Phenomena of the external sense are examined and set forth in physics; those of the internal sense in empirical psychology. Pure mathematics considers space in geometry and time in pure mechanics. To these is to be added a certain concept, intellectual to be sure in itself, but whose becoming actual in the concrete requires the auxiliary notions of time and space in the successive addition and simultaneous juxtaposition of separate units, which is the concept of number treated in arithmetic.
Immanuel KantRelated topics
arithmetic auxiliary becoming certain concept concrete forth geometry intellectual juxtaposition mathematics mechanics number psychology pure sense set space sureRelated quotes
Students using astrophysical textbooks remain essentially ignorant of even the existence of plasma concepts, despite the fact that some of them have been known for half a century. The conclusion is that astrophysics is too important to be left in the hands of astrophysicists who have gotten their main knowledge from these textbooks. Earthbound and space telescope data must be treated by scientists who are familiar with laboratory and magnetospheric physics and circuit theory, and of course with modern plasma theory.
Hannes Alfvén
I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.
G. H. Hardy
The most powerful influence exercised by the Arabs on general natural physics was that directed to the advances of chemistry; a science for which this race created a new era.(...) Besides making laudatory mention of that which we owe to the natural science of the Arabs in both the terrestrial and celestial spheres, we must likewise allude to their contributions in separate paths of intellectual development to the general mass of mathematical science.
Alexander von Humboldt
The idea of an isolated American painting, so popular in this country during the thirties, seems absurd to me, just as the idea of a purely American mathematics or physics would seem absurd... And in another sense, the problem doesn't exist at all; or, if it did, would solve itself: An American is an American and his painting would naturally be qualified by the fact, whether he wills or not. But the basic problems of contemporary painting are independent of any one country.
Jackson Pollock
The nude gains its enduring value from the fact that it reconciles several contrary states. It takes the most sensual and immediately interesting object, the human body, and puts it out of reach of time and desire; it takes the most purely rational concept of which mankind is capable, mathematical order, and makes it a delight to the senses; and it takes the vague fears of the unknown and sweetens them by showing that the gods are like men and may be worshiped for their life-giving beauty rather than their death-dealing powers.
Kenneth Clark