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There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.
Nikolai Ivanovich Lobachevsky
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Indeed we may consider the engine as the material and mechanical representative of analysis, and that our actual working powers in this department of human study will be enabled more effectually than heretofore to keep pace with our theoretical knowledge of its principles and laws, through the complete control which the engine gives us over the executive manipulation of algebraical and numerical symbols.
Ada Lovelace
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I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means "to break:" to create irregular fragments... how appropriate for our needs!
Benoît Mandelbrot
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The twentieth century return to Middle Age scholastics taught us a lot about formalisms. Probably it is time to look outside again. Meaning is what really matters.
Yuri I. Manin
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Kepler... thought it but reasonable, that as the sea has its whales and monsters, the air should have them likewise. These monsters are Comets...
Pierre Louis Maupertuis
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I had expressed my wish to have a thermometer of probability, with impossibility at one end, as 2 plus 2 makes 5, and necessity at the other as 2 plus 2 make 4.
Augustus De Morgan
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Most convincing to me of the spiritual relations between mathematics and music, is my own very personal experience. Composing in an amateurish way, I get exactly the same elevation from a prelude that has come to me at the piano, as I do from a new idea that has come to me in mathematics.
Marston Morse
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Rationality of thought imposes a limit on a person's concept of his relation to the cosmos.
John Forbes Nash, Jr.
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The most vitally characteristic fact about mathematics is, in my opinion, its quite peculiar relationship to the natural sciences, or more generally, to any science which interprets experience on a higher than purely descriptive level.
John von Neumann
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The design of this Memoir is to deduce strictly from a few principles, obtained chiefly by experiment, the rationale of those electrical phenomena which are produced by the mutual contact of two or more bodies, and which have been termed galvanic; its aim is attained if by means of it the variety of facts be presented as unity to the mind.
Georg Ohm
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The economy is a nonlinear fractal system, where the smallest scales are linked to the largest, and the decisions of the central bank are affected by the gut instincts of the people on the street.
David Orrell
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Mathematicks therefore is a Science which teaches or contemplates whatever is capable of Measure or Number as such. When it relates to Number, it is called Arithmetick; but when to measure, as Length, Breadth, Depth, Degrees of Velocity in Motion, Intenseness or Remissness of Sounds, Augmentation or Diminution of Quality, 6tc. it is called Geometry.
Jacques Ozanam
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The Ancients, having taken into consideration the rigorous construction of the human body, elaborated all their works, as especially their holy temples, according to these proportions; for they found here the two principal figures without which no project is possible: the perfection of the circle, the principle of all regular bodies, and the equilateral square.
Luca Pacioli
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Geometric calculus consists in a system of operations analogous to those of algebraic calculus, but in which the entities on which the calculations are carried out, instead of being numbers, are geometric entities which we shall define.
Giuseppe Peano
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[Science] advances by leaps; and the impulse for each leap is either some new observational resource, or some novel way of reasoning about the observations. Such novel way of reasoning might, perhaps, be considered as a new observation means, since it draws attention to reactions between facts which would previously have been passed by unperceived.
Charles Sanders Peirce
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A beautiful idea has a much greater chance of being a correct idea than an ugly one.
Roger Penrose
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As to the propriety and justness of representing sums of money, and time, by parts of space, tho' very readily agreed to by most men, yet a few seem to apprehend there may possibly be some deception in it, of which they are not aware...
William Playfair
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In repeating an argument that I have learned, I could readily have discovered it myself: or rather, even if this is an illusion, if I were not clever enough to have created it myself, I rediscover it myself, to the extent that I repeat it.
Henri Poincaré
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If anyone asked me to define time, I should reply: "Do you know what it is that you speak of?" If he said "Yes," I should answer, "Very well, let us talk about it." If he said "No," I should answer, "Very well, let us talk about something else."
Louis Poinsot
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The engineer should receive a complete mathematical education, but for what should it serve him? To see the different aspects of things and to see them quickly; he has no time to hunt mice.
Siméon Denis Poisson
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My method to overcome a difficulty is to go round it.
George Pólya
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Each atom of the Holy Spirit is intelligent, and like all other matter has solidity, form, and size, and occupies space.
Orson Pratt
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The heaven is spherical in shape, and moves as a sphere; the earth too is sensibly spherical in shape, when taken as a whole; in position it lies in the middle of the heavens very much like its center; in size and distance it has the ratio of a point to the sphere of the fixed stars; and it has no motion from place to place.
Ptolemy
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The more progress physical sciences makes, the more they tend to enter the domain of mathematics, which is a kind of center to which they all converge. We may even judge of the degree of perfection to which a science has arrived by the facility with which it may be submitted to calculation.
Adolphe Quetelet
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To preserve my brains I want food and this is now my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship...
Srinivasa Ramanujan
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Thinking is like loving and dying. Each of us must do it for himself.
Josiah Royce
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