Nils Henrik Abel - a tragic story of the fifth degree

Another story of a genius mathematician who grew up in poverty, wrote his first important mathematical paper at the age of 20 and died at the age of 27, when he was on the verge of fame

A clear rule is that a culture is based first and foremost on the people who create it and the way in which these people can give the potion of immortality to the group they live in is solely through the written book and education.

The country called Norway boasts of the beauty of its land, which places it among the few countries that we call - a small paradise. Apart from the fact that this is a culture that has enshrined hatred of foreign peoples for hundreds of years, it seems that the rule written above has completely disappeared from its notice. Culture, as defined, began to exist in Norway about ten thousand years ago, but the output resulting from the quality of the people who make up the Norwegian group is incredibly low.

There is a well-known proverb in the Yiddish language that claims that - "When luck comes, set up a throne for him!" ". A great mathematical luck was waiting for the Norwegians only about 200 years ago and they did put a throne for him, but it's a shame that they put it upside down. The following article tells about a culture empty of content that missed out on the kind of luck that only comes once.

Niels Henrik Abel (Niels Henrik Abel) was born in 1802 in Norway to a father who was a politician and a drinker and to a mother who was also a politician who was known for having an incredibly low moral level; How low it was I will leave that to the imagination of my readers. Nils was one of seven children in the horribly poor Abel family because at that time the economic situation in his homeland was very bad. This poverty, which reached the point where the food pantry in their home was empty, led to the fact that Abel's father - who could not afford his son's school expenses - gave him an independent education with the cooperation of a local priest until he reached the age of 13, at which time the family was able to send only Abel and his older brother to study at home The religious book Christiana. Two years before that, the best teachers were taken from there and transferred to a university that was a sort of continuation institution of the previous school, which lowered its educational level to an abysmal low. But he did not turn out to be a particularly successful student and was one of those people with a slight inclination towards mathematics and physics. The year 1817 was the point at which the dam broke for Abel after he had a new math teacher named Brent Holmboë. It is worth noting that Holombi replaced the previous math teacher after Hella punished one of the students so severely that he died.

Shortly after arriving, Hollomby noticed a spark of grief and began filling the young man's stomach with university papers from the mathematical studies of Euler, Newton and their friends and soon realized that this was a lift with tremendous potential. After about a year in which he had his eye on the rising star, Holombi began to direct Abel's ideas specifically towards the work of Lagrange and Laplace.

Unfortunately for Abel, in 1820 his father died in great disgrace as a result of his tendency to a drop of bitterness in a way that exceeded his standards as well as false legal scandals in which he was involved in his last years.

The father, who was the main supporter of the family, also brought down an even more serious financial disaster on his wife and children which actually dropped the academic ground from under Abel's feet. Hollomby did everything he could to help and indeed managed to get Abel a study and subsistence scholarship that gave him the ability to study at Christiana University at the age of 19. At the age of 20, Abel was able to present his first mathematical paper that dealt with one of the most important problems in algebra at the time: solving a fifth degree equation by radicals. In my previous article about the Italian mathematician Tartalia (Tartaglia) I explained in a "sports" example what it means to solve equations of the third degree, and this example is also true here when now the basketball player is supposed to score 5 balls simultaneously with one hand into the basket.

The history of solving equations began back in the days of the Greeks when Pythagoras or one of his students found the general solution for a quadratic equation, then the Italian mathematicians Tartellia, Cardano and Ferrari continued them with a third and fourth degree equation, and now it is Abel's turn to deal with fifth degree equations. The way he took is through a concept called radicals. It is difficult to specify exactly what it is but I will say that in general a radical means a root and hence a solution using a radical is done by using the roots. When we say that an equation has a "root" it means that we found its solution (or solutions) when we equated the equation to 0. For example, the expression X2-1 will become an equation when we compare it to something, assuming the comparison is to 0, then the solutions are as mentioned 1 and (1-) and these are the roots of the equation. The idea of ​​using radicals is to find an equation for the roots themselves using the coefficients (of the equation). But, as I recall, he proposed a solution to the problem in a mathematical article when he was only 20 years old, but upon repeated self-examination he discovered that a mistake had surfaced for which a different solution was required. In order to understand how brilliant and sharp Abel's mathematical mind was, it would be appropriate to compare it to an average guy nowadays who finished high school at the age of 18; Assuming that immediately after that he continues his studies for a bachelor's degree in mathematics, he is required to be able to deal with a main and fundamental mathematical problem that has occupied the best minds since the days of Tartellia and Cardano (about 250 years) and this after only two years in the academy.

Let's not forget that Abel was poor and the conditions in which he conducted his research were (even then) considered extremely difficult; So, despite the fact that the solution was not completely accurate, it would still be extremely difficult to find such a young person with such fantastic abilities. Following this mistake, the supervisor who was required to review the article advised him to focus on another important field that dealt with integrals. In the most simplistic way, it is said that an integral is a method of finding the area of ​​a certain region and constitutes, together with the differential, the two elements, apparently, the most important in the world of mathematics.

This recommendation was probably the most important in Abel's life and it did bear fruit; Immediately afterwards he was taken under the tutelage of Professor Hansteen from the Department of Astronomy at Christiana University. Hansteen supported him financially as well as morally and his wife even treated him as her own son. The year 1823 (when he was 21 years old) was significant for him, during which he published a number of fascinating articles in the aforementioned field. A year later he reached the peak of his life when he returned to work on the equation from the fifth degree and managed to prove that it cannot be solved using a radical. Again, although this is a complicated problem that this is not the place to explain, I can only say that only a few virtuous individuals are able to reach such a deep understanding of the world of mathematics. But he wanted his works to reach the desks of the great mathematicians in France and Germany, but he did not know the languages ​​spoken in these countries, so he studied them for two years until he knew them about Borin, something that helped him when he published a collection of articles in the French language with his personal money, which was also very little. Just to explain to the ear how bad his financial situation was even during the period in question, it is worth noting that Abel did not have a sufficient amount of money in his possession to describe his proofs in full and therefore he had to "shrink" them so that they all fit into a small number of pages.

During the next 4 years, Abel made a hopping trip between France and Germany in an attempt to be accepted into the local hegemony of mathematicians, but he received cold gestures from many of them, especially from the French whom he did not like, to say the least. In 1827 he returned to his home in Norway in poor health and even poorer after going into debt. When he returned to Christiana University, he was awarded a certain amount of money to get him back on his feet, but the heads of the institution made sure that this grant would be deducted from any future salary he would receive if he worked there. Although Abel was recognized in Norway as a mathematical genius, which was extremely rare at the time, not even the slightest effort was made to help him in a real way in his works that could bring honor and prestige to the country.

In order to raise some more money Abel started giving private lessons to school children while his wife was employed as a nanny in a family of Abel's friends. A slight improvement in his economic situation came when Professor Hansteen was sent to Siberia to study the magnetic force of the earth and Abel replaced him as a lecturer at the university and military academy.

In 1828 Abel returned to engage in the field he loved so much, which is finding a general solution for the use of radicals on equations - which would be proven a few years later by Everest visible (Galois).

But he also focused on the field called elliptic equations and worked together with another great mathematician named Jacobi; Legendre, who was a well-known French mathematician, commented that in his opinion these works place both of them in the first rank of the great minds of their time.

Comments of this kind helped Ebel to produce more and more mathematical studies whose importance is priceless, but at the same time his health deteriorated significantly and in fact it was the beginning of the end of the mathematical genius. Abel's colleague - the mathematician Carl (Crelle), did everything in his power to find him a suitable position in Germany and he did succeed in doing so, but it was too late and Abel died two days before Carl told him the happy news.

Abel's last days were spent in severe weakness and non-stop coughing, but this difficult situation did not prevent him from continuing to study mathematics, even though he could only get out of bed for a few minutes. But he used to tell about his severe poverty in the previous years and the kindness of Professor Hansteen's wife. The pain was especially unbearable on April 5th of the same year and in the morning of the next day, but it blew his soul and he is only 27 years old.

In 1830, the Parisian Academy awarded Yacovi Wabel (posthumously) an honorary award for their extraordinary work in its importance.