A Quote by Ernst Mach
The mathematician who pursues his studies without clear views of this matter, must often have the uncomfortable feeling that his paper and pencil surpass him in intelligence.
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A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence.
Instead of encouraging the student to devote himself to his studies for the sake of studying, instead of encouraging in him a real love for his subject and for inquiry, he is encouraged to study for the sake of his personal career; he is led to acquire only such knowledge as is serviceable in getting him over the hurdles which he must clear for the sake of his advancement.
A poet's soul must contain the perfect shape of all things good, wise and just. His body must be spotless and without blemish, his life pure, his thoughts high, his studies intense.
In a sense, the religious person must have no real views of his own and it is presumptuous of him, in fact, to have any. In regard to sex-love affairs, to marriage and family relations, to business, to politics, and to virtually everything else that is important in his life, he must try to discover what his god and his clergy would like him to do; and he must primarily do their bidding.
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It is essential for the photographer to know the effect of his lenses. The lens is his eye, and it makes or ruins his pictures. A feeling for composition is a great asset. I think it is very much a matter of instinct. It can perhaps be developed, but I doubt if it can be learned. To achieve his best work, the young photographer must discover what really excites him visually. He must discover his own world.
The master in the art of living makes little distinction between his work and his play, his labor and his leisure, his mind and his body, his information and his recreation, his love and his religion. He hardly knows which is which. He simply pursues his vision of excellence at whatever he does, leaving others to decide whether he is working or playing. To him he's always doing both.
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There are many who hold, as I do, that the most important part of life is not the age of university studies, but the first one, the period from birth to the age of six. For that is the time when a man's intelligence itself, his greatest implement, is being formed. But not only his intelligence; the full totality of his psychic powers.
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Man's mind is his basic tool of survival. Life is given to him, survival is not. His body is given to him, its sustenance is not. His mind is given to him, its content is not. To remain alive, he must act, and before he can act he must know the nature and purpose of his action. He cannot obtain his food without a knowledge of food and of the way to obtain it. He cannot dig a ditch-or build a cyclotron-without a knowledge of his aim and of the means to achieve it. To remain alive, he must think
The constructs of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow mathematician interested in the constructs of his imagination. We cannot help the feeling that certain mathematical structures which have evolved through the combined efforts of the mathematical community bear the stamp of a necessity not affected by the accidents of their historical birth.
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The person who experiences greatness must have a feeling for the myth he is in. He must reflect what is projected upon him. And he must have a strong sense of the sardonic. This is what uncouples him from belief in his own pretensions. The sardonic is all that permits him to move within himself. Without this quality, even occasional greatness will destroy a man.
Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him that he had not observed: he muttered: 'Il faut que j'y songe encore', and put the paper in his pocket.' [I must think about it again]
I must admit that outside the university, it is difficult to be a pure mathematician. No one in my family understands what I do. My neighbors wonder why I spend all my time in my study scribbling with pencil on a yellow pad of paper instead of going outside to mow the lawn.
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