Vaunted Quotes (1 quote)
Since the beginning of the century, computational procedures have become so complicated that any progress by those means has become impossible, without the elegance which modern mathematicians have brought to bear on their research, and by means of which the spirit comprehends quickly and in one step a great many computations.
It is clear that elegance, so vaunted and so aptly named, can have no other purpose. …
[But, the simplifications produced by this elegance will soon outrun the problems supplied by analysis. What happens then?]
Go to the roots, of these calculations! Group the operations. Classify them according to their complexities rather than their appearances! This, I believe, is the mission of future mathematicians. This is the road on which I am embarking in this work.
From the preface to his final manuscript, 'Two Memoirs in Pure Analysis', written (Dec 1831) while he was in Sainte Pélagie prison. Translation as quoted by B. Melvin Kiernan, 'The Development of Galois Theory from Lagrange to Artin', Archive for History of Exact Sciences (30 Dec 1971), 8, No. 1/2, 92. [The sentence in brackets above, is how Kiernan summarizes Galois, at the ellipsis. Kiernan introduces the conclusion with his own question.] Kiernan cites in a footnote Ecrits et Mémoires, 9. The French 'Preface' was published for the first time in René Taton, 'Les relations d’Evariste Galois Avec Les Mathématiciens de Son Temps', Revue d’Histoire des Sciences (1949), 1, No. 12, 114130. [Six months after writing his manuscript, Galois died in a duel (31 May 1832), at just 20 years old. In the papers he left after his death, he had established the foundation of the powerful Permutational Group Theory, hence “Group the Operations.” —Webmaster] The full Preface, in translation, is on the MacTutor website, titled, 'Évariste Galois’ Preface written in Sainte Pélagie'.
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) 
Carl Sagan
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