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Neils Henrik Abel lived his short life in Norway. He suffered great
poverty, owing partially to the economic conditions in Norway during
this period. His family's hard fortune is often attributed to his father's
severe drinking problems. Abel's best-known work revolves around the
solvability of fifth degree, or quintic, equations. As a teenager he
believed that he had developed a method for solving such equations using
radicals. This technique was similar in structure, albeit more complicated,
to the well-known quadratic equation used for solutions to second-degree
equations. He sent his results for verification to several surrounding
universities. It is believed that at least one working mathematician
replied with a challenge to apply his method to some specific numerical
examples. While examining these examples, he learned the error of his
initial findings. After a few years of work, he formulated a proof that
such equations are unsolvable using algebraic methods. The proof settled
what had been until that time an open question: Abel was the first to
establish that there were algebraic equations that could not be solved
with algebraic expressions. Abel also did extensive work into the theory
of elliptic functions. He died of complications from tuberculosis just
days before his household received word that he had been accepted for
a position at a major university in Berlin.
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