After he graduated, professors from university supported Abel financially, and Professor Christopher Hansteen let him live in a room in the attic of his home.
Abel would later view Ms. Hansteen as his second mother.
While living here, Abel helped his younger brother, Peder Abel, through examen artium.
He also helped his sister Elisabeth to find work in the town.

In early 1823, Niels Abel published his first article in "Magazin for Naturvidenskaberne", Norway's first scientific journal, which had been co-founded by Professor Hansteen.
Abel published several articles, but the journal soon realized that this was not material for the common reader.
In 1823, Abel also wrote a paper in French.
It was "a general representation of the possibility to integrate all differential formulas" (Norwegian: en alminnelig Fremstilling af Muligheten at integrere alle mulige Differential-Formler).
He applied for funds at the university to publish it.
However the work was lost, while being reviewed, never to be found thereafter.

In mid-1823, Professor Rasmussen gave Abel a gift of 100 speciedaler so he could travel to Copenhagen and visit Ferdinand Degen and other mathematicians there.
While in Copenhagen, Abel did some work on Fermat's Last Theorem.
Abel's uncle, Peder Mandrup Tuxen, lived at the naval base in Christianshavn, Copenhagen, and at a ball there Niels Abel met Christine Kemp, his future fiancée.
In 1824, Christine moved to Son, Norway to work as a governess and the couple got engaged over Christmas.

After returning from Copenhagen, Abel applied for a government scholarship in order to visit top mathematicians in Germany and France, but he was instead granted 200 speciedaler yearly for two years, to stay in Christiania and study German and French.
In the next two years, he was promised a scholarship of 600 speciedaler yearly and he would then be permitted to travel abroad.
While studying these languages, Abel published his first notable work in 1824, Mémoire sur les équations algébriques où 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).
For, in 1823, Abel had at last proved the impossibility of solving the quintic equation in radicals (now referred to as the Abel–Ruffini theorem).
However, this paper was in an abstruse and difficult form, in part because he had restricted himself to only six pages, 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, Abel wrote a personal letter to King Carl Johan of Norway/Sweden requesting permission to travel abroad.
He was granted this permission, and in September 1825 he left Christiania together with four friends from university (Christian P.B Boeck, Balthazar M. Keilhau, Nicolay B. Møller and Otto Tank).
These four friends of Abel were traveling to Berlin and to the Alps to study geology.
Abel wanted to follow them to Copenhagen and from there make his way to Göttingen.
The terms for his scholarship stipulated that he was to visit Gauss in Göttingen and then continue to Paris.
However, when he got as far as Copenhagen he changed his plans.
He wanted to follow his friends to Berlin instead, intending to visit Göttingen and Paris afterwards.

On the way, he visited the astronomer Heinrich Christian Schumacher in Altona, now a district of Hamburg.
He then spent four months in Berlin, where he became well acquainted with August Leopold Crelle, who was then about to publish his mathematical journal, Journal für die reine und angewandte Mathematik.
This project was warmly encouraged by Abel, who contributed much to the success of the venture.
Abel contributed seven articles to it in its first year.

From Berlin Abel also followed his friends to the Alps.
He went to Leipzig and Freiberg to visit Georg Amadeus Carl Friedrich Naumann and his brother the mathematician August Naumann.
In Freiberg Abel did research in the theory of functions, particularly, elliptic, hy
After he graduated, professors from university supported Abel financially, and Professor Christopher Hansteen let him live in a room in the attic of his home. Abel would later view Ms. Hansteen as his second mother. While living here, Abel helped his younger brother, Peder Abel, through examen artium. He also helped his sister Elisabeth to find work in the town.
In early 1823, Niels Abel published his first article in "Magazin for Naturvidenskaberne", Norway's first scientific journal, which had been co-founded by Professor Hansteen. Abel published several articles, but the journal soon realized that this was not material for the common reader. In 1823, Abel also wrote a paper in French. It was "a general representation of the possibility to integrate all differential formulas" (Norwegian: en alminnelig Fremstilling af Muligheten at integrere alle mulige Differential-Formler). He applied for funds at the university to publish it. However the work was lost, while being reviewed, never to be found thereafter.
In mid-1823, Professor Rasmussen gave Abel a gift of 100 speciedaler so he could travel to Copenhagen and visit Ferdinand Degen and other mathematicians there. While in Copenhagen, Abel did some work on Fermat's Last Theorem. Abel's uncle, Peder Mandrup Tuxen, lived at the naval base in Christianshavn, Copenhagen, and at a ball there Niels Abel met Christine Kemp, his future fiancée. In 1824, Christine moved to Son, Norway to work as a governess and the couple got engaged over Christmas.
After returning from Copenhagen, Abel applied for a government scholarship in order to visit top mathematicians in Germany and France, but he was instead granted 200 speciedaler yearly for two years, to stay in Christiania and study German and French. In the next two years, he was promised a scholarship of 600 speciedaler yearly and he would then be permitted to travel abroad. While studying these languages, Abel published his first notable work in 1824, Mémoire sur les équations algébriques où 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). For, in 1823, Abel had at last proved the impossibility of solving the quintic equation in radicals (now referred to as the Abel–Ruffini theorem). However, this paper was in an abstruse and difficult form, in part because he had restricted himself to only six pages, 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, Abel wrote a personal letter to King Carl Johan of Norway/Sweden requesting permission to travel abroad. He was granted this permission, and in September 1825 he left Christiania together with four friends from university (Christian P.B Boeck, Balthazar M. Keilhau, Nicolay B. Møller and Otto Tank). These four friends of Abel were traveling to Berlin and to the Alps to study geology. Abel wanted to follow them to Copenhagen and from there make his way to Göttingen. The terms for his scholarship stipulated that he was to visit Gauss in Göttingen and then continue to Paris. However, when he got as far as Copenhagen he changed his plans. He wanted to follow his friends to Berlin instead, intending to visit Göttingen and Paris afterwards.
On the way, he visited the astronomer Heinrich Christian Schumacher in Altona, now a district of Hamburg. He then spent four months in Berlin, where he became well acquainted with August Leopold Crelle, who was then about to publish his mathematical journal, Journal für die reine und angewandte Mathematik. This project was warmly encouraged by Abel, who contributed much to the success of the venture. Abel contributed seven articles to it in its first year.
From Berlin Abel also followed his friends to the Alps. He went to Leipzig and Freiberg to visit Georg Amadeus Carl Friedrich Naumann and his brother the mathematician August Naumann. In Freiberg Abel did research in the theory of functions, particularly, elliptic, hy
Niels Henrik Abel