A Quote by Edward Kasner
Mathematics is man's own handiwork, subject only to the limitations imposed by the laws of thought.
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Does man's freedom consist in revolting against all laws? We say no, in so far as laws are natural, economic, and social laws, not authoritatively imposed but inherent in things, in relations, in situations, the natural development of which is expressed by those laws. We say YES if they are political and juridical laws, imposed upon men by men.
Mathematics never reveals man to the degree, never expresses him in the way, that any other field of human endeavour does: the extent of the negation of man's corporeal self that mathematics achieves cannot be compared with anything. Whoever is interested in this subject I refer to my articles. Here I will say only that the world injected its patterns into human language at the very inception of that language; mathematics sleeps in every utterance, and can only be discovered, never invented.
Look for good things about where you are, and in your state of appreciation, you lift all self-imposed limitations - and all limitations are self-imposed - and you free yourself for the receiving of wonderful things.
I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.
The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.
On all levels primary, and secondary and undergraduate - mathematics is taught as an isolated subject with few, if any, ties to the real world. To students, mathematics appears to deal almost entirely with things whlch are of no concern at all to man.
If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
Logic is the science of the laws of thought, as thought,--that is of the necessary conditions to which thought considered in itself is a subject.
Man is the individualised expression or reflection of God imaged forth and made manifest in bodily form. How is it, then, I hear it asked, that man has the limitations that he has, that he is subject to fears and forebodings, that he is liable to sin and error, that he is the victim of disease and suffering? There is but one reason. He is not living, except in rare cases here and there, in the conscious realisation of his own true Being, and hence of his own true Self.
Laws, in their most general signification, are the necessary relations arising from the nature of things. In this sense all beings have their laws: the Deity His laws, the material world its laws, the intelligences superior to man their laws, the beasts their laws, man his laws.
If all consciousness is subject to essential laws in a manner similar to that in which spatial reality is subject to mathematical laws, then these essential laws will be of most fertile significance in investigating facts of the conscious life of human and brute animals.
The subject for which I am asking your attention deals with the foundations of mathematics. To understand the development of the opposing theories existing in this field one must first gain a clear understnding of the concept "science"; for it is as a part of science that mathematics originally took its place in human thought.
The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.
As mathematics had been my best subject at school, my parents proposed - and I accepted - studies at the University of Lund in mathematics, statistics, and economics. The choice of the latter subject is said to be due to the fact that at the age of five years, I was very fond of calculating the cost of the various cakes my mother used to bake.
I believe that the unity of man as opposed to other living things derives from the fact that man is the conscious life of himself. Man is conscious of himself, of his future, which is
death, of his smallness, of his impotence; he is aware of others as others; man is in nature, subject to its laws even if he transcends it with his thought.
The laws ought to be so framed as to secure the safety of every citizen as much as possible. ... Political liberty does not consist in the notion that a man may do whatever he pleases; liberty is the right to do whatsoever the laws allow. ... The equality of the citizens consists in that they should all be subject to the same laws.
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