Galois

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.