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Niels Henrik Abel

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Niels Henrik Abel
Niels Henrik Abel
Born(1802-08-05)August 5, 1802
Nedstrand, Norway
DiedApril 6, 1829(1829-04-06) (aged 26)
Froland, Norway
NationalityNorwegian
Alma materRoyal Frederick University
Known forAbelian function
Abelian group
Abel's theorem
Scientific career
FieldsMathematics

Niels Henrik Abel (August 5, 1802 – April 6, 1829) was a noted Norwegian mathematician who proved the impossibility of solving the quintic equation in radicals.

Early life

Abel was born in Nedstrand, near Finnøy, to Søren Georg Abel and Anne Marie Simonsen, "the daughter of a shipping merchant."[1] Abel's father had a degree in theology and philosophy and his grandfather was an active Protestant minister at Gjerstad near Risør. After the latter's death, Abel's father was appointed as minister at Gjerstad. In 1815, Abel entered the Cathedral School in Christiania. A new mathematics teacher, Bernt Michael Holmboe, was appointed in 1817. Seeing Abel's talent in mathematics he encouraged him to study the subject to an advanced level. When Abel's father died in 1820, the family was left in strained circumstances, and Holmboe supported Abel with a scholarship to remain at school and raised money from his friends to enable Abel to study at the Royal Frederick University. Abel entered the university in 1821 and graduated in 1822.

Career

After returning from a visit to Degen and other mathematicians in Copenhagen, Abel applied for economic support in order to visit top mathematicians in Germany and France. Instead, he was given funds to stay in Cristiania for two years, and he learned German and French in those years. While learning languages, Abel published his first notable work in 1824, Mémoire sur les équations algébriques ou on démontre l'impossibilité de la résolution de l'équation générale du cinquième degré (Memoir on algebraic equations, in which the impossibility of solving the general equation of the fifth degree is proven). Abel proved the impossibility of solving the quintic equation in radicals in 1823 (now referred to as the Abel–Ruffini theorem). This work was in abstruse and difficult form, in part because the page count was severely restricted in order to save money on printing. A more detailed proof was published in 1826 in the first volume of Crelle's Journal. In 1825, he was given a government scholarship that enabled him to travel abroad. During the travel, Abel visited the astronomer Heinrich Christian Schumacher in Altona, now a district of Hamburg. He spent six months in Berlin, where he became well acquainted with August Leopold Crelle, who was then about to publish his mathematical journal. This project was warmly encouraged by Abel, who contributed much to the success of the venture. From Berlin he passed to Freiburg, and here he made his brilliant researches in the theory of functions: elliptic, hyperelliptic, and a new class now known as abelian functions being particularly intensely studied.

In 1826 Abel moved to Paris, and during a ten-month stay he met the leading mathematicians of France; but he was poorly appreciated, as his work was scarcely known, and his modesty restrained him from proclaiming his research. Pecuniary embarrassments, from which he had never been free, finally compelled him to abandon his tour, and on his return to Norway he taught for some time at Christiania.

Death

While in Paris, Abel had contracted tuberculosis. For Christmas 1828, he traveled by sled to again visit his fiancée in Froland. He became seriously ill on the journey, although a temporary improvement allowed the couple to enjoy the holiday together. Crelle, at the same time, had been searching for a new job for Abel in Berlin, and did manage to have him appointed professor at a university. Crelle wrote to Abel on April 8, 1829 to tell him the good news, but Abel had died two days before.

Legacy

The early death of this talented mathematician, of whom Adrien-Marie Legendre said "quelle tête celle du jeune Norvégien!" ("what a head the young Norwegian has!"), cut short a career of extraordinary brilliance and promise. Under Abel's guidance, the prevailing obscurities of analysis began to be cleared, new fields were entered upon and the study of functions so advanced as to provide mathematicians with numerous ramifications along which progress could be made. His works, the greater part of which originally appeared in Crelle's Journal, were edited by Holmboe and published in 1839 by the Norwegian government, and a more complete edition by Ludwig Sylow and Sophus Lie was published in 1881. The adjective "abelian", derived from his name, has become so commonplace in mathematical writing that it is conventionally spelled with a lower-case initial "a" (e.g., abelian group, abelian category, and abelian variety).

On April 6, 1929, four Norwegian stamps were issued for the centenary of Abel's death. His portrait appears on the 500-kroner banknote (version V) issued during 1978–1985. On June 5, 2002, four Norwegian stamps were issued in honour of Abel two months before the bicentenary of his birth. There is also a 20-kroner coin issued by Norway in his honour. In Oslo stands a statue of Abel, and crater Abel on the Moon was named after him. In 2002, the Abel Prize was established in his memory.

See also

References

  1. ^ See page 91 of Livio, Mario (2005). The Equation That Couldn't be Solved. New York: Simon & Schuster. ISBN 0743258215.

Further reading

  • Livio, Mario (2005). The Equation That Couldn't be Solved. New York: Simon & Schuster. ISBN 0743258215.
  • Stubhaug, Arild (2000). Niels Henrik Abel and his Times. Springer. ISBN 3540668349. - translated by Richard R. Daly
Wikisource has the text of the 1911 Encyclopædia Britannica article "Abel, Niels Henrik".
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