Abel's life was dominated by poverty. After the death of his father,
who was a Protestant minister, in 1820 Abel had the responsibility of
supporting his mother and family.
Abel's teacher Holmboe, recognising his talent for mathematics, raised
money from his colleagues to enable Abel to attend Christiania
University. He entered the university in 1821, 10 years after the
university was founded, and graduated in 1822.
Abel published in 1823 papers on functional equations and integrals.
In it Abel gives the first solution of an integral equation. In 1824
he proved the impossibility of solving algebraically the general
equation of the fifth degree and published it at his own expense
hoping to obtain recognition for his work.
He eventually won a scholarship from the Norwegian government to
travel abroad, visiting Germany and France.
Abel was instrumental in establishing mathematical analysis on a
rigorous basis. His major work Recherches sur les fonctions
elliptiques was published in 1827 in the first volume of Crelle's
Journal, the first journal devoted entirely to mathematics. Abel met
Crelle on his visit to Germany.
After visiting Paris he returned to Norway heavily in debt. While in
Paris he visited a doctor who informed him he had tuberculosis.
Despite his bad health and poverty he continued writing papers on
equation theory and elliptic functions of major importance in the
development of the whole theory. Abel revolutionised the understanding
of elliptic functions by studying the inverse of these functions.
Abel travelled by sled to visit his fiance for Christmas 1828 in
Froland. He became seriously ill on the sled journey and died a couple
of months later.
Biographies of mathematicians are from the
Mathematics archive at the University of St. Andrews, and are
used with permission.