RePoSS #11: The Mathematics of Niels Henrik Abel: Continuation ...

2.2. “Study the masters” 23
as he sat down to provide the details, he must have realized that DEGEN had spared
him a humiliating entry onto the mathematical scene. Before 1824, ABEL realized that
no algebraic solution formula could be found for the general quintic, and thus that his
solution had been flawed and his search in vain. ABEL never sent an elaboration to
DEGEN, never published in the Transactions of the Royal Danish Academy of Science, and
when ABEL and DEGEN eventually met in person two years after their initial corre-
spondence, ABEL had other things on his mind.
2.2.2 A student at the young university
When ABEL enrolled at the university in 1821, the university was still in its constitu-
tional phase. Founded in 1811 and opened in 1813 as only the third university in the
twin monarchy (after Copenhagen and Kiel), the Christiania university initially only
offered degrees in theology, law, medicine, and philosophy. The study of science and
mathematics was subsumed under the philosophical faculty and no course of studies
led to any degree in the sciences. Thus, when ABEL enrolled, his determination to
study mathematics defied the existing structure of academic qualification. He must
have hoped that his extraordinary talents alone would be enough to secure him a fu-
ture in academia.
During his years at the university, ABEL attended lectures by the two professors in
mathematics and astronomy, RASMUSSEN and HANSTEEN. The mathematical lectures
were primarily on elementary mathematics, spherical geometry, and applications to
astronomy, and ABEL had soon learned all he could from these courses. As a comple-
ment, he continued studying the works of the masters of mathematics. In 1823, ABEL
came across the Disquisitiones arithmeticae of GAUSS, 17 which provided him with a rich
source of inspiration and problems for his own research. Itself an immensely impor-
tant work in the theory of numbers, the Disquisitiones arithmeticae influenced ABEL in
two other fields: the theory of equations and the rectification of the lemniscate.
During his years as a student, ABEL held a free room and board at the Regentsen,
a student residence for the most needy students. Until he was given a stipend from
the State in 1824, he was financially supported by some of the University professors,
including RASMUSSEN and HANSTEEN. 18
First publications in Magazin for Naturvidenskaberne. In 1823, professor HAN-
STEEN, together with two fellow professors at the university, tried to amend the lack of
Norwegian periodicals in natural science with the creation of the Magazin for Naturv-
idenskaberne [Magazine for the natural sciences]. Its aim was to convey Norwegian
research in the sciences to the educated lay audience and provide an emerging group
of young scientists with a forum for publication.
17 (C. F. Gauss, 1801).
18 (Stubhaug, 1996, 244–245).