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Time makes fools of us all. Our only comfort is that greater shall come after us.
– E. T. Bell
‘Obvious’ is the most dangerous word in mathematics.
It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.
Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.
The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future.
Fashion as King is sometimes a very stupid ruler.
The longer mathematics lives the more abstract – and therefore, possibly also the more practical – it becomes.
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.
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.
I have always hated machinery, and the only machine I ever understood was a wheelbarrow, and that but imperfectly.
Science makes no pretension to eternal truth or absolute truth.
If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.
Out of fifty mathematical papers presented in brief at such a meeting, it is a rare mathematician indeed who really understands what more than half a dozen are about.