World of Scientific Discovery on Niels Henrik Abel
Born near Stavanger, Norway, Abel was the son of Sören Georg Abel, a Lutheran minister and prominent figure in the Norwegian nationalist movement. Niels performed poorly in school but had an extraordinary ability in mathematics, which his teacher, Bernt Michael Holmboe, noticed almost immediately. In his last year of school, Abel declared that he had found the form to the solution of equations of the fifth degree, a mathematical problem that had puzzled mathematicians since the mid-sixteenth century. In Norway, no one could understand Abel's arguments, and there was no scientific journal in which he could publish his results. His " discovery" was forwarded to the Danish Academy, where it was received with interest, although Abel himself later found that his conclusions were false. The faculty of the newly instituted University of Oslo, in Norway, was alerted to Abel's work on the quintic equation and on elliptic integrals, which paved the way for his enrollment at the new university.
Penniless after the death of his father, Niels entered the University of Oslo in 1821 with the financial support of his professors. There were no advanced courses in mathematics, so Abel created his own curriculum. By 1823, he had published the first ever solution to an integral equation. The same year, he received a monetary gift that allowed him to visit several prominent Danish mathematicians in Copenhagen. When Abel returned to Oslo, he tackled the question of quintic equations, proving mathematically that there was no algebraic solution to such equations. Abel published this important result in a pamphlet, but it received little attention, even from as great a mathematician as Carl Friedrich Gauss, to whom Abel sent his paper.
Meanwhile, Abel's financial support diminished. He won a travel grant from the Norwegian government to study French and German languages abroad. In Berlin, Germany, Abel met Leopold Crelle, an engineer who published a new mathematical journal, and featured the best of Abel's work. It became the leading German mathematical periodical of the nineteenth century. Finally, Abel's work began to receive some public notice, including his rigorous proof of the binomial theorem. Yet his growing fame failed to help him to secure a teaching position in Norway. In 1826 he found himself in Paris, France, nearly destitute.
During this time, Abel wrote his most famous paper on the sum of integrals of a given algebraic function. Abel considered this work to be his masterpiece, but the French Academy of Sciences rejected it, maintaining that it was illegible! Disillusioned, Abel returned to Germany, where he worked as an editor on Crelle's journal. At this time, Abel suffered the first attack of the tuberculosis that would eventually claim his life. In 1827, Abel returned to Oslo, unemployed and in debt. He eked out a living by tutoring schoolboys. Even as Abel's health deteriorated, he rapidly wrote mathematical papers. In 1829, at age 26, Abel died of a tubercular hemorrhage, two days before Crelle wrote to inform him of his appointment to teach at a new scientific institute in Berlin.
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