole Polytechnique, Cauchy attended classes taught by French mathematicians Sylvestre Lacroix, Gaspard de Prony, and Jean Nicolas Pierre Hachette. His analysis tutor was electric and magnetic theorist Andre-Marie Ampere. Ampere thought highly of Cauchy and the two worked very closely with each another at the Academy.

After Cauchy submitted his first paper in 1811, scholar Legendre and mathematician Malus encouraged him to submit a second paper on polygons and polyhedra in 1812.

Cauchy came under constant criticism and dislike from his peers and the community for his staunch Catholic views and rigid loyalist ideals. Cauchy was a Jesuit which is a type of Roman Catholic and he sometimes brought his religion into his scientific work. For example, in 1824, Cauchy attacked an author for his view that Newton did not believe that people had souls during his report on the theory of light.

Furthermore, scientists were offended by the way Cauchy acted around them. Poncelet personally described a rude and abrupt encounter with Cauchy where Cauchy tried to avert conversation with him. Galois and Abel had negative experiences with Cauchy as well. Abel even described Cauchy as ”mad and there is nothing that can be done about him”. When Abel died, Belhoste criticized Cauchy for being untimely and uncooperative with his report that ended up being ”hasty, nasty, and superficial, unworthy of both his own brilliance and the real importance of the study he had judged.”

Cauchy’s unpopularity costed him many positions. His persistent refusal to accept an oath prevented him from holding a teaching position in Paris. Furthermore, Cauchy’s political views and religious activities with the Jesuits in the Ecole Normale Ecclesiastique ostracized him from other mathematicians and was the reason why Cauchy was not appointed for a mathematics chair at the College de France despite having the greatest mathematical ability. Another incident occurred when Joseph Liouville was appointed instead of Cauchy after a close election. Attempts were made to reverse this decision but that only led to worsening relations between Liouville and Cauchy.

Finally, during his last years, Cauchy and Duhamel disputed over a priority claim regarding a result on inelastic shocks. Duhamel called Cauchy out for claiming to be the first to give the results in 1832 when Poncelet referred to his own work on the subject six years prior proving Cauchy to be wrong. Cauchy was too sad and bitter to

5 admit he was wrong. He died never admitting his wrong.

Overall, Cauchy offended scholars in the community by his self-righteous arrogance and religious and political bigotry. In fact, he repressed the mathematical work of Nicolas Galois because Galois was a radical republican. His obstinate attitude, stubborn refusal to accept an oath, and heavy involvement with his religion costed him many positions and opportunities to collaborate with other scholars, including Niels Abel.

Historical events that marked Cauchy’s life.

The French Revolution had broke out around the same time Cauchy was born in 1789 and caused his father to lose his job and his family to flee for their lives from Paris to the village of Arcueil where Cauchy received his first education from his father. His family fled only a month after the storming of the Bastille. Cauchy and his family moved back to Paris once Robespierre was executed and the atmosphere had calmed.

Napoleon became the emperor of France and he provided job opportunities for Cauchy and his father. Cauchy’s father worked in Napoleon’s bureau. Cauchy, after graduating in civil engineering from the Ecole des Ponts et Chaussees in 1810, worked on Napoleon’s English invasion fleet in Cherbourg.

When Napoleon was defeated at Waterloo in 1815, the newly crowned King Louis XVIII re-established the Academie des Sciences in 1816. King Louis XVIII removed mathematician Monge from his membership at the Academy and gave Cauchy his position.

During the 1830 July Revolution in France, Cauchy left the country and went to Switzerland to get away from the failing political system in Paris. The political events in France now required Cauchy to accept and oath of allegiance to the new regime which he rejected and lost him most of his positions in Paris. In 1831, Cauchy accepted an offer from the King of Piedmont to teach theoretical physics in Turin. In 1833, Cauchy accepted the ousted king of France Charles X’s invitation and moved to Prague to tutor the Duke of Chambord.

He returned to Paris in 1838 but still was not allowed to be a full member at the Academy anymore because of his refusal of the oath. When the Catholic Church established its own branch of education after struggling with the separation of Church and State issue, Cauchy helped establish the Institut Catholique but that only hurt his popularity because it went against the Enlightenment ideals of the time. Cauchy was able to regain his university positions when Louis Philippe was overthrown in 1848 and the oath was abolished. After the Second Republique was established the same year, Cauchy resumed his position at the Sorbonne.

Significant historical events around the world during Cauchy’s life

Cauchy was born near the beginning of the French Revolution. The French Revolution was not very peaceful and it resulted in lasting political changes. The King of France was executed and Napoleon Bonaparte became emperor. Napoleon conquered Italy in 1800. Meanwhile, the United Kingdom and Ireland formed one Monarch and parliament, and the United States was ready to expand.

France owned a large territory in North America west of the Louisiana river. America’s president, Thomas Jefferson, made a deal with France’s Napoleon. Napoleon needed money to finance his campaign in Europe, so Jefferson paid him fifteen million dollars for France’s territory in North America known as the Louisiana Purchase of 1803. This doubled the size of the United States and allowed Napoleon to conquer more of Europe, namely Spain and Rome.

Napoleon’s downfall began when he invaded Russia in 1812. The harsh and brutal Russian climate and barren mountainous terrain was too hard on the French and, as a result, many starved or froze to death. With a

6 smaller army, Napoleon’s was weakened and was defeated by the allied soldiers in the War of Liberation in 1814. Napoleon was finally defeated at the Battle of Waterloo in 1815 and King Louis XVII took control of France. Meanwhile, Greece, with the help of France and Great Britain, gains its independence from Turkey. Mexico gains its independence from Spain after the United States writes the Monroe Doctrine.

The first photograph was made at this time by French inventor Fox Talbot who also worked on the first internal combustion engine. George Stephenson designed the first steam locomotive too the same year. In 1829, an American patents a typographer, which is not quite yet a typewriter which will come in the 1860s, a few years after Cauchy’s death.

In 1831, Poland is the first to revolt against Russia in the November Uprising of 1831. Lithuania, Ukraine, and Belarus worked with Poland but they were all put down by the Imperial Russian Army. However, Belgium was able to successfully revolt against the Netherlands and each formed independent nations.

In Britain, slavery was abolished by the Slavery Abolition Act, although slavery still existed in the United States. King William IV died in 1837 and Queen Victoria took over. Soon, Great Britain and the Chinese Qing Dynasty were involved in the Opium Wars which revolved around trading rights with China and the rest of the world. In 1838, Samuel Morse invents Morse Code which is used in telegraphs which allow for messages to be sent and received from long distances almost instantly.

In America, the British North America Act of 1840 consolidated upper and lower Canada. Meanwhile, the United States annexed Texas, declared war on Mexico, and gained Colorado, Arizona, Nevada, California, Utah, and New Mexico. Gold was discovered in California, so many Americans as well as foreign immigrants, such as the Chinese, travelled out west in pursuit of finding riches.

The last few years of Cauchy’s life, Russia had begun the Crimean War with Great Britain, the Ottoman Empire, and France. He died in 1857, five years before the American Civil war.

As a whole, Cauchy lived in a time where nations fell and nations were born. Nothing was really constant in the world during Cauchy’s life as revolutions and wars commonly took place.

Significant mathematical progress during the Cauchy’s lifetime

The same year Cauchy was born, Slovene mathematician Jurj Vega improved Machin’s formula and computed pi to 140 decimal places. 136 of these digits were correct. About five years later, he published his Thesaurus Logarithmorum Completus.

In 1796, German Carl Gauss proved that the regular 17-gon can be constructed using only a compass and a straightedge. The same year, French mathematician Adrien-Marie Legendre conjectured the prime number theorem. The following year, Norwegian-Danish Caspar Wesell studied complex numbers and applies them to vectors and geometry. in 1799, Gauss proved the fundamental theorem of algebra and Paolo Ruffini partially proved the Abel-Ruffini theorem.

In the early 1800s, Legendre developed the method of least squares, Poinsot finished the Kepler-Poinsot polyhedra, the Fundamental theorem of algebra proof is published along with the Argand diagram, and Joseph Fourier discovered the trigonometric decomposition of functions.

In 1811, Carl Gauss discussed integrals, limits, and integration. Four years later, Simeon Denis Poisson analyzed integrations along paths in the complex plane. Two years later, Bernard Bolzano presented the intermediate value theorem. In 1822, Cauchy presented the Cauchy integral theorem, and in 1825, Cauchy applied his integral theorem for general integration paths, thereby introducing the theory of residues in complex

7 analysis.

Also within the 1820s, Niels Henrik Abel partially proved the Abel-Ruffini theorem that Paolo Ruffini partially solved back in 1799. In 1825, Fermat’s Last theorem was proven for n = 5 by Peter Gustav Lejeune Dirichlet and Legendre while Andre-Marie Ampere found Stokes’ theorem. George Green proved his Green’s theorem and Bolyai, Gauss, and Lobachevsky created hyperbolic non-Euclidean geometry.

In the 1830s, Mikhail Vasilievich Ostrogradsky revived the divergence theorem described by Lagrange, Gauss, and Green. Galois invented group theory and Galois theory. Dirichlet proved Fermat’s Last Theorem for n = 14 and proved Dirichlet’s theorem about prime numbers. In 1837, Dirichlet developed analytic number theory while Pierre Wantzel proved two of the mathematical problems of the antiquity from classical Greece, specifically trisecting the angle and doubling the cube, is impossible with just a compass and a straightedge.

In the 1840s, Karl Weierstrass found the Laurent expansion theorem which was presented and published by Pierre-Alphonse Laurent two years later in 1843. Meanwhile, William Hamilton discovered the calculus of quaternions and found that they are non-commutative. In 1849, George Gabriel Stokes researched solitary waves and their relationship with periodic waves and proved Stokes’ theorem in 1850.

In the 1850s, the last few years before Cauchy’s death in 1857, essential singular points was conceptualized by Victor Alexandre Puiseux. Riemannian geometry was introduced by Bernhard Riemann in 1854 and Arthur Cayley presented that quaternions can represent rotations in four-dimensional space. Two years after Cauchy’s death, Riemann formulated the Riemann hypothesis about the distribution of prime numbers.

Connections between history and the development of mathematics

After the violent French Revolution and during the period following it, many French engineers were killed. As a result, there was a heavy emphasis to teach engineering and practical math to the younger generation to replace those who died. The French educational system was reformed and many prestigious French schools reopened under the direction of Napoleon Bonaparte. Arguably the most important of the schools, the Ecole Polytechnique, harvested many intelligent minds and thoughts as it recruited only the most disciplined students and hired the most competent teachers. And so, mathematical creativity and inspiration was at an all time high for France, especially from these universities, and soon other nations caught on to the importance and value of education including Germany and Russia.

In Germany, there existed Gauss, a brilliant mathematician who published dozens of papers on number theory, celestial mechanics, probability theory, and analysis. However, in comparison to France who focused on practical mathematics, German math supported on pure mathematics. This was because they weren’t as needy for engineers as France was because France’s revolutionary war was very violent and left a tremendous impact.

In Russia around the same time as Cauchy, Markov researched stochastic processes and developed Markov chains and processes. Russian education improved after Russian tsar Alexander I unified their educational system in 1804 and emphasized universities.

Meanwhile, in Britain, mathematicians were creating inventions and techniques for computation which would lead its way to computer sciences. Babbage created a device that could perform automatic calculations like a computer or calculator would. George Boole invented logical operators which include ’And’, ’Or’, and ’Not’ as well as establishing the Boolean data type computer scientists use today which are ’True’ and ’False’, or otherwise ’on/off’ or ’1/0’, respectively.

8 Remarks

Cauchy was a very interesting person and mathematician. He shocked the world and the community not only with his mathematical output, but with his determination, focus, and discipline. Even from a young age, Cauchy’s passion for math endured all obstacles and set-backs to the day he died.

Cauchy gifted the world with so much of his mathematical discoveries and research. Unfortunately, the world wasn’t all too kind to Cauchy. Cauchy was deprived from a number of positions and sent to exile multiple times due to the changing political climate of France throughout his entire life, beginning with the French Revolution. Everything Cauchy did was done out of the goodness of his heart; he remained loyal to the old political regime because he felt that was right, and he was a devout Catholic and believed in doing good for his Church and God.

Cauchy tragically yet understandably developed a negative attitude and offended many people. He was per- ceived to be arrogant, stubborn, and self-righteous. In some aspects, one can understand why Cauchy might have acted this way. Obviously, it may feel the world has dealt him great injustices: being senselessly rejected positions despite his clearly brilliant potential; being regarded as an outcast within the community; and so on and so forth. But even though Cauchy’s reputation and attitude wasn’t the greatest and most positive, he still remained focus on his passion and didn’t allow public perception, failure, or set-backs prevent him from reaching his goals and dreams.

For example, while he was in exile and away from Paris, he still studied math. When he gave up his engineering job and went on unpaid leave, he did that just to focus on math. He applied and applied to university after university until he was accepted to share his mathematical findings. He left his family behind to teach math in foreign countries. Even when he wasn’t allowed to be a formal member of the Bureau, he still focused on math and contributed. No matter whatever challenge was happening in Cauchy’s life at the time, he was unwavering in his beliefs (both political and religious) and unwilling to accept defeat just so he can help the state of math progress. His stoic determination is inspiring and proves how successful Cauchy really is.

To synthesize, Cauchy endured a lot of struggle in his life. Some of the unfair things Cauchy had to endure were external including revolutions and exiles while some were internal like dealing with a bad reputation. Cauchy’s unyielding passion for mathematics and his firm beliefs kept him centered and focused on his studies and dreams. Cauchy didn’t need to have those job positions that were deprived from him nor garner a graceful reputation and collaborate with many scholars because Cauchy stunned the world with his great mathematical output as is. It’s uncertain how much more Cauchy could have produced if his life was deplete of challenges, but it’s possible that he might not have worked as hard and his work and legacy would not be as remarkable. I believe it is Cauchy’s struggles and his response to challenges that make him the interesting and successful mathematician, husband, father, and person he was.

References

1. http://www-history.mcs.st-and.ac.uk/Biographies/Cauchy.html

2. http://www.thefamouspeople.com/profiles/augustin-cauchy-588.php

3. https://www.britannica.com/biography/Augustin-Louis-Baron-Cauchy

4. https://math.berkeley.edu/~robin/Cauchy/accomplishments.html

5. http://pirate.shu.edu/~wachsmut/ira/history/cauchy.html

9 6. http://www.knowthescientist.com/biography/augustin-louis-cauchy.php

7. http://kobotis.net/math/MathematicalWorlds/Fall2015/131/Projects/Biography/Cauchy.pdf

8. http://www.encyclopedia.com/people/science-and-technology/mathematics-biographies/augustin-louis-cauchy

9. http://theinventors.org/library/weekly/aa111100a.htm

10. https://en.wikipedia.org/wiki/Timeline_of_mathematics

11. https://books.google.com/books?id=K2DdBwAAQBAJ&pg=PA7&lpg=PA7&dq=ecole+centrale+du+pantheon& source=bl&ots=VlrCk7Zrlw&sig=AtEQS0fa-Gw5i0QxEynAo7EjQsc&hl=en&sa=X&ved=0ahUKEwjZhcas9_TPAhWI5CYKHbrtCxwQ6AEIRjAF# v=onepage&q=ecole%20centrale%20du%20pantheon&f=false

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