User:Karl-kjeks-Erik/Translations

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Niels Henrik Abel (født 5. august 1802Finnøy i Ryfylke, død 6. april 1829 på Frolands verk) var en norsk matematiker.

Sammen med Sophus Lie regnes Abel som den fremste norske matematikeren i det nittende århundre, og de to er også de mest anerkjente norske matematikerne gjennom alle tider. Innenfor matematikken har han fremdeles et stort navn internasjonalt. Han er kanskje mest kjent for å ha bevist at den generelle femtegradsligningen ikke kan løses med de elementære regningsartene addisjon, subtraksjon, multiplikasjon, divisjon og rotutdragning.

Contents

[edit] Biography

[edit] Early Life

Niels Henrik was born in Finnøy, where his father, Søren Georg Abel worked as vicar. Søren Georg was a prominent man, and preached man's ability to solve all of life's riddles by the use of one's mind. Niels Henrik's grandfather, Hans Mathias Abel, came to Gjerstad to work as vicar in 1785. When he died in 1804, Søren Henrik moved with his family to Gjerstad in Aust-Agder, and became vicar after his father. Here, Niels Henrik grew up with his older brother, three younger brothers and a sister.

In 1815, Niels Henrik was sent away from home to attend katedralskolen in Christiania. His family was at the time poor, but Niels Henrik and his older brother Hans received free scholarships. At that time, Hans Peter Bader taught mathematics. He was very old-fashioned and was known as a very violent man. If a student did anything wrong, he frequently used violence as a punishment. In november 1817 he hurt a student so badly he died, and were as a result of this removed from his position. The school hired Bernt Michael Holmboe as a replacement, and he became Abel's math teacher. Holmboe was a knowledgeable and good teacher, and before teaching at katedralskolen he worked as professor Christopher Hansteen's assistant at a university. Holmboe's way of teaching was quite different compared to Bader. He gave the students their own unique assignments, something that was not very common at the time. This appears to have kindled Abel's interest in mathematics, and after a short time, Holmboe discovered that Abel was something quite unique. Holmboe gave Niels Henrik private tutoring and a guide to mathematical literature. Niels Henrik borrowed Holmboe's textbooks from the universitety, and he studied them with great interest. One of the books that had the greatest effect on him was Leonhard Euler's guide to mathematical analysis. It has been said that without Bernt Michael Holmboe we might very well not have known Abel as the great mathematican we do today. The real question is, who the FUCK was he? TITS TITS TITS TITS TITS [1]

[edit] Life as a student

Even as a young student, Niels Henrik probably had a greater knowledge of mathematics than any other person in Norway. After Holmboe had taught him all he knew, Abel studied the works of great mathematicans like Newton, Euler, Lagrange and Gauss. There was no studies in mathematics at Det Kgl. Frederiks Universitet at the time, so Abel had to study on his own.

In spring 1823, Abel published an article in Magazin for Naturvidenskaberne, the first scientific journal in Norway. Some professors at the university understood that, to learn more, Abel had to go outside Norway, but the lack of funding meant that he had to stay in Christiania. In summer 1823 he got the opportunity to visit Copenhagen and visit the Nordic countries' greatest mathematican; Degen. It was here that Abel began his studies of elliptic functions, something he would later be widely known for. He also met Christine Kemp, and the two became engaged the following year.

[edit] Journey outside Norway

Abel, wishing intensely to travel to other countries, wrote a personal letter to king Karl III Johan, and was eventually granted a scholarship. In autum 1825 he left Norway. The plan was for him to go to Göttingen to visit Gauss, and from there travel to Paris. Upon arriving in Copenhagen he changed his plans and went to Berlin instead, where he met August Leopold Crelle, an engineer interested in mathematic. Crelle had for a long time wanted to publish a mathematical journal that could compete with the well-established french journals, and in spring 1826 the first issue of Journal für die reine und angewandte Mathematik (often called Crelle's Journal) was published. Here Abel published large parts of his work, and largely because of his articles, the journal quickly became known as one of Europe's finest.

In 1826, Abel published his first article in Crelle's Journal. The article was a proof of the impossibility of solving the quintic equation by radicals. (This investigation was first published in 1824, but in far more abstruse and difficult form.) After a four month stay in Berlin, Abel traveled further towards Paris. At that time, Paris represented the core of the world's mathematical community, so the town was a natural main goal of Abel's journey. Here, great mathematicans like Cauchy, Poisson, Legendre and Fourier lived and worked. Laplace was no longer active, but Abel had studied his works and respected him greatly. In the summer of 1826 he finally reached Paris, and started his work on the so-called Paris-thesis. The main focus of the thesis was the addition theorem for elliptic integrals. In October 1826 he turned the thesis in to the academy, and remained in Paris until the end of the year, awaiting an answer. No answer came, and Abel became increasingly dissatisfied with the city. He had also became ill. The stay in Paris ultimately became a dissapointment to Abel. He percieved the great Cauchy to be both eccentric and arrogant, and Poisson, Fourier and most of the other mathematicans worked primarily on physics at the time. Around the start of 1827, Abel went to Berlin. He was offered the position of editor of Crelle's Journal, but Abel refused, mainly because of homesickness. Crelle then started working to give Abel a position in Berlin.

[edit] Returning home

While Abel was in Paris, he got tuberculosis, and the illness had already started affecting him when he returned home in May 1827. The position in Berlin was not yet ready, and then there was the issue of payment. Abel still continued on his work, and in autumn 1827 he was primarily working on his thesis on elliptic functions. When the thesis was complete, he resumed his work on the theory of equations. Through his published articles in Crelle's Journal, Abel was gaining fame and recognition outside Norway, but back home he was living without much money. In September 1828, Legendre, Poisson, Lacroix and Baron de Maurice wrote a letter to king Karl Johan about Abel's situation. Their goal was to give Abel a position in Stockholm. Crelle was still working to get Abel a professorship in Berlin.

Abel's fiance, Christine Kemp, had a position as governess at Froland Verk, and they spent the Christmas 1928 together there. The tuberculosis was affecting Abel more and more, and after Christmas he did not manage returning to Christiania. When he understood the end was getting close, he started writing a summary of the proof of what is now known as Abel's theorem. This was sent to Crelle. The 6. April 1829 Abel died in poverty at Froland Verk. A few days later, Crelle wrote Abel a letter from Berlin, happily telling his friend that he now had a professorship and a bright future in the city.

Niels Henrik Abel died only 26 years old of tuberculosis. He is buried at Froland Cemetery.

[edit] Abel's mathematics

Niels Henrik Abel is perhaps best known for his work on quintic equations, but Abel have made significant contributions to many areas of mathematics. His work have probably affected three areas of mathematics the most: The theory of equations, the theory of elliptic functions, and infinite series.

[edit] Theory of Equations

Man has for thousands of years solved equations of differing kinds. The old Babylonian mathematicians could solve quadratic equations, while Italian mathematicians like Cardano, Tartaglia and Ferrari found methods for solving cubic and quartic equations. At Abel's time one of the greatest challenges was to find a method of solving quintic equations. In short, one wanted a method of finding the roots of the equation of the form

a1x5 + a2x4 + a3x3 + a4x2 + a5x + a6 = 0

Already while Abel studied at Katedralskolen he had found a formula for solving equations like these, and neither Abel nor any other Norwegian mathematicians found any problems in the formula. However, Abel eventually found that this formula would not work for all quintic equations, and eventually started believing that there was no such formula. At the time Abel had no idea that the Italian mathematician Paolo Ruffini had submitted a proof for this about 25 years earlier, but he eventually found that neither Ruffini's proof nor his own first attempt at the proof stood up to closer scrutiny. He later submitted two complete proofs of this, and the theorem is today known as the Abel-Ruffini theorem.

[edit] Elliptic functions

Elliptic functions can be seen as simplifications of trigonometric functions like the sine- and cosine-functions. Their applications include calculating the arc of an ellipse or how far a pendulum will swing. After travelling to Copenhagen in 1823, Abel did a lot of work on these functions. Abel's stroke of genius was looking at these functions in a totally different way than usual. Instead of studying the functions, he studied the inverse functions. Through methods like these, which Abel pioneered, he made several discoveries, including that elliptid functions had two indepentent periods.

A German mathematician, Carl Gustav Jacob Jacobi, also did a lot of work on elliptic functions at this time, and a race developed between him and Abel. When Abel came close to finishing his theory, he spent all his time on getting it done to prevent Jacobi from discovering anything similar and publishing it before him. Abel eventually finished first, and he himself described the final thesis as the "murder of Jacobi" in a private letter.

[edit] Infinite series

Two of the most acknowledged mathematicians at Abel's time was Gauss and Cauchy, and they had been leading figures of the process of re-establishing stringent logic in mathematics. Abel also agreed that mathematical theorems should have firm, logical proofs. One of the areas Abel believed to lack these proofs was the study of infinite series, and especially divergent series. In a thesis on the Binomial theorem, which Abel claimed still had not been proved in a good way, he showed how infinite series could be treated stringently. Through this thesis Abel made an important contribution to the formalization of the theory of infinite series.

[edit] The Paris-thesis

Even though Abel's stay in Paris became a personal disappointment, it was a period where Abel was very creative and productive. It was here he wrote his great thesis on integrals of elliptic functions. When he submitted it at the end of October 1826, the ususally modest Abel wrote home that he thought it was a good thesis, and that he was eager to hear other people's thoughts on it. [2] In this thesis he showed connections between algebra, matematical analysis and geometry that noone had seen before.

The grat Cauchy was tasked with judging Abels thesis, but he was far more focused on his own ideas, and the thesis was put aside and forgotten. Shortly after Abel's death it was discovered in Pairs, and the Academy decided that it was to be printed, and that Abel should recieve the Academy's great prize. Later the thesis vanished again, and when Holmboe wanted to publish Abel's collected works in 1839 it was nowhere to be found. It was later recovered in 1841 and finally printed. Shortly after this it vanished yet again, and was not found until 1859, when the Norwegian mathematician Viggo Brun eventually tracked it down in Firenze. The original manuscript is kept at the Universitety of Oslo.

[edit] Abel's heritage

In 1841 the Paris-thesis was printed, and is also part of Abel's gathered works, which were published in 1881. This great two-volume edition was edited and commented on by two of Norway's greatest mathematicians, Sophus Lie and Ludvig Sylow.

At Abel's 100-year anniversary in 1902, a memorial was planned in Oslo, a monument was to be raised, and there was also discussion on establishing an Abel-prize. The memorial was held with due grandeur in September 1902. In 1908 Gustav Vigeland's Abel-monument was raised in the Royal Castle's Courtyard at what is now called Abel Hill. The plans of an Abel-prize was for unknown reasons cancelled. However, in connection with Abel's 200-year anniversary, the idea of such a prize was realized, and the Abel Prize was established in memory of Niels Henrik Abel.

In later years a mathematical contest for Norwegian 9th graders - KappAbel - which eventually evolved into a Nordic contest, and the Niels Henrik Abels matematikk-konkurranse for students at Norwegian High Schools is arranged yearly as a qualifier for the International Mathematical Olympiad. Several mathematical terms also carry his name, such as abelian groups.

[edit] Steder oppkalt etter Abel

Abel er kanskje tidenes best kjente norske matematiker, og rundt om i verden er det flere steder som er oppkalt etter ham. Alle de største byene i Norge har gater eller plasser oppkalt etter Abel. Oslo har sin Niels Henrik Abels vei, Bergen har en Abelsgate, Trondheim har en allé oppkalt etter Abel, mens Stavanger har både Niels Abels gate og Abelstrappa. Berlin var en av de byene Abel tilbragte mest tid i på sine utenlandsopphold, og her finner vi også en Abelstrasse. I Paris har de en Rue Abel, også den oppkalt etter vår store matematiker.

Det er også flere bygninger som er oppkalt etter Abel, blant annet Niels Henrik Abels hus ved Universitetet i Oslo og Niels Henrik Abels hus ved Høgskolen i Agder.

[edit] Monumets and stamps

In 1902, a contest with the goal of making a monument of Abel was held. Ingrebrit Vik won the contest, but Gustav Vigeland was the person whose submission was deemed the official memorial. His well-known Statue of Abel standing in Slottsparken was fist shown at Høstutstillingen in 1904, with a finished statue uncovered in 1908.

Ingebrit Vik's submission for the contest was not moulded until 1966/67, and is now found in front of Niels Henrik Abel's house at the University of Oslo, and Vikmuseet in Øystese. Gustav Lærum has also made a statue of Abel, this one made from gypsum, which can be found at Froland Verk. At the rectory in Gjerstad, a bust can be found in the garden; and at Abel's place of birth Finnøy, another memorial rests.

At the 6. of April 1929, exactly 100 years after Abel's death, he was found on four Norwegian stamps. The stamps was engraved by Professor Schirnböck in Wien and came in four values:

  • 10 øre (colour: yellow-green, circulation: 6.265.000 copies, number NK172)
  • 15 øre (colour: copper, circulation: 3.120.000 copies, number MK173)
  • 20 øre (colour: scarlet, circulation: 9.697.000 copies, number NK174)
  • 30 øre (colour: ultramarine, circulation: 3.218.400, number NK175)

As of that, Abel was the only non-royal person to be portrayed on Norwegian stamps; only henrik Ibsen was before him, in 1928.

In connection with the 200 year anniversary in 2002, Abel once again got to adorn Norwegian stamps; one stamp with the value of 5,50 NOK (NK1469) and one with the value 22,00 NOK (NK1470).

[edit] Abels verker

[edit] Referanser

  1. ^ Bekken, 2003
  2. ^ Tunstad, 2002 (http://www.forskning.no/Artikler/2002/juni/1023272595.48)

[edit] Litteratur

Wikisource has original text related to this article:
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[edit] Eksterne lenker


Abel, Niels Henrik Abel, Niels Henrik Abel, Niels Henrik

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