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Math Quotes

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Math Quotes

“Please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life. [Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.]”

HappinessScienceTimePassionFearHealthMathematicsMathIntercourseEuclidLewdBolyaiEuclid S PostulateJanos BolyaiJános Bolyai
Author:Farkas Bolyai
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“Derrière la série de Fourier, d'autres séries analogues sont entrées dans la domaine de l'analyse; elles y sont entrees par la même porte; elles ont été imaginées en vue des applications. After the Fourier series, other series have entered the domain of analysis; they entered by the same door; they have been imagined in view of applications.”

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Book:The Value of Science: Essential Writings of Henri Poincare
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“France had recently switched to the metric system of measurement. This gave scientists a much-needed standardized system to measure and compare results, but it also required a whole new set of calculating tables. The sheer number of calculations was beyond what could be accomplished by all the mathematicians in France, so Riche established calculating 'factories' to manufacture logarithms the same way workers manufactured mercantile goods. Each factory employed between 60 and 80 human 'computers.' But they weren’t trained mathematicians; they were mostly out-of-work hairdressers who had found their skill at constructing elaborate pompadours for aristocrats much less in demand after so many former clients lost their heads at the height of the French Revolution. Riche had hit upon a rote system of compiling results based on a set of given values and formulas, and the workers just cranked out the answers in what must have been the world’s first mathematical assembly line. Babbage figured that if an army of untrained hairdressers could make the calculations, so could a computing 'engine.”

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Author:Jennifer Ouellette
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“Gödel’s scheme has nothing to do with mathematics in and of itself. It concerns false approaches (i.e. non-ontological approaches) to the definition of what math is. The incompleteness theorems proved that such approaches are doomed to failure. Gödel didn’t prove a single thing about what math is. What he proved is what’s it’s not. He proved that it definitely isn’t manmade.”

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Book:Gödel Versus Wittgenstein
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“Language as putative science. - The significance of language for the evolution of culture lies in this, that mankind set up in language a separate world beside the other world, a place it took to be so firmly set that, standing upon it, it could lift the rest of the world off its hinges and make itself master of it. To the extent that man has for long ages believed in the concepts and names of things as in aeternae veritates he has appropriated to himself that pride by which he raised himself above the animal: he really thought that in language he possessed knowledge of the world. The sculptor of language was not so modest as to believe that he was only giving things designations, he conceived rather that with words he was expressing supreame knowledge of things; language is, in fact, the first stage of occupation with science. Here, too, it is the belief that the truth has been found out of which the mightiest sources of energy have flowed. A great deal later - only now - it dawns on men that in their belief in language they have propagated a tremendous error. Happily, it is too late for the evolution of reason, which depends on this belief, to be put back. - Logic too depends on presuppositions with which nothing in the real world corresponds, for example on the presupposition that there are identical things, that the same thing is identical at different points of time: but this science came into existence through the opposite belief (that such conditions do obtain in the real world). It is the same with mathematics, which would certainly not have come into existence if one had known from the beginning that there was in nature no exactly straight line, no real circle, no absolute magnitude.”

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Book:Human, All Too Human: A Book for Free Spirits
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“If our sides were unequal our angles might be unequal. Instead of its being sufficient to feel, or estimate by sight, a single angle in order to determine the form of an individual, it would be necessary to ascertain each angle by the experiment of Feeling. But life would be too short for such a tedious groping. The whole science and art of Sight Recognition would at once perish; Feeling, so far as it is an art, would not long survive; intercourse would become perilous or impossible; there would be an end to all confidence, all forethought; no one would be safe in making the most simple social arrangements; in a word, civilization would relapse into barbarism.”

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Book:Flatland: A Romance of Many Dimensions
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“The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon... when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms.”

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Author:Jean-Baptiste-Joseph Fourier
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“In mathematics, in physics, people are concerned with what you say, not with your certification. But in order to speak about social reality, you must have the proper credentials, particularly if you depart from the accepted framework of thinking. Generally speaking, it seems fair to say that the richer the intellectual substance of a field, the less there is a concern for credentials, and the greater is concern for content.”

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Author:Noam Chomsky
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“A Puritan twist in our nature makes us think that anything good for us must be twice as good if it's hard to swallow. Learning Greek and Latin used to play the role of character builder, since they were considered to be as exhausting and unrewarding as digging a trench in the morning and filling it up in the afternoon. It was what made a man, or a woman -- or more likely a robot -- of you. Now math serves that purpose in many schools: your task is to try to follow rules that make sense, perhaps, to some higher beings; and in the end to accept your failure with humbled pride. As you limp off with your aching mind and bruised soul, you know that nothing in later life will ever be as difficult. What a perverse fate for one of our kind's greatest triumphs! Think how absurd it would be were music treated this way (for math and music are both excursions into sensuous structure): suffer through playing your scales, and when you're an adult you'll never have to listen to music again. And this is mathematics we're talking about, the language in which, Galileo said, the Book of the World is written. This is mathematics, which reaches down into our deepest intuitions and outward toward the nature of the universe -- mathematics, which explains the atoms as well as the stars in their courses, and lets us see into the ways that rivers and arteries branch. For mathematics itself is the study of connections: how things ideally must and, in fact, do sort together -- beyond, around, and within us. It doesn't just help us to balance our checkbooks; it leads us to see the balances hidden in the tumble of events, and the shapes of those quiet symmetries behind the random clatter of things. At the same time, we come to savor it, like music, wholly for itself. Applied or pure, mathematics gives whoever enjoys it a matchless self-confidence, along with a sense of partaking in truths that follow neither from persuasion nor faith but stand foursquare on their own. This is why it appeals to what we will come back to again and again: our **architectural instinct** -- as deep in us as any of our urges.”

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Book:Out of the Labyrinth: Setting Mathematics Free
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“I am no friend of probability theory, I have hated it from the first moment when our dear friend Max Born gave it birth. For it could be seen how easy and simple it made everything, in principle, everything ironed and the true problems concealed. Everybody must jump on the bandwagon [Ausweg]. And actually not a year passed before it became an official credo, and it still is.”

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Author:Erwin Schrödinger
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“Put it this way. If you or I were to build a machine, we'd go about it logically, with the fewest necessary parts moving in clean, efficient ways. But living nature doesn't work that way at all. It builds via the most fantastic redundancies and curlicues, millions of little variations around a theme, so that if three-quarters go haywire, life survives. The results are Rube Goldberg devices, but sturdy Rube Goldberg devices, unimaginably weird and densely layered Rube Goldberg devices, literally unimaginable in that our brains aren't adequate to comprehend the sort of microscopic megacities hidden within the tiniest cell. I thought that was neat.”

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Book:All the Beauty in the World: The Metropolitan Museum of Art and Me
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“The consequence model, the logical one, the amoral one, the one which refuses any divine intervention, is a problem really for just the (hypothetical) logician. You see, towards God I would rather be grateful for Heaven (which I do not deserve) than angry about Hell (which I do deserve). By this the logician within must choose either atheism or theism, but he cannot possibly through good reason choose anti-theism. For his friend in this case is not at all mathematical law: the law in that 'this equation, this path will consequently direct me to a specific point'; over the alternative and the one he denies, 'God will send me wherever and do it strictly for his own sovereign amusement.' The consequence model, the former, seeks the absence of God, which orders he cannot save one from one's inevitable consequences; hence the angry anti-theist within, 'the logical one', the one who wants to be master of his own fate, can only contradict himself - I do not think it wise to be angry at math.”

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Book:Healology
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“As you know, there was a famous quarrel between Max Planck and Einstein, in which Einstein claimed that, on paper, the human mind was capable of inventing mathematical models of reality. In this he generalized his own experience because that is what he did. Einstein conceived his theories more or less completely on paper, and experimental developments in physics proved that his models explained phenomena very well. So Einstein says that the fact that a model constructed by the human mind in an introverted situation fits with outer facts is just a miracle and must be taken as such. Planck does not agree, but thinks that we conceive a model which we check by experiment, after which we revise our model, so that there is a kind of dialectic friction between experiment and model by which we slowly arrive at an explanatory fact compounded of the two. Plato-Aristotle in a new form! But both have forgotten something- the unconscious. We know something more than those two men, namely that when Einstein makes a new model of reality he is helped by his unconscious, without which he would not have arrived at his theories...But what role DOES the unconscious play?...either the unconscious knows about other realities, or what we call the unconscious is a part of the same thing as outer reality, for we do not know how the unconscious is linked with matter.”

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Book:Alchemy: An Introduction to the Symbolism and the Psychology
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“The sciences are not sectarian. People do not persecute each other on account of disagreements in mathematics. Families are not divided about botany, and astronomy does not even tend to make a man hate his father and mother. It is what people do not know, that they persecute each other about. Science will bring, not a sword, but peace.”

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Book:Some Mistakes of Moses
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“Light takes eight minutes to travel from the sun to Earth, so if you look at it one way there’s a grace period between when the star stops burning and when the light runs out. But if you look at the first moment without light as the first possible information heralding the end of the star, there’s no time in between the star’s collapse and the light running out. The eight minutes carry the moment of collapse on their backs.”

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Book:Singer Distance
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“Einstein completely failed to address the elephant in the room, namely that light – from its own perspective – isn’t in any inertial reference frame. We can therefore legitimately say that it obeys entirely different laws of physics – those of non-locality (singularities) rather than locality (spacetime) – and, in fact, actually the laws of pure mathematics. Light is the non-inertial container for all inertial reference frames, and ensures that they are all part of an absolute system, not a relative system. It imposes a principle of absolutism, not a principle of relativism!”

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Book:Ontological Mathematics Versus Einstein's Special Theory of Relativity
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“The secret of existence is that, ontologically, mathematics is indistinguishable from light, and light is the basis of mind. Your mind is nothing other than a complete and consistent set of natural photons. Photons have no extension in space and time, meaning that they are outside space and time. They are in the frequency Singularity of immortal things rather than the spacetime world of mortal things. Light World is Soul World, and only math is relevant to this world. Science, the subject that deals with matter, has no application to Soul World. Photons have no mass, hence are not part of material existence. Photons have no extension, no dimensions, and do not experience space and time, all of which is exactly what we require of the immortal soul. When you switch on a light, light does not flood into spacetime. Rather, spacetime interacts with Soul World – spacetime flows through Soul World – producing the characteristic glow of light. Photons are the thoughts of the Cosmic Soul.”

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Book:The Mathematics of Angels
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“You can't. Do you hear me? You think you've figured something out? You run over here so pleased with yourself because you changed your mind. Now you're certain. You're so... sloppy. You don't know anything. The book, the math, the dates, the writing, all that stuff you decided with your buddies, it's just evidence. It doesn't finish the job. It doesn't prove anything.”

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Author:David Auburn
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“All I wanted to do was put together one of the best home maths systems in the world, and that's what we've done. I've loved numbers since I was two or three, and I get really excited about them. Now, I'm allowing myself to get excited about things. If you're doing it for a TV network or any major corporation, you have to put a lid on it a little.”

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Author:Carol Vorderman
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“Well done is better than well said.”

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Book:The Way to Wealth and Poor Richard's Almanac
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“The interaction between math and physics is a two-way process, with each of the two subjects drawing from and inspiring the other. At different times, one of them may take the lead in developing a particular idea, only to yield to the other subject as focus shifts. But altogether, the two interact in a virtuous circle of mutual influence.”

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Author:Edward Frenkel
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