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Math Quotes

“These estimates may well be enhanced by one from F. Klein (1849-1925), the leading German mathematician of the last quarter of the nineteenth century. 'Mathematics in general is fundamentally the science of self-evident things.' ... If mathematics is indeed the science of self-evident things, mathematicians are a phenomenally stupid lot to waste the tons of good paper they do in proving the fact. Mathematics is abstract and it is hard, and any assertion that it is simple is true only in a severely technical sense—that of the modern postulational method which, as a matter of fact, was exploited by Euclid. The assumptions from which mathematics starts are simple; the rest is not.”

HardScienceMathematicsMathAbstractMathematicianEuclidTechnicalEstimatesFelix Klein
Book:Mathematics: Queen and Servant of Science
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“My sub doesn't pay for me,” he says, pulling me to my feet. “That just doesn't happen.” “But we ordered so much,” I say helplessly. “It made you happy,” he says simply. “Now I get to play with you. And that makes me happy.” “I don't think it's that simple an equation.” “Maybe not,” he concedes. “But then, if if sex were the same thing as math, a lot more people would be lining up to take calculus.”

HumorSexHumorousMathematicsSexyMathSubmissionBdsmSubmissiveSexy HumorBdsm RomanceBdsm EroticaSexy MenNenia CampbellBdsm QuotesBound To Attract
Book:Bound to Accept
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“There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities... I cannot tell you how grateful I am for our little infinity. You gave me forever within the numbered days, and I'm grateful.”

NumbersMathJohn GreenHazel GraceAugustus WatersTfiosInfinities
Book:The Fault in Our Stars
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“People with no qualifications whatsoever in mathematics, science and philosophy continuously proclaim, “My ignorance is just as good as your knowledge.” In fact, one of their tactics is to attempt to demolish knowledge by claiming that whatever anyone says is just “subjective”. Are science and math as “subjective” as Eastern religion? Science and math objectively landed men on the moon!”

TruthScienceMathRelativismSubjectivismDiscordianism
Book:Illuminism Contra Discordianism
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“There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, ... the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the ideas of time and force are at an end; the very elements of the orbit have disappeared, or only exist as arbitrary characters in a mathematical formula.”

ScienceMathematicsMathPhysicsInquiryNewtonIsaac NewtonFormulaLagrangeJoseph Louis LagrangeMotion Of The Planets
Author:George Boole
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“When one day Lagrange took out of his pocket a paper which he read at the Académe, and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This demonstration rested on an obvious paralogism, which appeared as such to everybody; and probably Lagrange also recognised it such during his lecture. For, when he had finished, he put the paper back in his pocket, and spoke no more of it. A moment of universal silence followed, and one passed immediately to other concerns.”

ScienceMathematicsMathEuclidLagrangeJoseph Louis LagrangeGiuseppe Luigi LagranciaTheory Of Parallels
Author:Jean-Baptiste Biot
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“Ze všeho nejvíce Gausse rozčilovaly stále nové a nové pokusy různých geometrů dokázat pátý postulát. Nyní, když znal nový geometrický svět, když do něj bezpečně nahlížel, odhaloval v těchto domnělých důkazech chybu vždy hned při prvním pohledu. Jasně viděl, jak geometři tápají v tmách, jak plýtvají silami na těchto beznadějných pokusech - a pomoci jim nemohl; nesměl.”

InsightMathNon Euclidean Geometry
Book:Trýznivé tajemství
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“It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.”

HumorFunnyScienceNatureMysteryMathematicsMathLaws Of NatureLaws Of PhysicsPhysicistsMathematiciansTheoremHenri PoincaréPoincaré
Book:Statistical Independence in Probability, Analysis, and Number Theory
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“A parabola opens at a certain direction, allowing for infinitely many points to reside inside the area from which it opens. As a student, I do not like to specialize in a single discipline; specialization seems unfulfilling in my own mind. Hence, the graph of a straight line is not an appropriate analogy to the depths of my curiosity. A line only goes in one direction, and unlike a parabola, a line cannot encase that infinite amount of white space on a coordinate plane—it can only pass through it. Rather than being like a rigid line, I try to be more open to a wider variety of academic subjects. I do admit—a parabola still opens in a certain direction, and of course, my interests are still skewed toward particular subjects. However, the open curve of the parabola can still encompass infinitely many points as the graph extends, the same way my curiosity can still expand to multiple different subjects. This is why I see myself more in the curvaceous parabola than the rigid line.”

PhilosophyEducationMathSelf ReflectionParabolaGraph
Book:For the Intellect
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“I entered Princeton University as a graduate student in 1959, when the Department of Mathematics was housed in the old Fine Hall. This legendary facility was marvellous in stimulating interaction among the graduate students and between the graduate students and the faculty. The faculty offered few formal courses, and essentially none of them were at the beginning graduate level. Instead the students were expected to learn the necessary background material by reading books and papers and by organising seminars among themselves. It was a stimulating environment but not an easy one for a student like me, who had come with only a spotty background. Fortunately I had an excellent group of classmates, and in retrospect I think the "Princeton method" of that period was quite effective.”

MathematicsMathMathematicianBiographyLegendaryPrincetonPrinceton UniversityGraduate StudentInstitute For Advanced StudyPrinceton Method
Author:Phillip A. Griffiths
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“Before an experiment can be performed, it must be planned—the question to nature must be formulated before being posed. Before the result of a measurement can be used, it must be interpreted—nature's answer must be understood properly. These two tasks are those of the theorist, who finds himself always more and more dependent on the tools of abstract mathematics. Of course, this does not mean that the experimenter does not also engage in theoretical deliberations. The foremost classical example of a major achievement produced by such a division of labor is the creation of spectrum analysis by the joint efforts of Robert Bunsen, the experimenter, and Gustav Kirchhoff, the theorist. Since then, spectrum analysis has been continually developing and bearing ever richer fruit.”

ScienceNatureTheoryMathematicsMathAnalysisSpectrumExperimentBunsenRobert BunsenGustav KirchhoffKirchhoff
Author:Max Planck
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“I confess that Fermat's Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can easily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the principal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries. {In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.}”

ScienceTheoryMathematicsMathGoalsFermatPierre De FermatFermat S TheoremHeinrich Wilhelm Matthias OlbersOlbers
Author:Carl Friedrich Gauss
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“I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind. (Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.)”

ScienceMathematicsSolveMathFermat S Last TheoremFermatPierre De FermatTheorem
Author:Andrew John Wiles
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“... I left Caen, where I was living, to go on a geological excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.”

ScienceWorkTravelMathematicsMathGeometryEuclidEuclidean GeometryFuchsian FunctionsGeological
Author:Henri Poincaré
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“INTROSPECTION AND INSANITY: A GODELIAN PROBLEM I think it can have suggestive value to translate Godel's Theorem into other domains, provided one specifies in advance that the translations are metaphorical and are not intended to be taken literally. That having been said, I see two major ways of using analogies to connect Godel's Theorem and human thoughts. One involves the problem of wondering about one's sanity. How can you figure out if you are sane? This is a Strange Loop indeed. Once you begin to question your own sanity, you can get trapped in an ever-tighter vortex of self-fulfilling prophecies, though the process is by no means inevitable. Everyone knows that the insane interpret the world via their own peculiarly consistent logic; how can you tell if your own logic is 'peculiar' or not, given that you have only your own logic to judge itself? I don't see any answer. I am just reminded of Godel's second Theorem, which implies that the only versions of formal number theory which assert their own consistency are inconsistent...”

ConsciousnessMental HealthMathAiSanityTheorems
Author:Douglas Hofstadter
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“The spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didn't bother to remember things. He computed them. You asked him a question, and if he didn't know the answer, he thought for three seconds and would produce and answer.”

SciencePowerComputerPraiseMathematicsMemoryInsightMathSpeedClarityMathematicianSpectacularVon NeumannJohn Von NeumannNeumannJohnny Von NeumannLogarithm
Author:Paul R. Halmos
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“Ohm found that the results could be summed up in such a simple law that he who runs may read it, and a schoolboy now can predict what a Faraday then could only guess at roughly. By Ohm's discovery a large part of the domain of electricity became annexed by Coulomb's discovery of the law of inverse squares, and completely annexed by Green's investigations. Poisson attacked the difficult problem of induced magnetisation, and his results, though differently expressed, are still the theory, as a most important first approximation. Ampere brought a multitude of phenomena into theory by his investigations of the mechanical forces between conductors supporting currents and magnets. Then there were the remarkable researches of Faraday, the prince of experimentalists, on electrostatics and electrodynamics and the induction of currents. These were rather long in being brought from the crude experimental state to a compact system, expressing the real essence. Unfortunately, in my opinion, Faraday was not a mathematician. It can scarcely be doubted that had he been one, he would have anticipated much later work. He would, for instance, knowing Ampere's theory, by his own results have readily been led to Neumann's theory, and the connected work of Helmholtz and Thomson. But it is perhaps too much to expect a man to be both the prince of experimentalists and a competent mathematician.”

MathematicsGreenMathMathematicianElectricityMagnetismFaradayMichael FaradayPoissonAmpereAndré Marie AmpèreCoulombHelmholtzJ J ThomsonNeumannOhmSiméon Denis PoissonCharles Augustin De CoulombFranz Ernst NeumannGeorg OhmGeorge GreenHermann Von HelmholtzThomson
Book:Electromagnetic Theory
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“For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view.”

ScienceDifficultNatureResearchMathematicsMathCalculationsThoroughAbridgedAuxiliarySimplified
Author:Louis Poinsot
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“Suppose every life was written as a storybook; assuming this was true, the only storybook each person would completely know is their own. I know my own story, as I own my own thoughts and my own consciousness. Hence, I have not finished reading the books of other lives, because I am still writing my own. Therefore, since I live in and am the main character of my own book, I appear to be at the center of life itself. From my vantage point, I’m at the center of the world—I have not finished the stories of others, because I’m at the center of my own. This is why I compare myself to the midpoint formula: the midpoint does not begin a line nor end the line, but rather becomes a part of it—from an individualistic vantage point, I am a part of or even at the center of life itself.”

LifePhilosophyCreativeMathAnalogyMidpoint
Book:For the Intellect
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“Mathiness: British economic journalist John Kay defines mathiness as a “use of algebraic symbols and quantitative data to give an appearance of scientific content to ideological preconceptions.” Expressing an idea in mathematical symbols instead of straightforward literary terms helps legitimize it in the minds of many people, thanks to a seeming similarity with natural science. In this respect math is basically a form of numerical rhetoric. “The American economist Paul Romer has recently written of ‘mathiness,’ by analogy with ‘truthiness,’ a term coined by American talk show host Stephen Colbert. Truthiness presents narratives which are not actually true, but consistent with the world view of the person who spins the story. It is exemplified in rightwing fabrications about European health systems – their death panels and forced euthanasia.” Paul Samuelson, for instance, trivialized economics in terms that give the outward appearance of science by being expressed mathematically, even when its assumptions are purely hypothetical (and not all realistic)and there are no quantitative statistics to illustrate its categories.”

EconomicsMathematicsMathDeceptionFraudNeoclassical Economics
Book:J Is for Junk Economics: A Guide to Reality in an Age of Deception
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“One of the first steps toward gaining expertise in math and science is to create conceptual chunks—mental leaps that unite separate bits of information through meaning. Once you chunk an idea or concept, you don’t need to remember all the little underlying details; you’ve got the main idea—the chunk—and that’s enough.”

ScienceMathMeaningIdeaConceptChunk
Book:A Mind for Numbers: How to Excel at Math and Science
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