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Would Abel have received the Abel Prize?
On Niels Henrik Abel and his prize
Foredrag på NTVA-møte i Trondheim
12.
november
2013
Helge Holden, Professor of Mathematics. Norwegian University of Science and
Technology, and Chair of the Abel Board
Niels Henrik Abel's lite
To try to answer this hypothetical question, we have to make a careful evaluation of Abel's
mathematics and how he was assessed by his contemporaries. Let us start with a brief
presentation of Niels Henrik Abel. He was bom in
1802,
the second oldest of 6 siblings. His
father, Søren Georg Abel, was a vicar in Gjerstad, where Niels Henrik grew up. Søren Georg
was a rationalist, who believed in education and the improvement of living conditions for the
poor. He was a member of the Norwegian
Storting
(Parliament). However, after getting
involved in political and religious controversies, he returned to Gjerstad a broken man and
died young in
1820.
Niels Henrik's mother seems to have cared little for her children, and
there is evidence !hat she became an alcoholic.
Niels Henrik was granted free admission to
Katedralskolen
(The Cathedral School) in
Christiania (now Oslo) in
1815.
There his luck changed for the better- his teacher, Bernt
Michael Holmboe. soon discovered Niels Henrik's exceptional talent. and Holmboe was able
to stimulate Niels Henrik's interest in mathematics by giving him books by the masters:
Newton, Euler, Lagrange, Laplace, etc. In
1821
he entered the newly opened university in
Christiania (Oslo}. Soon
it
became clear to the few mathematicians in Norway that Niels
Henrik would have to travel abroad in order to develop further. Supported by the King, the
Storting
and the University, he started his joumey in
1825,
planning to visit Gottingen and
Paris, two of the world's leading centers of mathematics. Niels Henrik changed his plans and
went to Berlin instead of Gottingen, where he met the publisher, August Leopold Grelle, who
recognized Abel's potential. Grelle created
Journal fOr de reine und angewandte Mathematik,
and with a steady publication of Abel's works, the journal began to gain recognition. Today, it
is a premier journal referred to as
Crelle's Journal.
However, the main destination of his
journey was Paris. He found Itl e French difficult to interact with, and Niels Henrik worked
hard on what was to be his main oeuvre, the Paris treatise, which he handed in to the French
Academy in October
1826.
However, the sole copy was misplaced by the Academy's
secretary, and Abel waited in vain in Paris for a response for another half year. Most likely,
that was where he contracted the tuberculosis that would later end his life. He returned
disillusioned to Christiania, and never saw the Paris treatise again. His big journey was
considered a failure: he had not met the famous mathematician Gauss in Gottingen, he had
published in an unknown journal, he had lost his main work, and he had no strong letters of
praise from the elite in Paris.
Upon returning he was given a temporary appointment at the university, where he
commenced a frenetic mathematical activity, pu'::>lishing many papers in Cre//e's
Journal.
His
health started
to
deteriorate, and on his deathbed he wrote a brief proof of the main result of
his Paris treatise. He died on 6 April
1829.
His friend and mentor Grelle had worked to
secure Abel a professorship in Berlin, and on
8
April
1829
a letter arrived with an offer from
Berlin. Shortly thereafter, the Paris treaty was found, and Abel was posthumously awarded
the Academy's gold medal. Such is the sad stor1 of Niels Henrik Abel's life.
Abel's mathematics
Already at the tender age of
19,
Niels Henrik had started to work on one of the biggest
unsolved problems of the day - that of salving the quintic equation with formulas involving
only root extraction. The solution of first-degree equations had been known since time
immemorial. The solution of the second-deQree equations was already well-known in
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