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Mathematical Quotes

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Mathematical Quotes

“How then shall mathematical concepts be judged? They shall not be judged. Mathematics is the supreme arbiter. From its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play.”

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Author:David van Dantzig
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“Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world.”

ThinkingWorldWayRealProblemTodaySchoolCertainAbilityEducationKeysMathematicsEverydayBoxesValuableSolveMathAriseMathematicalFeaturesContrastMathematicianKey To SuccessProceduresReal ProblemsSchool SystemToday's WorldOutside The BoxThink Outside The Box
Author:Keith Devlin
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“I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. ... True, he was very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to start reading more difficult mathematical books on my own and to study them as diligently as I could; if I came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon and he kindly explained to me everything I could not understand.”

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Author:Leonhard Euler
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“...the science of calculation also is indispensable as far as the extraction of the square and cube roots: Algebra as far as the quadratic equation and the use of logarithms are often of value in ordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; but not be in indulged in by one who is to have a profession to follow for his subsistence.”

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Book:Jefferson: Writings
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“The mathematical question is "Why?" It's always why. And the only way we know how to answer such questions is to come up, from scratch, with these narrative arguments that explain it. So what I want to do with this book is open up this world of mathematical reality, the creatures that we build there, the questions that we ask there, the ways in which we poke and prod (known as problems), and how we can possibly craft these elegant reason-poems.”

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Author:Paul Lockhart
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“How often might a man, after he had jumbled a set of letters in a bag, fling them out upon the ground before they would fall into an exact poem, yea, or so much as make a good discourse in prose? And may not a little book be as easily made by chance as this great volume of the world?”

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Book:The works of the most reverend Dr. John Tillotson, late Lord Archbishop of Canterbury: containing fifty four sermons and discourses on several occasions. Together with The Rule of Faith. Being all that were published by His Grace himself and now collected into one volume, to which is added an alphabetical table of the principle matter
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“All was predicted by the mathematical cycles of the Mayan calendars. -- It will change --everything will change. Mayan Day-keepers view the Dec. 21, 2012 date as a rebirth, the start of the World of the Fifth Sun. It will be the start of a new era resulting from and signified by the solar meridian crossing the galactic equator and the Earth aligning itself with the center of the galaxy.”

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Author:Carlos Barrios
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“By the time the average person finishes college, he or she will have taken over 2,600 tests, quizzes, and exams. The right answer approach becomes deeply ingrained in our thinking. This may be fine for some mathematical problems where there is in fact only one right answer. The difficulty is that most of life isn’t this way. Life is ambiguous; there are many right answers- all depending on what you’re looking for. But if you think there is only one right answer, then you’ll stop looking as soon as you find one.”

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Author:Roger von Oech
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“To tell the truth, in Pacific 231 I was on the trail of a very abstract and quite ideal concept, by giving the impression of a mathematical acceleration of rhythm, while the movement itself slowed . I first called this piece Mouvement symphonique. On reflection I found that a bit colorless. Suddenly, a rather romantic image crossed my mind, and when the work was finished, I wrote the title Pacific 231, which indicates a locomotive for heavy loads and high speeds (a type unfortunately disappeared, alas, and sacrificed to electric traction).”

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Author:Arthur Honegger
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“Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May. How old is the captain?”

GivingMayProblemPastThreeLeftBoysStudyWindBrokenMonthsOceanMathematicsBoundsMathEastShipsMathematicalClockAfternoonQuartersSailCaptainsBostonGeometryPassengersDeckCabinsWoolCargoMathematical ProblemsTrigonometryNorth East
Author:Gustave Flaubert
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“Four circles to the kissing come, The smaller are the benter. The bend is just the inverse of The distance from the centre. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of squares of all four bends Is half the square of their sum.”

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Author:Frederick Soddy
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“...from the time of Kepler to that of Newton, and from Newton to Hartley, not only all things in external nature, but the subtlest mysteries of life and organization, and even of the intellect and moral being, were conjured within the magic circle of mathematical formulae.”

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Book:Hints towards the formation of a more comprehensive theory of life
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“Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties, and we may confidently look forward to a time when they shall form but one body with one soul.”

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Book:The Laws of Verse: Or Principles of Versification Exemplified in Metrical Translations, Together with an Annotated Reprint of the Inaugural Presidential Address to the Mathematical and Physical Section of the British Association at Exeter
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“In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life.”

LifeInspirationalArtDreamLightNightHeavenStarsWonderWonderfulMoonStonesMiracleMathematicsInspiredLeavingProofChecksMathematicalBroadsMathematicianFloatingEquationsFloatsFull MoonRigourDifferential EquationsQuadratic Equation
Book:Michael Atiyah Collected Works: 2002-2013
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“There are two versions of math in the lives of many Americans: the strange and boring subject that they encountered in classrooms and an interesting set of ideas that is the math of the world, and is curiously different and surprisingly engaging. Our task is to introduce this second version to today's students, get them excited about math, and prepare them for the future.”

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Book:What's Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success
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“Suppose that you want to teach the 'cat' concept to a very young child. Do you explain that a cat is a relatively small, primarily carnivorous mammal with retractible claws, a distinctive sonic output, etc.? I'll bet not. You probably show the kid a lot of different cats, saying 'kitty' each time, until it gets the idea. To put it more generally, generalizations are best made by abstraction from experience.”

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Author:Ralph P. Boas, Jr.
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“First, it is necessary to study the facts, to multiply the number of observations, and then later to search for formulas that connect them so as thus to discern the particular laws governing a certain class of phenomena. In general, it is not until after these particular laws have been established that one can expect to discover and articulate the more general laws that complete theories by bringing a multitude of apparently very diverse phenomena together under a single governing principle.”

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Author:Augustin-Louis Cauchy
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“Everyone engaged in research must have had the experience of working with feverish and prolonged intensity to write a paper which no one else will read or to solve a problem which no one else thinks important and which will bring no conceivable reward - which may only confirm a general opinion that the researcher is wasting his time on irrelevancies.”

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Book:The Essential Chomsky
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