A Quote by Richard Courant
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection.
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Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.
When the contemplative mind is a French mind, it is content, for the most part, to contemplate France. When the contemplative mind is an English mind, it is liable to be seized at any moment by an importunate desire to contemplate Morocco or Labrador.
Blindness to the aesthetic element in mathematics is widespread and can account for a feeling that mathematics is dry as dust, as exciting as a telephone book... Contrariwise, appreciation of this element makes the subject live in a wonderful manner and burn as no other creation of the human mind seems to do.
There is no thing as a man who does not create mathematics and yet is a fine mathematics teacher. Textbooks, course material-these do not approach in importance the communication of what mathematics is really about, of where it is going, and of where it currently stands with respect to the specific branch of it being taught. What really matters is the communication of the spirit of mathematics. It is a spirit that is active rather than contemplative-a spirit of disciplined search for adventures of the intellect. Only as adventurer can really tell of adventures.
Almost all crime is due to the repressed desire for aesthetic expression.
Let us realise [that] we are the infinite power. Who put a limit to the power of mind? Let us realise we are all mind. Every drop has the whole of the ocean in it. That is the mind of man. The Indian mind reflects upon these [powers and potentialities] and wants to bring [them] all out. For himself he doesn't care what happens. It will take a great length of time [to reach perfection]. If it takes fifty thousand years, what of that!
This is the path of prayer-contemplative prayer, that is, as distinct from simple prayers of supplication and thanksgiving-which is a specific discipline of thought, desire, and action, one that frees the mind from habitual prejudices and appetites, and allows it to dwell in the gratuity and glory of all things. As an old monk on Mount Athos once told me, contemplative prayer is the art of seeing reality as it truly is; and, if one has not yet acquired the ability to see God in all things, one should not imagine that one will be able to see God in himself.
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.
A human being in perfection ought always to preserve a calm and peaceful mind and never to allow passion or a transitory desire to disturb his tranquility.
Does the human being reason? No; he thinks, muses, reflects, but does not reason...that is, in the two things which are the peculiar domain of the heart, not the mind, politics and religion. He doesn't want to know the other side. He wants arguments and statistics for his own side, and nothing more.
Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon. It is a pity, but in that case he does not matter a great deal anyhow, and it would be silly to bother about him.
Was it Aristotle who said the human soul is composed of reason, will, and desire?” “No, that was Plato. Aristotle and Plato were as different as Mel Tormé and Bing Crosby. In any case, things were a lot simpler in the old days,” Komatsu said. “Wouldn’t it be fun to imagine reason, will, and desire engaged in a fierce debate around a table?
The research reported on in our book "A=B", has moved a whole active field of mathematics from the province of human thought to the realm of computer-fodder. It is quite exciting to think about what other fields of pure mathematics, hitherto thought to be reserved to human intelligence, might be moved to that realm next. The goal is to put ourselves out of business completely, and the work is well underway.
Either mathematics is too big for the human mind or the human mind is more than a machine.
I can fool you because you're a human. You have a wonderful human mind that works no different from my human mind. Usually when we're fooled, the mind hasn't made a mistake. It's come to the wrong conclusion for the right reason.
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