AUGUSTIN-LOUIS CAUCHY: BIOGRAPHY, CONTRIBUTIONS, WORKS - BIOGRAPHIES - 2024

Augustin-Louis Cauchy (1789-1857) was a French engineer, mathematician, professor, and researcher. It is considered that he was one of the scientists who redesigned and promoted the analytical method, since he thought that logic and reflection should be the center of reality.

For this reason, Cauchy stated that the task of the students was to seek the absolute. Likewise, despite the fact that he professed rational ideology, this mathematician was characterized by following the Catholic religion. Therefore, he trusted that the truth and order of events were possessed by a superior and imperceptible being.

Augustin-Louis Cauchy was a French engineer, mathematician, professor, and researcher. Source: Anonymous (public domain)

However, God shared the key elements so that individuals - through inquiry - deciphered the structure of the world, which was made up of numbers. The works carried out by this author excelled in the faculties of physics and mathematics.

In the field of mathematics, the perspective on number theory, differential equations, the divergence of infinite series, and determining formulas changed. While in the area of ​​physics he was interested in the thesis on the elasticity and linear propagation of light.

Likewise, he is credited with having contributed to the development of the following nomenclatures: principal tension and elemental balance. This specialist was a member of the French Academy of Sciences and received several honorary degrees due to the contribution of his research.

Biography

Augustin-Louis Cauchy was born in Paris on August 21, 1789, being the eldest of the six children of the civil servant Louis François Cauchy (1760-1848). When he was four years old, the family decided to move to another region, settling in Arcueil.

The events that motivated the move were the sociopolitical conflicts caused by the French Revolution (1789-1799). At that time, society was in chaos, violence, and despair.

For this reason, the French lawyer made sure that his children grew up in another environment; but the effects of the social demonstration were felt throughout the country. For this reason, Augustin's first years of life were determined by financial obstacles and poor well-being.

Despite the difficulties, Cauchy's father did not displace his education, since from an early age he taught him to interpret artistic works and to master some classical languages ​​such as Greek and Latin.

Academic life

At the beginning of the 19th century this family returned to Paris and constituted a fundamental stage for Augustin, because it represented the beginning of his academic development. In that city he met and was related to two friends of his father, Pierre Laplace (1749-1827) and Joseph Lagrange (1736-1813).

These scientists showed him another way of perceiving the surrounding environment and instructed him in subjects of astronomy, geometry and calculus with the aim of preparing him to enter a college. This support was essential, since in 1802 he entered the central school of the pantheon.

In this institution he stayed for two years studying ancient and modern languages. In 1804, he began an algebra course and in 1805 he took the entrance exam at the polytechnic school. The proof was examined by Jean-Baptiste Biot (1774-1862).

Biot, who was a renowned teacher, accepted it instantly for having the second best average. He graduated from this academy in 1807 with a degree in engineering and a diploma that recognized his excellence. He immediately joined the school of bridges and roads to specialize.

Work experience

Before completing the master's degree, the institution allowed him to exercise his first professional activity. He was hired as a military engineer to rebuild the port of Cherbourg. This work had a political purpose, since the idea was to expand the space for the French troops to circulate.

It should be noted that throughout this period, Napoleon Bonaparte (1769-1821) tried to invade England. Cauchy approved the restructuring project, but in 1812 he had to withdraw due to health problems.

From that moment on, he dedicated himself to researching and teaching. He deciphered Fermat's polygonal number theorem and showed that the angles of a convex polyhedron were ordered by their faces. In 1814 he secured a post as a tenured teacher at the institute of science.

In addition, he published a treatise on complex integrals. In 1815 he was appointed as an analytical instructor at the polytechnic school, where he was preparing for the second course, and in 1816 he received the nomination of a legitimate member of the French academy.

Last years

In the middle of the nineteenth century, Cauchy was teaching at the Colegio de Francia - a place he obtained in 1817 - when he was summoned by Emperor Charles X (1757-1836), who asked him to visit various territories in order to spread his scientific doctrine.

To fulfill the promise of obedience that he had made before the House of Bourbon, the mathematician gave up all his work and visited Turin, Prague and Switzerland where he worked as a professor of astronomy and mathematics.

In 1838 he returned to Paris and resumed his place at the academy; but he was forbidden to assume the role of professor for breaking the oath of allegiance. Even so, he collaborated with the organization of the programs of some graduate programs. He died in Sceaux on May 23, 1857.

Contributions to mathematics and calculus

The investigations carried out by this scientist were essential for the formation of schools of accounting, administration and economics. Cauchy put forward a new hypothesis about continuous and discontinuous functions and tried to unify the branch of physics with that of mathematics.

This can be appreciated when reading the thesis on the continuity of functions, which exhibits two models of elementary systems. The first is the practical and intuitive way of drawing the graphs, while the second consists of the complexity that deviating a line represents.

That is, a feature is continuous when designed directly, without the need to lift the pen. On the other hand, the discontinuous one is characterized by having a varied meaning: to do it it is necessary to move the pen from one side to the other.

Both properties are determined by a set of values. Likewise, Augustin adhered to the traditional definition of integral property to decompose it, stating that this operation belongs to the system of addition and not of subtraction. Other contributions were:

- Created the concept of complex variable to categorize holomorphic and analytical processes. She explained that holomorphic exercises can be analytical, but this principle is not carried out in reverse.

- Developed the convergence criterion to check the results of operations and eliminated the divergent series argument. He also established a formula that helped solve the systematic equations and will be shown below: f (z) dz = 0.

- He verified that the problem f (x) continuous in an interval acquires the value that is between the factors f (a) or f (b).

Infinitesimal theory

Thanks to this hypothesis, it was expressed that Cauchy gave a solid base to mathematical analysis, it is even possible to point out that it is his most important contribution. The infinitesimal thesis refers to the minimum quantity that comprises a calculation operation.

At first, the theory was called the vertical limit and was used to conceptualize the foundations of continuity, derivation, convergence, and integration. The limit was the key to formalizing the specific meaning of the succession.

It is worth noting that this proposition was linked to the concepts of Euclidean space and distance. Besides, it was represented in the diagrams by two formulas, which were the abbreviation lim or a horizontal arrow.

The vertical limit theory was used to conceptualize the foundations of continuity, derivation, convergence and integration. Source: pixabay.com

Published works

The scientific studies of this mathematician stood out for having a didactic style, since he was concerned with transmitting the exposed approaches in a coherent way. In this way it is observed that his role was pedagogy.

This author was not only interested in externalizing his ideas and knowledge in classrooms, but also gave various conferences on the European continent. He also participated in the exhibitions of arithmetic and geometry.

It is worth mentioning that the research and writing process legitimized Augustin's academic experience, since in the course of his life he published 789 projects, both in magazines and in editorials.

The publications included extensive texts, articles, reviews and reports. The outstanding writings were The Lessons of Differential Calculus (1829) and The Memory of the Integral (1814). Texts that laid the foundations for recreating the theory of complex operations.

The numerous contributions he made in the area of ​​mathematics led to their name being given to certain hypotheses, such as the Cauchy integral theorem, the Cauchy-Riemann equations and the Cauchy sequences. Currently, the most relevant work is:

Lessons on the infinitesimal calculus

The purpose of this book was to specify the characteristics of the exercises in arithmetic and geometry. Augustin wrote it for his students so that they would understand the composition of each algebraic operation.

The theme that is exposed throughout the work is the function of the limit, where it is exhibited that the infinitesimal is not a minimal property but a variable one; this term indicates the starting point of every integral sum.

References

1. Andersen, K. (2004). About calculus and integral theory. Retrieved on October 31, 2019 from Stanford Mathematics Faculty: mathematics.stanford.edu
2. Ausejo, E. (2013). Cauchy: the foundation of the infinitesimal calculus. Retrieved on November 1, 2019 from the Journal of History and Social Sciences: dialnet.uniroja.es
3. Caramalho, DJ (2008). Cauchy and the calculus. Retrieved on October 31, 2019 from the Department of Mathematics Faculty: math.cornell.edu
4. Ehrhardt, C. (2009). Introduction of the Augustin Louis Cauchy theory. Retrieved on November 1, 2019 from All Faculty: math.berkeley.edu
5. Flores, J. (2015). Towards a concept by Augustin Cauchy. Retrieved on October 31, 2019 from Historical Processes: saber.ula.ve
6. Jephson, T. (2012). History of French mathematicians. Retrieved on October 31, 2019 from the Department of History: history.princeton.edu
7. Vallejo, J. (2006). Memory on the curvatures of the lines at their different points. Retrieved on November 1, 2019 from Revista de Economía: sem-wes.org