A penniless Norwegian student settled a puzzle that had beaten mathematicians for 250 years
At nineteen, Niels Henrik Abel believed he had found a formula solving every fifth-degree equation. Nobody could spot the flaw until he tried a worked example and found it himself. That mistake turned him around: by 1823 he had shown that no such general formula can exist, a result now called the Abel–Ruffini theorem.
Abel was born on 5 August 1802, probably in Nedstrand, to a Norwegian pastor, Søren Georg Abel. His father taught the boys at home from handwritten books, one of which states that 1 plus 0 equals 0. Søren was elected to the first Storting in 1814, then wrecked his career in public quarrels and drank himself to death by 1820. Niels had been sent to Christiania's Cathedral School at thirteen only because his older brother was too homesick to go.
In 1818 a new teacher, Bernt Michael Holmboe, noticed the boy's gift, tutored him privately, and later raised money so he could attend the Royal Frederick University. By his arrival in 1821 Abel already knew more mathematics than anyone else in the country. Professor Christopher Hansteen gave him an attic room, and Abel came to regard Hansteen's wife as a second mother. One early French paper on integration vanished during review and was never found.
To save printing costs he squeezed his 1824 proof about the quintic into six pages, making it nearly unreadable; a fuller version appeared in 1826 in the first volume of Crelle's Journal. A travel grant, secured partly through a letter to King Carl Johan, sent him abroad in 1825. In Berlin he befriended August Leopold Crelle and supplied seven articles in the journal's first year. In Freiberg he worked on elliptic functions and a new family now named abelian functions.
Paris was a disappointment. He finished a major theorem on adding algebraic differentials in October 1826 and handed it to the French Academy, where Augustin-Louis Cauchy was to review it; it was shelved and forgotten until after his death. Money ran out in January 1827. Having neither met Gauss nor published in Paris, he lost his scholarship, borrowed 200 speciedaler from Norges Bank and never repaid it. Engaged to Christine Kemp, he died of tuberculosis on 6 April 1829, aged 26.
Source: Niels Henrik Abel
