Niels Henrik Abel ( AH-bəl, Norwegian: [ˌnɪls ˈhɛ̀nːɾɪk ˈɑ̀ːbl̩]; 5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This question was one of the outstanding open problems of his day, and had been unresolved for over 250 years. He was also an innovator in the field of elliptic functions and the discoverer of Abelian functions. He made his discoveries while living in poverty and died at the age of 26 from tuberculosis. Most of his work was done in six or seven years of his working life. Regarding Abel, the French mathematician Charles Hermite said: "Abel has left mathematicians enough to keep them busy for five hundred years." Another French mathematician, Adrien-Marie Legendre, said: "What a head the young Norwegian has!"
Life
Early life
Niels Henrik Abel was born prematurely in Nedstrand, Norway, as the second child of the pastor Søren Georg Abel and Anne Marie Simonsen. When Niels Henrik Abel was born, the family was living at a rectory on Finnøy. Much suggests that Niels Henrik was born in the neighboring parish, as his parents were guests of the bailiff in Nedstrand in July and August of his year of birth. Niels Henrik Abel's father, Søren Georg Abel, had a degree in theology and philosophy and served as pastor at Hesby Church on Finnøy. Søren's father, Niels's grandfather, Hans Mathias Abel, was also a pastor, at Gjerstad Church near the town of Risør. Søren had spent his childhood at Gjerstad, and had also served as chaplain there; and after his father's death in 1804, Søren was appointed pastor at Gjerstad and the family moved there. The Abel family originated in Schleswig and came to Norway in the 17th century.
Anne Marie Simonsen was from Risør; her father, Niels Henrik Saxild Simonsen, was a tradesman and merchant ship-owner, and said to be the richest person in Risør. Anne Marie had grown up with two stepmothers, in relatively luxurious surroundings. At Gjerstad rectory, she enjoyed arranging balls and social gatherings. Much suggests she was early on an alcoholic and took little interest in the upbringing of the children. Niels Henrik and his brothers were given their schooling by their father, with handwritten books to read. An addition table in a book of mathematics reads: 1+0=0.
Cathedral School and Royal Frederick University With Norwegian independence and the first election held in Norway, in 1814, Søren Abel was elected as a representative to the Storting. Meetings of the Storting were held until 1866 in the main hall of the Cathedral School in Christiania (now known as Oslo). Almost certainly, this is how he came into contact with the school, and he decided that his eldest son, Hans Mathias, should start there the following year. However, when the time for his departure approached, Hans was so saddened and depressed over having to leave home that his father did not dare send him away. He decided to send Niels instead. In 1815, Niels Abel entered the Cathedral School at the age of 13. His elder brother Hans joined him there a year later. They shared rooms and had classes together. Hans got better grades than Niels; however, a new mathematics teacher, Bernt Michael Holmboe, was appointed in 1818. He gave the students mathematical tasks to do at home. He saw Niels Henrik's talent in mathematics, and encouraged him to study the subject to an advanced level. He even gave Niels private lessons after school. In 1818, Søren Abel had a public theological argument with the theologian Stener Johannes Stenersen regarding his catechism from 1806. The argument was well covered in the press. Søren was given the nickname "Abel Treating" (Norwegian: "Abel Spandabel"). Niels' reaction to the quarrel was said to have been "excessive gaiety". At the same time, Søren also almost faced impeachment after insulting Carsten Anker, the host of the Norwegian Constituent Assembly; and in September 1818 he returned to Gjerstad with his political career in ruins. He began drinking heavily and died only two years later, in 1820, aged 48. Bernt Michael Holmboe supported Niels Henrik Abel with a scholarship to remain at the school and raised money from his friends to enable him to study at the Royal Frederick University. When Abel entered the university in 1821, he was already the most knowledgeable mathematician in Norway. Holmboe had nothing more he could teach him and Abel had studied all the latest mathematical literature in the university library. During that time, Abel started working on the quintic equation in radicals. Mathematicians had been looking for a solution to this problem for over 250 years. In 1821, Abel thought he had found the solution. The two professors of mathematics in Christiania, Søren Rasmussen and Christopher Hansteen, found no errors in Abel's formulas, and sent the work on to the leading mathematician in the Nordic countries, Carl Ferdinand Degen in Copenhagen. He too found no faults but still doubted that the solution, which so many outstanding mathematicians had sought for so long, could really have been found by an unknown student in far-off Christiania. Degen noted, however, Abel's unusually sharp mind, and believed that such a talented young man should not waste his abilities on such a "sterile object" as the fifth degree equation, but rather on elliptic functions and transcendence; for then, wrote Degen, he would "discover Magellanian thoroughfares to large portions of a vast analytical ocean". Degen asked Abel to give a numerical example of his method. While trying to provide an example, Abel found a mistake in his paper. This led to a discovery in 1823 that a solution by formula to a fifth- or higher-degree equation was not necessarily possible. Abel graduated in 1822. His performance was exceptionally high in mathematics and average in other matters.
Career
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