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If I hadn't an absolute faith in the harmony of creation, I wouldn't have tried for thirty years to express it in a mathematical formula. It is only man's consciousness of what he does with his mind that elevates him above the animals, and enables him to become aware of himself and his relationship to the universe.
Albert Einstein
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I doubt not but it will be easily granted, that the knowledge we have of mathematical truths is not only certain, but real knowledge; and not the bare empty vision of vain, insignificant chimeras of the brain.
John Locke
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The science we are after is not about mathematicals either none of them, you see, is separable.
Aristotle
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When mathematical men will build systems upon fancy, and not upon demonstration, they are as liable to mistakes as others.
John Locke
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Evolution has ensured that our brains just aren't equipped to visualise 11 dimensions directly. However, from a purely mathematical point of view it's just as easy to think in 11 dimensions, as it is to think in three or four.
Stephen Hawking
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Einstein's relativity work is a magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king... its exponents are brilliant men but they are metaphysicists rather than scientists.
Nikola Tesla
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Thinking for its own sake, as in music! When I have no special problem to occupy my mind, I love to reconstruct proofs of mathematical and physical theorems that have long been known to me. There is no goal in this, merely an opportunity to indulge in the pleasant occupation of thinking.
Albert Einstein
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Although I'm regarded as a dangerous radical by particle physicists for proposing that there may be loss of quantum coherence, I'm definitely a conservative compared to Roger. I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation. I think Roger [Penrose] is a Platonist at heart but he must answer for himself.
Stephen Hawking
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Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.
Leonardo da Vinci
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In the great majority of mathematical text-books there is a total lack of unity in method and of systematic development of a central theme. Propositions of very diverse kinds are proved by whatever means are thought most easily intelligible, and much space is devoted to mere curiosities which in no way contribute to the main argument.
Bertrand Russell
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One should not forget that the functions, like all mathematical constructions, are only our own creation, and that when the definition with which one begins ceases to make sense, one should not ask, what is, but what is convenient to assume in order that it [remain] significant.
Carl Friedrich Gauss
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Life is not an illogicality; yet it is a trap for logicians. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wildness lies in wait.
G. K. Chesterton
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If there is anything that can bind the heavenly mind of man to this dreary exile of our earthly home and can reconcile us with our fate so than one can enjoy living, — then it is verily the enjoyment of the mathematical sciences and astronomy.
Johannes Kepler
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As a proposition of linguistics: "Energy" is the name of the mathematical expression in question...As a propo sition of psychology: our senses are such that we notice what is roughly the mathematical expression in question, and we are led nearer and nearer to it as we refine upon our crude perceptions by scientific observation.
Bertrand Russell
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Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.
Aristotle
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It is difficult even to attach a precise meaning to the term "scientific truth." So different is the meaning of the word "truth" according to whether we are dealing with a fact of experience, a mathematical proposition or a scientific theory. "Religious truth" conveys nothing clear to me at all.
Albert Einstein
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In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.
Albert Einstein
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I have presented principles of philosophy that are not, however, philosophical but strictly mathematical-that is, those on which the study of philosophy can be based. These principles are the laws and conditions of motions and of forces, which especially relate to philosophy.
Isaac Newton
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Fundamental ideas play the most essential role in forming a physical theory. Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory. The ideas must later take the mathematical form of a quantitative theory, to make possible the comparison with experiment.
Albert Einstein
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It is a mathematical fact that if a line be not perfectly directed towards a point, it will actually go further away from it as it comes nearer to it.
G. K. Chesterton
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One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?
Stephen Hawking
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We have heard much about the poetry of mathematics, but very little of it has as yet been sung. The ancients had a juster notion of their poetic value than we. The most distinct and beautiful statements of any truth must take at last the mathematical form. We might so simplify the rules of moral philosophy, as well as of arithmetic, that one formula would express them both.
Henry David Thoreau
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I also ask you my friends not to condemn me entirely to the mill of mathematical calculations, and allow me time for philosophical speculations, my only pleasures.
Johannes Kepler
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I know that most men — not only those considered clever, but even those who are very clever and capable of understanding most difficult scientific, mathematical, or philosophic, problems — can seldom discern even the simplest and most obvious truth if it be such as obliges them to admit the falsity of conclusions they have formed, perhaps with much difficulty — conclusions of which they are proud, which they have taught to others, and on which they have built their lives.
Leo Tolstoy
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First Shakespeare sonnets seem meaningless; first Bach fugues, a bore; first differential equations, sheer torture. But training changes the nature of our spiritual experiences. In due course, contact with an obscurely beautiful poem, an elaborate piece of counterpoint or of mathematical reasoning, causes us to feel direct intuitions of beauty and significance. It is the same in the moral world.
Aldous Huxley
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The eruption of lived pleasure is such that in losing myself I find myself; forgetting that I exist, I realize myself.
Raoul Vaneigem
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