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antiquity, and formulas for third- and fourth-degree equations had been found during the
Renaissance. However, the solution of the fifth degree equation, the quintic, had eluded
mathematidans for 250 years. Abel thought he had found the solution, but soon discovered
his own mistake. Then, with a stroke of genf.us, he radically changed his point of view and
proved that no such solution could exist! Assuming the formula's existence, he derived the
consequences !hat this would have for the original equation. and through an ingenious
insight, he came to the conclusion that not all quintic equations had the necessary form. He
reported this result in a very brief paper and published it privately in Christiana, where, not
surprisingly, it remained unnoticed. However, he wrote a more complete version of the proof
in Cre//e's
Journal.
He then started to work on elliptic functions and elliptic integrals. This was
technically more demanding, and even now., two centuries later, it is still even difficult to
explain to professionals. The crowning glory of his Paris treatise was the addition theorem for
elliptic integrals. Once it had been digested by his peers, recognition came fast. The German
mathematician Alfred Clebsch (1833-72) claimed that algebraic geometry, one of the basic
mathematical disciplines, starts with Abel's addition theorem. For a more detailed
presentation of Abel's mathematics, see Houzel, 2004.
The French mathematician Adrien-Marie Legendre (1752-1833), stated that the Paris
treatise was "Monumentum aere perennius
1
".
The German Carl Gustav Jacob Jacobi (1804-
51 ), one of Abel's fiercest competitors, said "...die grosste mathematische Entdeckung
unserer Zeit, obgleich erst eien kOnftige, vielleicht spate grosse Arbeit ihre ganze Bedeutung
aufweisen k<>nne". The French mathematician Charles Emile Picard (1856-1941), who
belongs to the generation following Abel, stated "...il n'y peut-etre pas dans l'historire de la
Science, de proposition aussi importante obtenie
a
l'aide de considerations aussi simples".
The leading Norwegian mathematician of the 20
111
century, Atle Selberg, had !his to say about
Abel's addition theorem, "Det står for meg som den rene magi. Hverken hos Gauss eller
Riemann eller noen annen har jeg funnet noe som kan riktig måle seg med dette
2
" .
Sir
Michael Atiyah, the Abel Laureate in 2004, said in his acceptance speech "Abel was really
the first modern mathematician. His whole approach, with its generality, its insight and
its
elegance sel the tone for the next two centuries. His early death was a terrible loss - imagine
if Mozart had died at a similar age. It has been said that, had Abel lived longer, he would
have been the natura! successor to the great Gauss ... except for the fact that Abel was a
much nicer man, modest, friendly and likeable".
The Abel Prize
In August 2001, the Norwegian Prime Minister, Jens Stoltenberg, announced at a meeting at
the University of Oslo that his government would establish a fund with a dual purpose,
namely (1) to award an annua! international Abel Prize in mathematics and (2) to stimulate
an interest in mathematics among the yOI!Jth. The history leading up to this event is
interesting, (see Helsvig, 2013
&
2014}, and really starts with the aborted attempts to create
an Abel Prize at the centennial of his birth in 1902. A serendipitous meeting in a bookstore in
Risør between Abel biographer, Arild Stubhaug, and the CEO of Televerket, Tormod
Hermansen, restarted the process that eventually led to the creation of the annua! Abel
Prize.
The Abel Laureates
The first prize, awarded in 2003, went to the French mathematician Jean-Pierre Serre. The
subsequent laureates are Sir Michael Atiyah (UK) and lsadore Singer (USA) in 2004, Peter.
D. Lax (USA) in 2005, Lennart Carlseon (Sweden) in 2006, Srinivasa Varadhan (lndia/USA)
1
A monument more lasting than bronze.
2
It seems like pure magic to me. l have found nothing in the works of Gauss, Riemann or
anyone else that can compare with it.
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