Famous for his contributions to group theory, Galois produced a method
of determining when a general equation could be solved by radicals.
Galois's life was dominated by politics and mathematics. An ardent
republican, he was in the unfortunate position of having Cauchy, an
ardent royalist, as the only French mathematician capable of
understanding the significance of his work.
In 1829 he published his first paper on continued fractions, followed
by a paper that dealt with the impossibility of solving the general
quintic equation by radicals. This led to Galois theory, a branch of
mathematics dealing with the general solution of equations.
Famous for his contributions to group theory, he produced a method of
determining when a general equation could be solved by radicals. This
theory solved many long-standing unanswered questions including the
impossibility of trisecting the angle and squaring the circle.
He introduced the term 'group' when he considered the group of
permutations of the roots of an equation. Group theory made possible
the unification of geometry and algebra.
In 1830 he solved f(x) = 0 (mod p) for an irreducible polynomial f(x)
by introducing a symbol j as a 'solution' to f(x) = 0 as for complex
numbers. This gives the Galois field GF(p).
Galois's work made an important contribution to the transition from
classical to modern algebra. Having spent some time in prison for
political offences, he was killed in a duel at the age of 21 shortly
after his release.
Biographies of mathematicians are from the
Mathematics archive at the University of St. Andrews, and are
used with permission.