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The piano's world encompasses glass-nerved virtuos and stomping barrel-housers in fedoras; it is a world of pasture and storm, of perfumed smoke, of liquid mathematics.
If you help others, you will be helped, perhaps tomorrow, perhaps in one hundred years, but you will be helped. Nature must pay off the debt. It is a mathematical law and all life is mathematics.
It is a well-known experience that the only truly enjoyable and profitable way of studying mathematics is the method of "filling in details" by one's own efforts.
There are all sorts of things embodied in the Lego brick - geometry and mathematics and truth and proportion and shape and colour... It is a faintly spiritual activity that everybody connects with.
In most sciences one generation tears down what another has built and what one has established another undoes. In mathematics alone each generations adds a new story to the old structure.
Very often in mathematics the crucial problem is to recognize and discover what are the relevant concepts; once this is accomplished the job may be more than half done.
As for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra.
If you refuse to study anatomy, the arts of drawing and perspective, the mathematics of aesthetics, and the science of color, let me tell you that this is more a sign of laziness than of genius.
Nature's economy shall be the base for our own, for it is immutable, but ours is secondary. An economist without knowledge of nature is therefore like a physicist without knowledge of mathematics.