9 quotes
The quality of the human mind, considered in its collective aspect, which most strikes us, in surveying this record, is its colossal patience.
Squaring the Circle (1913)
The objects of abstract Geometry possess in absolute precision properties which are only approximately realized in the corresponding objects of physical Geometry.
Squaring the Circle (1913)
The history of our problem falls into three periods marked out by fundamentally distinct differences in respect of method, of immediate aims, and in equipment in possession of intellectual tools.
Squaring the Circle (1913)
Success, even in a comparatively limited field, is some compensation for failure in a wider field of endeavour.
Squaring the Circle (1913)
If the question be raised, why such an apparently special problem as the quadrature of the circle, is deserving of the sustained interest which has attained to it, and which it still possesses, the answer is only to be found in a scrutiny of the history of the problem, and especially in the closeness of the connection of that history with the general history of Mathematical Science.
Squaring the Circle (1913)
Perhaps the least inadequate description of the general scope of modern Pure Mathematics—I will not call it a definition—would be to say that it deals with form, in a very general sense of the term; this would include algebraic form, functional relationship, the relations of order in any ordered set of entities such as numbers, and the analysis of the peculiarities of form of groups of operations.
Presidential Address British Association for the Advancement of Science, Section A (1910)
The utilitarian notion...has the fatal limitation that it attempts to assign limits to what is, or may in the future become, useful, in accordance with a more or less arbitrarily restricted standard of what constitutes utility.
Who has studied the works of such men as Euler, Lagrange, Cauchy, Riemann, Sophus Lie, and Weierstrass, can doubt that a great mathematician is a great artist? The faculties possessed by such men, varying greatly in kind and degree with the individual, are analogous with those requisite for constructive art. Not every mathematician possesses in a specially high degree that critical faculty which finds its employment in the perfection of form, in conformity with the ideal of logical completeness; but every great mathematician possesses the rarer faculty of constructive imagination.
Presidential Address British Association for the Advancement of Science, Section A (1910)
We are able to appreciate the difficulties which in each age restricted the progress which could be made within limits which could not be surpassed by the means then available; we see how, when new weapons became available, a new race of thinkers turned to the further consideration of the problem with a new outlook.
Squaring the Circle (1913)