The mathematician is entirely free, within the limits of his imagination, to construct what worlds he pleases. What … - J. W. N. Sullivan

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J. W. N. Sullivan

The mathematician is entirely free, within the limits of his imagination, to construct what worlds he pleases. What he is to imagine is a matter for his own caprice; he is not thereby discovering the fundamental principles of the universe nor becoming acquainted with the ideas of God.

Ideas, Imagination, Limits, Math, Pleases, Thereby

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It is only in exceptional moods that we realize how wonderful are the commonest experiences of life. It seems to me sometimes that these experiences have an "inner" side, as well as the outer side we normally perceive. At such moments one suddenly sees everything with new eyes; one feels on the brink of some great revelation. It is as if we caught a glimpse of some incredibly beautiful world that lies silently about us all the time.

Life, Beautiful, Lying, Inner, Moments, Commonest

We have reached one of the great stages in the adventure of thought … We are required to see the universe with new eyes, and it is because it makes such demands and also holds out the promise of realizing them, that the study of science is so supremely worth while.

Adventure, Eye, Promise, Realizing, Universe

It is certain that the real function of art is to increase our self-consciousness; to make us more aware of what we are, and therefore of what the universe in which we live really is. And since mathematics, in its own way, also performs this function, it is not only aesthetically charming but profoundly significant. It is an art, and a great art.

Art, Function, Real, Science

If a man in order to shoot a hare, were to discharge thousands of guns on a great moor in all possible directions; if in order to get into a locked room, he were to buy ten thousand casual keys, and try them all; if, in order to have a house, he were to build a town, and leave all the other houses to wind and weather - assuredly no one would call such proceedings purposeful and still less would anyone conjecture behind these proceedings a higher wisdom, unrevealed reasons, and superior prudence.

Men, Gun, Keys, Superior, Thousand, Reasons

It is much easier to make measurements than to know exactly what you are measuring

Measurement, Easier, Measuring, Measurements, Know