I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. . . But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming-- and a little mad.
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I would by no means wish a daughter of mine to be a progeny of learning; I don't think so much learning becomes a young woman: for instance, I would never let her meddle with Greek, or Hebrew, or algebra, or simony, or fluxions, or paradoxes, or such inflammatory branches of learning; nor will it be necessary for her to handle any of your mathematical, astronomical, diabolical instruments; but... I would send her, at nine years old, to a boarding-school, in order to learn a little ingenuity and artifice: then, sir, she would have a supercilious knowledge in accounts, and, as she grew up, I would have her instructed in geometry, that she might know something of the contagious countries: this is what I would have a woman know; and I don't think there is a superstitious article in it.
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Einstein is an analytical mathematician seeking to give a physical interpretation to the conclusions of his mathematical process. In this he is hampered by a load of contradictory and absurd assumptions of the school that he follows, which throws him into all manner of difficulty. Einstein has such a faculty for embracing both sides of a contradiction that one would have to be of the same frame of mind to follow his thought, it is so peculiarly his own. The whole Relativity theory is as easy to follow as the path of a bat in the air at night.
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A free-enterprise economy depends only on markets, and according to the most advanced mathematical macroeconomic theory, markets depend only on moods: specifically, the mood of the men in the pinstripes, also known as the Boys on the Street. When the Boys are in a good mood, the market thrives; when they get scared or sullen, it is time for each one of us to look into the retail apple business.
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Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry... If mathematical analysis should ever had prominent place in chemistry - an aberration, which is happily almost impossible - it would be a rapid and widespread degeneration of that science.
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Blaise Pascal used to mark with charcoal the walls of his playroom, seeking a means of making a circle perfectly round and a triangle whose sides and angle were all equal. He discovered these things for himself and then began to seek the relationship which existed between them. He did not know any mathematical terms and so he made up his own. Using these names he made axioms and finally developed perfect demonstrations, until he had come to the thirty-second proposition of Euclid.
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The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method
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The stars which shone over Babylon and the stable in Bethlehem still shine as brightly over the Empire State Building and your front yard today. They perform their cycles with the same mathematical precision, and they will continue to affect each thing on earth, including man, as long as the earth exists.
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I just have this feeling if I take pi, well past all this static, take pi to 10 million, 20 million digits, that I'll find something really incredible. Not just a pattern, not just an order, but a sign. A mathematical sign.
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Nobody before the Pythagorean had thought that mathematical relations held the secret of the universe. Twenty-five centuries later, Europe is still blessed and cursed with their heritage. To non-European civilizations, the idea that numbers are the key to both wisdom and power, seems never to have occurred.
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The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work.
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Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts... A graphic representation of data abstracted from the banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellations of data. Like city lights, receding...
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In studying mathematics or simply using a mathematical principle, if we get the wrong answer in sort of algebraic equation, we do not suddenly feel that there is an anti-mathematical principle that is luring us into the wrong answers.
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How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.
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Data from dose-response relationships are sometimes employed to estimate the expected tumour incidence at dose levels very much lower than those which could possibly be employed in conventional [animal] experiments. A number of mathematical models have been employed in such estimates and the results obtained vary considerably. Despite these uncertainties - and the possibly greater ones in extrapolating from animals to man - such models are often employed in some quarters to estimate the likely risk to man.
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It is from this absolute indifference and tranquillity of the mind, that mathematical speculations derive some of the most considerable advantages; because there is nothing to interest the imagination; because the judgment sits free and unbiased to examine the point. All proportions, every arrangement of quantity, is alike to the understanding, because the same truths result to it from all; from greater from lesser, from equality and inequality.
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The mere formulation of a problem is far more essential than its solution, which may be merely a matter of mathematical or experimental skills. To raise new questions, new possibilities, to regard old problems from a new angle requires creative imagination and marks real advances in science.
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One cannot really argue with a mathematical theorem.
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It is a mathematical fact that the casting of this pebble from my hand alters the centre of gravity of the universe.
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The circumstances of human society are too complicated to be submitted to the rigor of mathematical calculation.
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It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient...
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All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.
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A technique succeeds in mathematical physics, not by a clever trick, or a happy accident, but because it expresses some aspect of a physical truth.
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To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers.
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I chose to deal with the science of cryptography. Cryptography began in mathematics. Codes were developed, even from Caesar's time, based on number theory and mathematical principles. I decided to use those principles and designed a work that is encoded.
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Unfortunately, extrapolations from animal results to man remains largely problematic and no amount of mathematical sophistication can render such extrapolation more certain. .
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It is my conviction that pure mathematical construction enables us to discover the concepts and the laws connecting them, which gives us the key to the understanding of nature ... In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.
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Has the mathematical abilities of a Clydesdale.
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[F]or academic men to be happy, the universe would have to take shape. All of philosophy has no other goal: it is a matter of giving a frock coat to what is, a mathematical frock coat. On the other hand, affirming that the universe resembles nothing and is only formless amounts to saying that the universe is something like a spider or spit.
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In this age of specialization, I sometimes think of myself as the last 'generalist' in economics, with interests that range from mathematical economics down to current financial journalism. My real interests are research and teaching...
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