Baron Augustin-Louis Cauchy was a French engineer, mathematician, and physicist born in 1789. He is known for making and pioneer several contributions to the field of mathematical analysis and continuum mechanics. Additionally, he was the first one to prove calculus theorems and almost singlehandedly founded the complex study of permutation groups in abstract algebra.
As a result, Cauchy received a tremendous amount of respect and recognition from his colleagues and successors. In total, he came up with eight hundred research articles and five complete textbooks, proving him a prolific writer. So let’s discuss how Augustin-Louis Cauchy was able to influence the era of the 18th century.
Cauchy was born to Louis Francois Cauchy and Marie-Madeleine Desestre. Cauchy had two brothers. Alexandre Laurent Cauchy who became the president of a division of the court of appeal in 1847. Eugene Francois Cauchy was a publicist and wrote several mathematical works.
In 1818, Cauchy married Aloise de Bure. She was a close relative to the publicist who published most of Cauchy’s work. Cauchy’s father was employed in the Parisian Police of the Ancient Regime as a high-ranking officer but soon left his position during the French Revolution, which broke out after a month Cauchy was born.
As a result, the Cauchy family escaped the revolution and the terror that followed by moving to Arcueil. This was where Cauchy received his initial education from his father. Upon the execution of Robespierre, it was safe for the family to return to Paris.
The year 1800 saw Louis-Francois Cauchy accepting a bureaucratic job and quickly moved high up in the ranks. When Napoleon Bonaparte came into power, Louis Cauchy became the Secretary-General of the Senate working directly under Laplace.
At the same time, the well-known mathematician Lagrange was also a close friend of the family. Then, in the fall of 1802, Augustin-Louis was enrolled in the second-best school of Paris, Ecole Centrale de Pantheon on the advice of Lagrange.
Since Augustin was a brilliant student, he won many prizes in both Latin and humanities. Despite the success, he chose a career in engineering and prepared himself to enter Ecole Polytechnique.
In 1805, he earned the second position amongst 293 applicants and was admitted. The school worked under stringent military disciplines, which sometimes made it complicated for Cauchy to adapt. Nevertheless, at the age of 18, he was done with Polytechnique and then moved to Ecole des Ponts et Chaussees.
Upon finishing school in 1810, Cauchy accepted a junior engineering job in Cherbourg, where a naval base was supposed to be built by Napoleon. Augustin-Louis stayed here for three years and was assigned to the Ourcq Canal Project and the Saint-Cloud Bridge.
At the time, although he was quite busy with his managerial responsibilities but managed to take out some time to prepare mathematical manuscripts when were then submitted to the Premiere Classe of the Institut de France. The first two manuscripts of Cauchy were accepted whereas the third was rejected.
In 1812, Cauchy returned home when he was 23 since he had become ill due to overwork. Another important reason was that he was losing interest in his engineering job and was gradually moving towards mathematics.
And at the time, Cauchy could have easily secured a mathematics-related position. Therefore, according to Augustin Louis Cauchy’s biography, he never returned to Cherbourg. He was still formally employed as an engineer but was transferred from the payroll of the Ministry of the Marine to the Ministry of the Interior.
Therefore, for the next three years, Cauchy spent, as sick unpaid leave while fruitfully working on his mathematics interest. Then, he attempted to enter the First Class of the Institut de France but failed thrice. In 1815, when Napoleon was defeated at Waterloo, several major changes came up.
For instance, the Academie des Sciences was re-established and Lazare Carnot and Gaspard Monge were removed from the Academy for political reasons. As a result, the King appointed Cauchy to replace one of them. His appointment attracted harsh criticism from his peers and thereby, created many enemies in his scientific circle as well.
Professor at Ecole Polytechnique
In 1815, an associate professor at the Ecole Polytechnique Louis Poinsot asked to be exempted from his teaching duties due to health reasons. Cauchy was a rising mathematical star at the time and certainly gained a professorship.
At the time, his proof of Fermat’s polygonal number theorem was one of his greatest achievements. However, it was well-known that Cauchy was very loyal to the Bourbons, he succeeded Poinsot.
Finally, he quit his engineering job and earned a 1-year contract to teach mathematics to the students of the Ecole Polytechnique. In 1816, while this non-religious and Bonapartist school was re-organized, Cauchy was promoted to full professor.
The year 1830 saw the July Revolution taking place in France. Charles X fled the country while Louis-Philippe succeeded him. Riots took place quite close to Cauchy’s home in Paris, which also included the uniformed students of the Ecole Polytechnique.
This was a turning point in Cauchy’s mathematical career. Some of Augustin-Louis Cauchy achievements would come up as a result of this while he had to leave the country due to being heartbroken and angry over liberals taking over.
Therefore, he left the country, leaving his family behind, and spent a short amount of time in Switzerland. This was where he had to decide whether he would swear a required oath of allegiance to the new regime. As a result, Cauchy lost all his jobs in Paris, excluding his position at the Academy, which did not require an oath.
In 1831, Cauchy went to the Italian City of Turin, where he accepted an offer from the King of Sardinia for the chair of theoretical physics, made especially for him. In 1831, he was made a member of the Royal Swedish Academy of Sciences and after a year a Foreign Honorary Member of the American Academy of Arts and Sciences.
In 1833, Cauchy left Turin for Prague to give private science tuition to the thirteen-year-old Duke of Bordeaux, who was the exiled crowned prince at the time. While serving as a professor at the Ecole Polytechnique, Cauchy carried a reputation of being a teacher who possessed a level of understanding that only a few of his students could match and cramming a lot of material in the allotted time.
Cauchy returned to Paris and assumed his position at the Academy of Sciences in late 1838. However, he could not retrieve his teaching positions due to refusing to swear an oath of allegiance.
In 1839, a vacancy appeared in the Bureau des Longitudes. It resembled the Academy in many ways, especially when it came to not requiring the oath of allegiance. The same year, Cauchy was elected to the Bureau and discovered immediately that the matter of oath was not easily dispensed with. Therefore, while Cauchy was elected, he was not approved.
Throughout the nineteenth century, the French educational system struggled to separate the church and state. In the meantime, Cauchy passed his information and knowledge to the Ecole Normale Ecclesiastique to train teachers for colleges. Cauchy remained a professor at the University until his death at the age of 67.
Cauchy was a genius individual who illustrated it by presenting a simple solution to the problem of Apollonius, which he discovered in 1805. His generalization of Euler’s formula on polyhedra in 1811 and several other elegant problems helped him gain much recognition.
Furthermore, Cauchy also worked on Fresnel’s wave theory and on the polarization and dispersion of light. He wrote on the rods and elastic membranes and on waves in elastic media. Additionally, he introduced a 3 x 3 symmetric matrix of numbers that is now known as the Cauchy stress tensor.
In his book Cours d’Analyse, Cauchy stressed the importance of rigor in analysis. In this case, rigor meant the rejection of the principle of Generality of algebra and its replacement by infinitesimals and geometry. Judith Grabiner wrote that Cauchy was the one who taught rigorous analysis to all of Europe. In addition to that, Cauchy was also the first one to prove Taylor’s theorem.
He wrote a complete textbook in return for his students at the Ecole Polytechnique in which he developed the basic theorems of mathematical analysis.
Augustin Cauchy goes down in the history books as one of the most successful, influential, and prominent scientists of the 18th century. Although he was a genius at large but his contributions were a result of major disappointments and complications especially during his early days as a mathematician.
He was known as someone who always stood his ground and never compromised on his principles. Considering the level of success and recognition he received in his lifetime, it is not every day that a scientist like Cauchy is born.