Galois Quotes

Here, however, is where his genius truly took off. Galois managed to associate with each equation a sort of "genetic code" of that equation-the Galois group of the equation-and to demonstrate that the properties of the Galois group determine whether the equation is solvable by a formula or not. Symmetry became the key concept, and the Galois group was a direct measure of the symmetry properties of an equation. ~ Mario Livio

Unfortunately what is little recognized is that the most worthwhile scientific books are those in which the author clearly indicates what he does not know; for an author most hurts his readers by concealing difficulties. ~ Evariste Galois

[As a young teenager] Galois read Legendre]'s geometry from cover to cover as easily as other boys read a pirate yarn. ~ Eric Temple Bell

No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. ... Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; ... [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. ... A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas. ~ G.H. Hardy

Until when will the poor youngsters be obliged to listen or to repeat all day long? When will they be given some time to reflect on this accumulation of knowledge, to be able to coordinate [find a pattern in] this endless multitude of propositions, in these unrelated calculations?...Students are less interested in learning than passing their exams. ~ Evariste Galois

The analysts try in vain to conceal the fact that they do not deduce: they combine, they compose ... when they do arrive at the truth they stumble over it after groping their way along. ~ Evariste Galois

Galois's ideas, with all their brilliance, did not appear out of thin air. They addressed a problem whose roots could be traced all the way back to ancient Babylon. Still, the revolution that Galois had started grouped together entire domains that were previously unrelated. Much like the Cambrian explosion-that stunning burst of diversification in life forms on Earth-the abstraction of group theory opened windows into an infinity of truths. Fields as far apart as the laws of nature and music suddenly became mysteriously connected. The Tower of Babel of symmetries miraculously fused into a single language. ~ Mario Livio

An author never does more damage to his readers than when he hides a difficulty. ~ Evariste Galois