He is one of the founders of modern mathematics: Who is Niels Henrik Abel?

The short life of Abel, the son of a poor clergyman with seven children, was always spent in poverty. But despite his absence, he managed to break new ground in mathematics with his great intelligence. He was only 27 years old when he died:

By William James Published on 18 Ocak 2023 : 15:16.
He is one of the founders of modern mathematics: Who is Niels Henrik Abel?

(1802-1829) Norwegian mathematician. He showed that fifth-degree polynomials cannot be solved with radical expressions; He made important studies on elliptic functions, series, and convergence of series.

He was born on August 5 in Finney village of Kristiansand city. Norway, which fought against England and Sweden in Abel's early youth, was under extremely difficult economic conditions. For this reason, the short life of Abel, the son of a poor clergyman with seven children, was always spent in poverty.

Moreover, when he lost his father at the age of 18, the livelihood of the family fell entirely on Abel's shoulders. While trying to support his family by giving private lessons, he continued his mathematics studies. In the end, unable to endure these harsh conditions, he contracted tuberculosis. He was not even 27 years old when he died on April 6, 1829.

At the beginning of the 19th century, corporal punishment was practiced in schools in Norway, as in many other countries. Abel, a 15-year-old high school student, was fired after his homeroom teacher beat and killed one of his students and was replaced by Bernt Michael Holmboe, a highly talented math-loving teacher. Holmboe and Abel's relationship soon turned into a friendship based on love and respect. Noticing Abel's mathematical talent and playing a very important role in his success, Holmboe worked for Abel to get a scholarship from the Norwegian Government and to find a job, who struggled to deliver his student's work to the great mathematicians of the time.

As a matter of fact, under the supervision and control of Holmboe, Abel soon learned, understood, and even criticizes the works of Newton, Euler, Lagrange, and Gauss. In the end, he showed that the proofs of many theorems proved by ancient mathematicians were not valid within the framework of the judgment of mathematics of that day, even if the result was true.

In this sense, the most misunderstood subjects were the series and the convergence of the series and their results. One of Abel's early works was the examination of the convergence of binomial series used by Newton and Euler, but whose validity area has not been determined.

It was understood in the Renaissance that there were similar solutions for third and fourth-degree polynomials. However, until Abel's arrival, for exactly three centuries, no one had succeeded in demonstrating whether a fifth-degree polynomial could be solved with the aid of radical expressions. Abel, thinking that he had a solution for a while after starting to deal with the solution to this problem, sent his work to the well-known mathematicians of Denmark; but soon realized that his proof was wrong. Thereupon, Abel, who was not afraid of failure, started to investigate whether the problem could be solved instead of looking at the problem from another direction and finding a solution by investigating where his mistake was. Thus, he proved that this problem, which played an important role in the development of algebra, cannot be solved with radical expressions. Abel was 19 when he came to this conclusion. This proof is important in terms of methodology; because, as has been done until then, he emphasizes that before starting to search for the solution to an equation, it is necessary to start by investigating whether the equation in question has a solution.

Abel sent this work to the great German mathematician Gauss, whereas Gauss did not even need to read it after learning the title of the work in question.

Norwegian mathematicians, especially his teacher and close friend Holmboe, who understood the greatness of Abel, tried to get a scholarship for Abel from the Norwegian Government, declaring that he had to make a one or two-year study trip to Germany and France in order to increase his knowledge and experience. After much effort, a scholarship was available to cover Abel's expenses for one year of study abroad.

Beginning his tour in September 1825, Abel moved to Berlin after meeting with well-known mathematicians and astronomers from Norway and Denmark. There, he met the engineer A. Leopold Crelle, who worked for the spread of mathematics. Crelle soon realized Abel's worth. At that time, Crelle was preparing to publish a mathematics journal. When this project was realized as a result of the cooperation between them, Crelle published Abel's works in the Journal für die Reine und Angewandte Mathematik (“Journal of Basic and Applied Mathematics”), helping him to be known in the world of mathematics; The value of Abel's work also greatly increased the reputation of Crelle's magazine.

Abel's most important work is the work he presented to the French Academy of Sciences on January 10, 1826. This work on elliptic functions was entitled Memoire sur une Propriete Generale d'une Classe Tres Etendue des Fonctions Transcendantes (“A Study of a General Property of a Very Large Class of Transcendental Functions”). Those who were most interested in this subject at the time were the French mathematician Le Gendre and the German mathematician Jacobi.

When the value of this magnificent work presented to the French Academy of Sciences was realized, Abel was no longer alive. The Academy appointed Le Gendre and Cauchy to review the work. At that time, however, Le Gendre was too old to delve deeply into the subject, and Cauchy was too busy to devote time to anything but his own work. Thus, the work was forgotten in a corner. However, two years later, as a result of the efforts of Jacobi and the Norwegian Government, who had just learned of the existence of such a study, it was removed from the dusty files and finally introduced to the world of mathematics. Learning the content of the work, Jacobi said, "How could such a study, which will be perhaps the most important invention of this century, escape the eyes of the mathematicians of the French Academy of Sciences?" said, and later on Le Gendre evaluated the same work as "A monument that will live forever", and Hermite as "Abel left 500 years of work to future generations of mathematicians".

Abel, whose financial means were completely exhausted, returned to his country in May 1827. In Paris, his health had deteriorated, and he had learned that it was not due to the cold, as he thought, but to tuberculosis. Still, Abel, who did not lose his will to live and his strength, hoped that when he arrived in Norway, his genius would be accepted by everyone and he would definitely be given a lecture at a university. Nothing turned out the way Abel expected. The faculty he had hoped for was not given to him, but to his teacher, Holmboe. Although Holmboe suggested that this task be given to Abel, the university administration did not accept this proposal and took Abel, who was unemployed and broke, with a benevolent family. Abel, whose illness was progressively worsening and could no longer care for himself, went to Froland with his fiancee but died in the same city on April 6, 1829, a short time later.

Two days after his death, a letter from Crelle stated that, at Crelle's suggestion, the German Government had agreed to appoint Abel a professor at the University of Berlin. A year after his death, the French Academy awarded the "Grand Prix" to Abel and Jacobi.