Mathematical Quotes
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Here at Wisconsin we didn't get an undergraduate course in mathematical logic until the '60s.
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Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts.
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Those of us who teach math should try to turn this bug into a feature. We should be up front about the fact that word problems force us to make simplifying assumptions. That’s a valuable skill—it’s called mathematical modeling.
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I had made an empirical discovery and it carried all the weight of a mathematical proof.
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One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden.
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When I speak of the beauty of a game of chess, then naturally this is subjective. Beauty can be found in a very technical, mathematical game for example. That is the beauty of clarity.
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What appear to be the most valuable aspects of the theoretical physics we have are the mathematical descriptions which enable us to predict events. These equations are, we would argue, the only realities we can be certain of in physics; any other ways we have of thinking about the situation are visual aids or mnemonics which make it easier for beings with our sort of macroscopic experience to use and remember the equations.
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When the difficulty of a problem lies only in finding out what follows from certain fixed premises, mathematical methods furnish invaluable wings for flying over intermediate obstructions.
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As a single atom man is an enigma: as a whole he is a mathematical problem. As an individual he is a free agent, as a species the offspring of necessity.
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Music is a science, in many ways it's mathematical.
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If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.
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Unlike mathematical theorems, scientific results can't be proved. They can only be tested again and again, until only a fool would not believe them. I cannot prove that electrons exist..........if you don't believe in them I have a high voltage cattle prod I'm willing to apply as an argument on their behalf. Electrons speak for themselves.
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In accordance with the foregoing investigations on mathematical principles, let bronze vessels be made, proportionate to the size of the theatre, and let them be so fashioned that, when touched, they may produce with one another the notes of the fourth, the fifth, and so on up the double octave.
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College is the grinding machine of the Mathematical Establishment, a conveyor belt that takes individuals from one cookie cutter to another so that the product comes within tight control limits out of the assembly line.
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Dull minds are never either intuitive or mathematical.
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A geometrical theory in physical interpretation can never be validated with mathematical certainty ... ; like any other theory of empirical science, it can acquire only a more or less high degree of confirmation.
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The Grand Duke [of Tuscany] ...after observing the Medicaean plants several times with me ... has now invited me to attach myself to him with the annual salary of one thousand florins, and with the title of Philosopher and Principal Mathematicial to His Highness; without the duties of office to perform, but with the most complete leisure; so that I can complete my Treatises.
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It is clear that Economics, if it is to be a science at all, must be a mathematical science ... simply because it deals with quantities... As the complete theory of almost every other science involves the use of calculus, so we cannot have a true theory of Economics without its aid.
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Inspiration is constantly in the air. It's up to us to develop the sensitivity to pick up on it.
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Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be solidly backed up. It's just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about mathematical ideas.
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We could tell them alien civilization things that we have discovered in the realm of mathematical physics, but there is stuff that I would like to know. There are some famous problems like how to bring gravitation and quantum physics together, the long-sought-after theory of quantum gravity. But it may be hard to understand the answer that comes back.
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Experience has shown repeatedly that a mathematical theory with a rich internal structure generally turns out to have significant implications for the understanding of the real world, often in ways no one could have envisioned before the theory was developed.
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Homeopathy seemed . . . both mathematical and poetic.
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Without leaving his study, without even looking at the sky—had found the unknown planet Neptune solely by mathematical calculation, and, as it were, touched it with the tip of his pen!
