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Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic something more than logic, he believed, makes mathematics what it is.

Eric Temple Bell

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Eric Temple Bell
Age: 77 †
Born: 1883
Born: February 7
Died: 1960
Died: December 21
Historian Of Mathematics
Mathematician
Novelist
Science Fiction Writer
Writer
John Taine
Something
Believed
Logic
Rewritten
Mathematics
Elementary
Notion
Notions
Terms
Vigorous
Theory
Opponent
Term
Classical
Makes
Opponents

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Galois read the geometry from cover to cover as easily as other boys read a pirate yarn.
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Nevertheless, the consuming hunger of the uncritical mind for what it imagines to be certainty or finality impels it to feast upon shadows in the prevailing famine of substance.
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Science makes no pretension to eternal truth or absolute truth.
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Time makes fools of us all. Our only comfort is that greater shall come after us.
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It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.
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The only royal road to elementary geometry is ingenuity.
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The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular.
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Any impatient student of mathematics or science or engineering who is irked by having algebraic symbolism thrust upon him should try to get along without it for a week.
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If Number rules the universe as Pythagoras asserted, Number is merely our delegate to the throne, for we rule Number.
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Even stranger things have happened and perhaps the strangest of all is the marvel that mathematics should be possible to a race akin to the apes.
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Obvious is the most dangerous word in mathematics.
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Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.
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Pick the assumptions to pieces till the stuff they are made of is exposed to plain view - this is the cardinal rule for understanding the basis of our beliefs.
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Archimedes, Newton, and Gauss, these three, are in a class by themselves among the great mathematicians, and it is not for ordinary mortals to attempt to range them in order of merit.
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Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos.
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The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated it might even be just to designate him as a Copernicus of all thought.
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Fashion as King is sometimes a very stupid ruler.
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