# The history of the competition

The Norwegian Mathematical Society was founded in 1918, and it was here the idea of holding an annual mathematical competition first surfaced. The competition was held for the first tine in 1921, and was held annually until the mid 1970s. A prize was awarded by Crown prince Olav, and later Crown prince Harald, commonly called “the Crown prince's prize”. The participation was low, however; usually less than 10 participants, and sometimes none at all. So, in the mid 1970's, the competition quietly faded away.

It wasn't long until talk began of reviving the competitions. In 1979–80, on the 150th anniversary of Niels Henrik Abels death, a competition was held for Nordic high school students. This gathered 28 contestants.

In 1981 the Abel competition was started as a cooperative venture between the Norwegian Mathematical Society and Aftenposten (a newspaper). There were 65 participants the first year, but this fell so dramatically over the next three years that a new form of competition was considered.

In 1985 the competition was turned into a mass event for the first time: a 100-minute initial round held locally at the schools, followed by a final with roughly the 20 top students, and an invitation to the IMO for the six best. The participation level has risen steadily, and reached 4000 by 1994. On the way, the Nordic Mathematical Competition was started.

In the fall of 1994 a change was made: to hold two rounds in the schools before the final. The purpose was partly to have a better selection of students before the final, and also to give the better students some additional challenges. The change was well received, and is now considered permanent.

# About Niels Henrik Abel

The man after whom the competition is named was born at Finnøy by Stavanger on august 5, 1802, and died at Frolands Verk by Arendal on april 6, 1829.

Finnøy Prestegård, Th. Fearnley, 1826 © Matematisk
institutt, UiO.
Niels Henrik Abel was the second son of priest Søren Georg Abel and his wife Anne Marie Simonsen. In 1804, Søren Georg Abel took over his father's congregation at Gjerstad by Risør. Niels Henrik lived and grew up here until he was 13 years old. In 1815 he entered Christiania (Oslo) Cathedral School. His remarkable talent for mathematics was discovered by his teacher Bernt Michael Holmboe in 1818. The young Holmboe taught Abel both classical and contemporary mathematical literature. He studied works by Isaac Newton, Leonhard Euler, Joseph-Louis Lagrange and Carl Friedrich Gauss, along with more recent mathematical journals from Paris. Towards the end of his time at the school, he started working on a problem that had kept mathematicians at bay for over 200 years: solving the general quintic using radicals.

Bernt Michael Holmboe © Matematisk institutt, UiO.
In 1820 Niels Henriks father died, and his family experienced difficult times, economically as well as personally. Thanks to private support and a free place at the student home Regentsen, Niels Henrik could none the less begin studying at *The Royal University of Frederik* in Christiania in 1821. After passing the general exam in 1822, he kept studying mathematics on his own – there was no mathematical study program. He received economical support from some professors, and prof. Hansteen allowed the gifted student to stay in his home.

Niels Henrik Abel published his first works in the recently initiated *Magazin for Naturvidenskaberne* (magazine for the natural sciences) in 1823 and 1824. In one of the articles he solves, as the first, an integral equation. In the winter of 1825 he published, at his own expense, the proof for the non-solvability of the quintic by radicals. In the summer of 1825 he applied to the King for support to visit Gauss in Göttingen, and thereafter to travel to Paris to study mathematics. His application was approved in September that year, and shortly thereafter he left to travel Europe for two years. Initially, he traveled with friends who were to study geology in Germany and Switzerland.

He spent the winter of 1826 in Berlin, where he met the mathematically interested engineer August Leopold Crelle. They quickly became friends, and Crelle was encouraged to realize his dream of publishing a mathematical journal. The first number of *Journal für die reine und angewandte Mathematik* was published in the spring of 1826, and Abel published most of his works there.

After the stay in Berlin, the trip went on through Switzerland and Italy, until Abel reached Paris in june of 1826, the center of the mathematical world at the time. He had saved his finest work for the prestigious Academy. Publishing a paper there would be noticed, and would give him a name. In October he finished the paper *Memoire sur une propriété générale d'une classe très étendue de fonctions transcendates* (known later simply as the Paris paper), and submitted it to the Academy on October 30. His paper was sidetracked and did not reach the public until after his death. While he lived in Paris he met the norwegian artist Johan Gørbitz who painted the only known contemporary portrait of Abel in the fall of 1826.

That Christmas Abel left Paris for Berlin, where he again met Crelle. The following may he returned to Norway, and was left with no money and no work. To survive, he gave private tuition, while he mass-produced papers which he sent to Crelle in Berlin. In the spring of 1828 his situation improved somewhat when he temporarily took the job of prof. Cristopher Hansteen, who was going on an expedition to Siberia. After the fall term was over, Abel traveled to Frolands Verk, where his fiancé lived and worked. During a christmas ball he fell ill and started spitting blood. His condition turned out to be fatal, and he died on April 6, 1829. A week later, Niels Henrik Abel was buried at Froland cemetary.