Popularity: 3
Vote:   | Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics. |
Popularity: 5
Vote: | All of these dislikes and objections are of course themselves meaningless unless they can be backed by a definite program to replace what is rejected. |
Popularity: 0
Vote: | Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. |
Popularity: 1
Vote: | Fashion as King is sometimes a very stupid ruler. |
Popularity: 1
Vote: | 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. |
Popularity: 3
Vote: | I have always hated machinery, and the only machine I ever understood was a wheelbarrow, and that but imperfectly. |
Popularity: 4
Vote: | If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics. |
Popularity: 1
Vote: | 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. |
Popularity: 3
Vote: | If there is any virtue in talking about situations which arise in analysis as if we were back with Archimedes drawing diagrams in the dust, it has yet to be revealed. Pictures after all may be suitable only for very young children; Lagrange dispensed entirely with such infantile aids when he composed his analytical mechanics. Our propensity to 'geometrize' our analysis may only be evidence that we have not yet grown up. |
Popularity: 1
Vote: | Intuition (male, female or mathematical) has been greatly overrated. Intuition is the root of all superstition. |
Popularity: 1
Vote: | It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences. |
Popularity: 3
Vote: | 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. |
Popularity: 1
Vote: | 'Obvious' is the most dangerous word in mathematics. |
Popularity: 0
Vote: | 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. |
Popularity: 2
Vote: | Science makes no pretension to eternal truth or absolute truth. |
Popularity: 2
Vote: | The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry. |
Popularity: 2
Vote: | The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes. |
Popularity: 1
Vote: | The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future. |
Popularity: 3
Vote: | 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. |
Popularity: 2
Vote: | The whole of mathematics may be interpreted as a battle for supremacy between these two concepts. This conflict may be but an echo of the older strife so prominent in early Greek philosophy, the struggle of the One to subdue the Many. But the image of a battle is not wholly appropriate, in mathematics at least, as the continuous and the discrete have frequently helped one another to progress. |
Popularity: 2
Vote: | Time makes fools of us all. Our only comfort is that greater shall come after us. |
Popularity: 3
Vote: | To appreciate the living spirit rather than the dry bones of mathematics, it is necessary to inspect the work of a master at first hand... The very crudities of the first attack on a significant problem by a master are more illuminating than all the pretty elegance of the standard texts which has been won at the cost of perhaps centuries of finicky polishing. |
Popularity: 5
Vote: | Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos. |