All About Abel Dayanara Serges Niels Henrik Abel (August 5, 1802-April 6,1829) Was a Norwegian Mathematician Known for Numerous Contributions to Mathematics

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All About Abel Dayanara Serges Niels Henrik Abel (August 5, 1802-April 6,1829) was a Norwegian mathematician known for numerous contributions to mathematics. Abel was born in Finnoy, Norway, as the second child of a dirt poor family of eight. Abels father was a poor Lutheran minister who moved his family to the parish of Gjerstad, near the town of Risr in southeast Norway, soon after Niels Henrik was born. In 1815 Niels entered the cathedral school in Oslo, where his mathematical talent was recognized in 1817 by his math teacher, Bernt Michael Holmboe, who introduced him to the classics in mathematical literature and proposed original problems for him to solve. Abel studied the mathematical works of the 17th-century Englishman Sir Isaac Newton, the 18th-century German Leonhard Euler, and his contemporaries the Frenchman Joseph-Louis Lagrange and the German Carl Friedrich Gauss in preparation for his own research. At the age of 16, Abel gave a proof of the Binomial Theorem valid for all numbers not only Rationals, extending Euler’s result. Abels father died in 1820, leaving the family in straitened circumstances, but Holmboe and other professors contributed and raised funds that enabled Abel to enter the University of Christiania (Oslo) in 1821. Abels first papers, published in 1823, were on functional equations and integrals; he was the first person to formulate and solve an integral equation. He had also created a proof of the impossibility of solving algebraically the general equation of the fifth degree at the age of 19, which he hoped would bring him recognition. He sent the pamphlet to Gauss, who dismissed it entirely. Abel spent the winter of 182526 with Norwegian friends in Berlin, where he met August Leopold Crelle, civil engineer and self-taught enthusiast of mathematics, who became his close friend and mentor. With Abels warm encouragement, Crelle founded Crelles Journal. Crelles Journal contains Abels papers including a more elaborate version of his work on the quintic equation, and Abels theory of elliptic functions, which are complex functions that generalize the usual trigonometric functions. In 1826 Abel went to Paris, then the world centre for mathematics, where he called on the foremost mathematicians and completed a major paper on the theory of integrals of algebraic functions. His central result, known as Abels theorem, is the basis for the later theory of Abelian integrals and Abelian functions, a generalization of elliptic function theory to functions of several variables. However, Abels visit to Paris was unsuccessful in securing him an appointment, and the memoir he submitted to the French Academy of Sciences was lost. Abel’s work was scarcely known in Paris, and his modesty restrained him from proclaiming

1 his research. The theorem was put aside and forgotten until his death. After returning to Norway heavily in debt, he became very ill and was informed he had tuberculosis. Despite his bad health and poverty he continued writing papers on equation theory and elliptic functions. This continued work had major importance in the development of the whole theory of elliptic functions. Abel revolutionized the understanding of elliptic functions by studying the inverse of these functions. Abel passed away April 6th 1829 at the age of 26. Two days later a letter came informing him he had gotten an appointment in Berlin which would have given him a job at a University. Abels Work-

Abels binomial expansion theorem

Proof of the impossibility of solving algebraically the general equation of the ﬁfth degree

Invented Group Theory

The ﬁrst solution of an integral equation

Theory of elliptic integrals

Abels Environment

Niels Abel’s life was revolved around poverty. Norway had political problems which led to economic problems in Norway. At the end of the 18th century Norway was part of Denmark and the Danish tried to remain neutral through the Napoleonic wars. However a neutrality treaty in 1794 was considered a aggressive act by Britain and, in 1801, the British fleet destroyed most of the Danish fleet in a battle in the harbour at Copenhagen. Despite this Denmark-Norway avoided wars until 1807 when Britain feared that the Danish fleet might be used by the French to invade. Using the philosophy that attack is the best form of defense, the English attacked and captured the whole Danish fleet in October 1807. Denmark then joined the alliance Britain. The continental powers blockaded Britain, and as a counter to this Britain blockaded Norway. The twin blockade was a catastrophe to Norway preventing their timber exports, which had been largely to Britain, and preventing their grain imports from Denmark. An economic crisis in Norway followed with the people suffering hunger and

2 extreme poverty. In 1813 Sweden attacked Denmark from the south and, at the treaty of Kiel in January 1814, Denmark handed over Norway to Sweden. An attempt at independence by Norway a few months later led to Sweden attacking Norway in July 1814. Sweden gained control of Norway, setting up a complete internal self-government for Norway with a government in Christiania (which is called Oslo today). In this diﬃcult time Abel was growing up in Gjerstad in south-east Norway.

Abel’s Misfortunes

Niels Henrik Abel was a genius mathematician who lived a tragic life. When Abel sent his paper on elliptical functions to Gauss, Gauss threw it away without even reading it, thinking it was a joke. When Abel traveled to France in 1825, Legendre and Cauchy (also 2 very famous mathematicians) described Abel as a monument more lasting than bronze. In spite of this, Cauchy also misplaced Abels manuscript. In Berlin, Abel became friends with mathematician August Crelle. However, Abel was still not offered a post as professor, nor were his works widely acknowledged. Unable to find a job and living in poverty, Abel died of tuberculosis in 1829 at only 26 years old. Unfortunately, a letter arrived to Abel from his friend August Crelle informing him that he had been offered a position as professor at the University of Berlin two days after Abels death. Abel lived a short life filled with many amazing accomplishments. He was under appreciated due partially to the fact that he was Norwegian; he would have been more famous if he had come from France or Germany. Today an Abels Prize exists in Niels Abels honor. The term Abelian has been coined in several concepts like Abelian category, Abelian variety, Abelian group, and so much more.