| Technology means the systematic application of scientific or other organized knowledge to practical tasks. | |
| J. K. Galbraith, quoted in Harper's Quotes. | 128 |
| Truly I begin to understand that although logic is an excellent instrument to govern our reasoning, it does not compare with the sharpness of geometry in awakening the mind to discovery. | |
| Galileo, | 935 |
| Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined. | |
| Galileo, quoted in To Infinity and Beyond: A Cultural History of the Infinite by Eli Maor, p. 179 where it is attributed to a statement made by Salviati in "Dialogues of Two New Sciences" (1638) | 1499 |
| In my mind God wrote two books. The first book is the Bible, where humans can find the answers to their questions on values and morals. The second book of God is the book of nature, which allows humans to use observation and experiment to answer our own questions about the universe. | |
| Galileo, Quoted in Death by Black Holes by Neil DeGrasse Tyson, attributed to Discoveries and Opinions of Galileo by Stillman Drake, 1957, p. 173. | 1450 |
| Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined. | |
| Galileo Galilei, quoted in To Infinity and Beyond by Eli Maor. | 656 |
| Let us remember that we are dealing with infinities and indivisibles, both of which transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness. In spite of this men cannot refrain from discussing them, even though it must be done in a roundabout way. | |
| Galileo Galilei, quoted in Infinity and the Mind by Rudy Rucker. | 518 |
| We can only infer that the totality of all numbers is infinite, and that the number of squares is infinite...; neither is the number of squares less than the totality of all numbers, nor the latter greater than the former; and finally, the attrbutes "equal," "greater," and "less," are not applicable to infinite, but only to finite quantities. | |
| Galileo Galilei, quoted in Infinity and the Mind by Rudy Rucker. | 522 |
| [Paradoxes of the infinite arise] only when we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this I think is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another. | |
| Galileo Galilei, quoted in Infinity and the Mind by Rudy Rucker. | 521 |
| The Universe is a grand book which cannot be read until one first learns to comprehend the language and become familiar with the characters in which it is composed. It is written in the language of mathematics. | |
| Galilei Galileo, | 130 |
| In questions of science the authority of a thousand is not worth the humble reasoning of an individual. | |
| Galilei Galileo, quoted in The World of Mathematics, by J.R. Newman. | 129 |
| The universe stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth. | |
| Galileo, quoted in The Joy of Mathematics, by Theoni Pappas. | 496 |
| Since the beginning of the century, computational procedures have become so complicated that any progress by those means has become impossible, without the elegance which modern mathematicians have brought to bear on their research, and by means of which the spirit comprehends quickly and in one step a great many computations.
It is clear that elegance, so vaunted and so aptly named, can have no other purpose. ... Go to the roots, of these calculations! Group the operations. Classify them according to their complexities rather than their appearances! This, I believe, is the mission of future mathematicians. This is the road on which I am embarking in this work. | |
| Galois, From the preface to his final manuscript | 823 |
| There is nothing that wastes the body like worry, and one who has any faith in God should be ashamed to worry about anything whatsoever. | |
| Mahatma Gandhi, | 839 |
| An error does not become truth by reason of multiplied propagation, nor does truth become error because nobody sees it. | |
| Mahatma Gandhi, | 1636 |
| When I despair, I remember that all through history the ways of truth and love have always won. There have been tyrants, and murderers, and for a time they can seem invincible, but in the end they always fall. Think of it - always. | |
| Mahatma Gandhi, | 1683 |
| A surprising proportion of mathematicians are accomplished musicians? Is it because music and mathematics share patterns that are beautiful? | |
| Martin Gardner, quoted in More Mathematical People by D.J. Albers, G.L. Alexanderson, and C. Reid. | 710 |
| As writers, mathematicians are notoriously inept. | |
| Martin Gardner, quoted in The Fourth Dimension: A Guided Tour of the Higher Universes by Rudy Rucker. | 659 |
| One would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery--and more totally useless--than the perfect numbers. | |
| Martin Gardner, quoted in "Even Perfect Numbers: (Update)^2", by S. Bezuszka and M. Kenney, The Mathematics Teacher, vol. 90, no. 8, November 1997. | 705 |
| All mathematicians share... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics. | |
| Martin Gardner, quoted in More Mathematical People by D.J. Albers, G.L. Alexanderson, and C. Reid. | 711 |
| If present trends continue, our country may soon find itself far behind many other nations in both science and technology--nations where, if you inform strangers that you are a mathematician, they respond with admiration and not by telling you how much they hated math in school, and how they sure could use you to balance their checkbooks. | |
| Martin Gardner, quoted in More Mathematical People by D.J. Albers, G.L. Alexanderson, and C. Reid. | 713 |
| Life is the art of drawing without an eraser. | |
| John W. Gardner, | 808 |
| Biographical history, as taught in our public schools, is still largely a history of boneheads; ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant general - the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all. | |
| M. Gardner, quoted in the American Mathematical Monthly, Dec. 1994. | 131 |
| No longer is theology embarrassed by the contradiction between God's immanence and transcendence. Hyperspace touches every point of three-space. God is closer to us than our breathing. He can see every portion of our world, touch every particle without moving a finger through our space. Yet the Kingdom of God is completely "outside" of three-space, in a direction in which we cannot even point. | |
| Martin Gardner, quoted in The Fourth Dimension: A Guided Tour of the Higher Universes by Rudy Rucker. | 661 |
| I have need to be all on fire, for I have mountains of ice about me to melt. | |
| William Lloyd Garrison, | 1447 |
| I have need to be all on fire, for I have mountains of ice about me to melt. | |
| William Lloyd Garrison, | 1029 |
| And these are the suppositions from which Mathematicians, within the gates of pure and abstract Geometry and almost constituting a kingdom of their own, weave those famous demonstrations, some so extraordinary that they even exceed credibility, like what the famous Cavalieri and Torricelli showed of a certain acute solid infinitely long which nevertheless is equal to a parallelepiped or to a finite cylinder. It is clear, therefore, how they protect that kingdom of theirs in which they find so many remarkable and pleasurable things and take care not to mix anything with matter. | |
| Pierre Gassendi, quoted in "Torricelli"s Infinitely Long Solid and Its Philosophical Reception in the Seventeenth Century," by P. Mancosu and E. Vailati, Isis, vol. 82, 1991. | 623 |
| Effort is only effort when it begins to hurt. | |
| Jose Ortega y Gassett, | 1584 |
| Imagination is the one weapon in the war against reality. | |
| Jules de Gaultier, | 1632 |
| As to your proof, I must protest most vehemently against your use of the infinite as something consummated, as that is never permitted in mathematics... No contradictions will arise as long as Finite Man does not mistake the infinite for something fixed. | |
| Gauss, quoted in Using History to Teach Mathematics: An International Perspective, edited by Victor Katz | 1137 |
| It may be true that people who are merely mathematicians have specific shortcomings; however, that is not the fault of mathematicians, but is true of every exclusive occupation. | |
| Carl Friedrich Gauss, quoted in Bartlett's Familiar Quotations. | 137 |
| Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers. | |
| Carl Friedrich Gauss, quoted in Theory of Complex Functions, by Reinhold Rommert. | 136 |
| In the theory of parallels we are even now not further than Euclid. This is a shameful part of mathematics. | |
| C.F. Gauss, | 762 |
| At the very beginning I would ask anyone who wants to introduce a new function into analysis to clarify whether he intends to confine it to real magnitudes [real values of its argument] and regard the imaginary values as just vestigial - or whether he subscribes to my fundamental proposition that in the realm of magnitudes the imaginary ones a+b(sqrt(-1))=a+bi have to be regarded as enjoying equal rights with the real ones. We are not talking about practical utility here; rather analysis is, to my mind, a self-sufficient science. It would lose immeasurably in beauty and symmetry from the rejection of any fictive magnitudes. At each stage truths, which otherwise are quite generally valid, would have to be encumbered with all sorts of qualifications. | |
| Carl Friedrich Gauss, quoted in Theory of Complex Functions, by Reinhold Rommert. | 135 |
| [On Sophie Germain] When a person of the sex which, according to our customs and prejudices, must encounter infinitely more difficulties than men... succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of [number theory], then without doubt she must have the noblest courage, quite extraordinary talents and superior genius. | |
| Carl Friedrich Gauss, | 134 |
| Were it not for your [Duke of Brunswick] unceasing benefits in support of my studies, I would not have been able to devote myself totally to my passionate love, the study of mathematics. | |
| C.F. Gauss, quoted in The History of Mathematics by David M. Burton. | 904 |
| Mathematics is the queen of the sciences and number theory the queen of mathematics. | |
| Carl Friedrich Gauss, | 133 |
| Does the pursuit of truth give you as much pleasure as before? Surely it is not the knowing but the learning, not the possessing but the acquiring, not the being-there but the getting there that afford the greatest satisfaction. If I have exhausted something, I leave it in order to go again into the dark. Thus is that insatiable man so strange: when he has completed a structure it is not in order to dwell in it comfortably, but to start another. | |
| Carl Friedrich Gauss, quoted in A Mathematical Journey, by Gudder. | 132 |
| I protest above all against the use of an infinite quntity as a completed one, which in mathematics is never allowed. The Infinite is only a manner of speaking. | |
| Carl Friedrich Gauss, quoted in Journey Through Genius by William Dunham. | 548 |
| I am ever more convinced that the necessity of our geometry cannot be proved -- at least not by human reason. It is possible that in another lifetime we will arrive at other conclusions on the nature of space that we now have no access to. In the meantime we must not put geometry on par with arithmetic that exists purely a priori but rather with mechanics. | |
| C.F. Gauss, quoted in Mathematical Expeditions by R. Laubenbacher and D. Pengelley. | 966 |
| Whatever you can do, or dream you can do, begin it. Boldness has genius, power and magic in it. | |
| Geothe, | 139 |
| When the boy begins to understand that the visible point is preceded by an invisible point, that the shortest distance between two points is conceived as a straight line before it is ever drawn with pencil and paper...the fountain of all thought has been opened to him...the philosopher can reveal him nothing new, as a geometrician he has discovered the basis of all thought. | |
| Geothe, quoted in Memorabilia Mathematica, by R.E. Moritz. | 138 |
| We must be the change we wish to see in the world. | |
| M. Ghandi, | 140 |
| Live as if you were to die tomorrow. Learn as if you were to live forever. | |
| Mahatma Ghandi, | 939 |
| Your children are not your children. They are the sons and daughters of Life's longing for itself. | |
| Kahlil Gibran, | 1015 |
| Victory is often a thing deferred, and rarely at the summit of courage... What is at the summit of courage, I think, is freedom. The freedom that comes with the knowledge that no earthly power can break you; that an unbroken spirit is the only thing that you cannot live without; that in the end it is the courage of conviction that moves things, that makes all change possible. | |
| Paula Giddings, quoted in Wisdom for the New Millennium edited by Helen Exley. | 1071 |
| In order to be utterly happy the only thing necessary is to refrain from comparing this moment with other moments in the past, which I often did not fully enjoy because I was comparing them with other moments of the future. | |
| Andre' Gide, | 1370 |
| The most decisive actions of our life - I mean those that are most likely to decide the whole course of our future - are, more often than not, unconsidered. | |
| Andre' Gide, | 1371 |
| Education in this country is designed by people who don't need it, for people who don't need it. | |
| Bernie Gifford, | 141 |
| I've come to the frightening conclusion that I am the decisive element in the classroom. It's my personal approach that creates the climate. It's my daily mood that makes the weather. As a teacher, I possess a tremendous power to make a child's life miserable or joyous. I can be a tool of torture or an instrument of of inspiration. I can humiliate or humor, hurt or heal. In all situations, it is MY response that decides whether a crisis will be escalated or de-escalated and a child humanized or dehumanized. | |
| Hiam Ginott, from "Bringing Light...," in Teacher and Child, Jan. 1994. | 142 |
| What radical constructivism may suggest to educators is this: the art of teaching has little to do with the traffic of knowledge, its fundamental purpose must be to foster the art of learning. | |
| Ernst von Glasersfeld, from Radical Constructivism: A Way of Knowing and Learning. | 771 |
| Of course mathematics works in physics! It is designed to discuss exactly the situation that physics confronts; namely, that there seems to be some order out there--let"s find out what it is. | |
| Andrew Gleason, quoted in More Mathematical People by D.J. Albers, G.L. Alexanderson, and C. Reid. | 712 |
| Proofs aren't there to convince you that something is true - they're there to show you why it is true. | |
| Andrew Gleason, from Proofs Without Words II | 1209 |
| For the mass of practicing scientists... the change did not matter immediately... But they were aware of something called chaos... More and more of them realized that chaos offered a fresh way to proceed with old data... chaos was the end of the reductionist program in science. | |
| James Gleick, from Chaos. | 477 |
| Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc. But the next quite natural step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of differential calculus. | |
| Kurt Godel, quoted in Mathematical Expeditions by R. Laubenbacher and D. Pengelley. | 965 |
| The set-theoretical paradoxes are hardly any more troublesome for mathematics than deceptions of the senses are for physics. | |
| Kurt Godel, quoted in Understanding the Infinite by Shaughan Lavine. | 546 |
| There are good reasons to believe that non-standard analysis, in some version or other, will be the analysis of the future. | |
| Kurt Godel, quoted in Mathematical Expeditions by R. Laubenbacher and D. Pengelley. | 964 |
| Good teaching is one-fourth preparation and three fourths pure theatre. | |
| Gail Godwin, | 887 |
| A joy shared is a joy doubled. | |
| Goethe, quoted in Listening to Nature by Joseph Cornell. | 765 |
| What man does not know,
Or has not thought of, Wanders in the night Through the labyrinth of the mind. | |
| Goethe, | 562 |
| If in the infinite you want to stride, Just walk in the finite to every side. | |
| Johann Wolfgang von Goethe, quoted in To Infinity and Beyond by Eli Maor. | 653 |
| Until one is committed, there is hesitancy, the chance to draw back...the moment one definitely commits oneself...all sort of things occur to help one that would never otherwise have occurred. | |
| Goethe, | 940 |
| Correction does much, but encouragement does more. | |
| Goethe, | 845 |
| If you treat an individual as he is, he will stay that way. But if you treat him as if he were what he could be, he will become what he could be. | |
| Goethe, | 846 |
| Art is long, life is short. | |
| Goethe, | 1440 |
| This is the highest wisdom that I own; freedom and life are earned by those alone who conquer them each day anew. | |
| Johann Wolfgang von Goethe, | 985 |
| Behavior is a mirror in which every one displays his own image. | |
| Johann Wolfgang von Goethe, | 987 |
| Anyone who can handle a needle convincingly can make us see a thread which is not there. | |
| E.H. Gombrich, Art and Illusion, 1960 | 1631 |
| The Bible isn’t a single book, it isn’t a single historical or philosophical or theological treatise. It has 66 books in it. It is a library. | |
| Peter Gomes, Rev. Peter J. Gomes Is Dead at 68; A Leading Voice Against Intolerance By Robert D. McFadden March 1, 2011, New York Times. | 1716 |
| Could it be that we spend so much time trying to make sense of the Bible, or making it conform to our set of social expectations, that we have failed to take to heart the essential content of the preaching and teaching of Jesus? | |
| Peter Gomes, from The Scandalous Gospel of Jesus, p. 23 | 1738 |
| If we are sincere in wanting to know what Jesus would do, we must risk the courage to ask what he says, what he asks, and what he demands. Only if we do so will we be able to move, however cautiously and imperfectly, from the Bible to the gospel. | |
| Peter Gomes, from The Scandalous Gospel of Jesus, p. 23 | 1742 |
| I want you to remember the high expectations and feelings of this moment. They will be very precious to you in the days to come. For it always begins well. It doesn’t always end well, but it always begins well. And you must remember how well it began, with what great hopes and expectations you gathered here. | |
| Peter Gomes, at the Investiture of Evan S. Dobelle as President of Westfield State College on 27 September, 2008. | 1777 |
| I do worry that with so much religion about, and with the ever-increasing polarization of our convictions, sooner rather than later we will discover that the problem in our culture is not religion but the religious. | |
| Peter Gomes, from The Scandalous Gospel of Jesus, p. 5 | 1713 |
| The last thing the faithful wish for is to be disturbed. Thus it is easy to favor the Bible over the gospel. | |
| Peter Gomes, from The Scandalous Gospel of Jesus, p. 19 | 1714 |
| It is for the Commonwealth and for the health of the Republic that institutions of higher learning such as this are maintained. It is the best investment that we have. And the best capital that we have is human capital. | |
| Peter Gomes, at the Investiture of Evan S. Dobelle as President of Westfield State College on 27 September, 2008. | 1781 |
| The chief product of this Commonwealth is education. Instead of a Codfish there should be a brain hanging in the House chamber. It should remind us that the chief thing that we do here is prepare bright, able minds. | |
| Peter Gomes, at the Investiture of Evan S. Dobelle as President of Westfield State College on 27 September, 2008. | 1780 |
| Henry Ward Beecher used to tell of the Free Will Methodist preacher and the Presbyterian preacher who agreed to exchange pulpits. As they met on the road, each on the way to the other's pulpit, the Presbyterian said, 'Brother, does it not give you pleasure and glory to God that before the earth itself was formed, we were destined in the mind of God to have this exchange this morning?' To which the Methodist replied, 'Well, if that is so, then I ain't going,' and he turned his horse around. | |
| Peter J. Gomes, from The Good Book: Reading the bible with Mind and Heart, p. xi. | 1796 |
| We are wed together now, you and I. | |
| Peter Gomes, at the Investiture of Evan S. Dobelle as President of Westfield State College on 27 September, 2008. | 1802 |
| What does labor want? We want more schoolhouses and less jails, more books and less arsenals, more learning and less vice, more constant work and less crime, more leisure and less greed, more justice and less revenge. In fact, more of the opportunities to cultivate our better natures, to make manhood more noble, womanhood more beautiful and childhood more happy and bright. | |
| Samuel Gompers, | 843 |
| Especially in a technological age, when airplanes can become powerful bombs, rare acts of depravity seem to overwhelm our landscape, both geographical and psychological. But the ordinary human decency of a billion tiny acts of kindness, done by millions of good people, sets a far more powerful counterweight, too often invisible for lack of comparable "news value." The trickle of one family that began on September 11, 1901, multiplied by so many million similar and "ordinary" stories, will overwhelm the evil of a few on September 11, 2001.
My native city of New York, and the whole world, suffered grievously on September 11, 2001. But Papa Joe's message of September 11, 1901, properly generalized across billions of people, will triumph through the agency of ordinary human decency. We have landed. Lady Liberty still lifts her lamp beside the golden door. And that door leads to the greatest, and largely successful, experiment in democracy ever attempted in human history, upheld by basic goodness across the broadest diversity of ethnicities, economies, geographies, languages, customs and employments that the world has ever known as a single nation. We fought our bloodiest war to keep our motto, I stress this greatly underappreciated point because our error in equating a | |
| Stephen Jay Gould, from I Have Landed. | 1474 |
| The center of human nature is rooted in ten thousand ordinary acts of kindness that define our days. | |
| Stephen Jay Gould, quoted in Wisdom for the New Millennium edited by Helen Exley. | 1069 |
| Science, in contrast [to Western religion], is based solidly on empathy. It posits a shared experience of the world, because, otherwise, how could we agree on explanations for, and verification of, natural phenomena? More deeply, it finds and celebrates in humans a capacity to learn about the world and share our experiences through reason, logic, language, music, and art. | |
| Gregg Graffin, from Anarchy Evolution: Faith, Science and Bad Religion in a World Without God (with Steve Olsen), p. 185. | 1689 |
| Juggling is sometimes called the art of controlling patterns, controlling patterns in time and space. | |
| Ron Graham, | 1384 |
| Martin [Gardner] has turned thousands of children into mathematicians, and thousands of mathematicians into children. | |
| Ronald Graham, quoted in "For Decades, Puzzling People with Mathematics" by John Tierney, 10/20/2009 New York Times. | 1298 |
| The trouble with the integers is that we have examined only the small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't get our hands on or even begin to think about in any very definite way. So maybe all the action is really inaccessible and we're just fiddling around. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions. | |
| Ronald Graham, quoted in Wonders of Numbers by Clifford A. Pickover | 1064 |
| Godel did not destroy mathematics. He inspired it. Everyone was inspired by Godel, particularly Turing. Cantor proved that you could always add infinities to infinity. Godel proved that you can always add new axioms to mathematics - and never be sure that it's possible to prove something that is true. Turing proved that there are some computer programmes that may simply never terminate. It's very exciting, when you think about it… Sometimes you just can't know if a problem has a solution or not. | |
| Alice's Grandmother, character from PopCo by Scarlett Thomas. | 1296 |
| Labor disgraces no man; unfortunately, you occasionally find men who disgrace labor. | |
| Ulysses S. Grant, | 1585 |
| To me this is in marked contrast to most mathematics books of today, which almost universally suffer from the Bourbakiist school of thought that everyone must speak the same highly technical language to appreciate what is going on (and so, those who do not know the jargon are doomed to not understand what is going on). | |
| Andrew Granville, from "Review of Notes on Fermat's Last Theorem," American Mathematical Monthly, vol. 106, no. 2, February 1999. | 1228 |
| Why do so many authors actas if mathematics has to be such a very serious business, correct only if every "i" is dotted? That people might learn more, and more quickly, by being excited, inspired, and challenged to think about the question of the day, has escaped this strangely dominant school of educational thought. | |
| Andrew Granville, from "Review of Notes on Fermat's Last Theorem," American Mathematical Monthly, vol. 106, no. 2, February 1999 | 1229 |
| The most important outcome of education is to help students to become independent of formal education. | |
| Paul E. Gray, | 143 |
| Roulette is a pleasant, relaxed, and highly comfotable way to lose your money. | |
| Jimmy the Greek, | 602 |
| Most people are unaware that around a century and a half ago a revolution took place in the field of geometry that was as scientifically profound as the Copernican revolution in astronomy and, in its impact, as philosophically important as the Darwinian theory of evolution | |
| Marvin Jay Greenberg, from Euclidean and Non-Euclidean Geometries: Development and History. | 1552 |
| Only impractical dreamers spent two thousand years wondering about proving Euclid's parallel postulate, and if they hadn't done so, there would be no spaceships exploring the galaxy today. | |
| M.J. Greenberg, from Euclidean and Non-Euclidean Geometries | 876 |
| People at war with reality cannot help those that are suffering. | |
| Rev. Georgann Greene, | 1433 |
| Spend less time at war with reality, more time alive in it. | |
| Rev. Georgann Greene, | 1432 |
| It is curious that almost all aspects of geometry relevant to the 'man on the street' are ignored by our educational systems. Geometry has been almost squeezed out of school and university syllabuses, and what little remains is rarely of any use to people who wish to apply geometric ideas in their work - engineers, scientists, architects, artists, and the like. There are two causes of this state of affairs. At high-school level it has long been traditional to use geometry as a vehicle for teaching logical reasoning and the deductive method, without much regard for the geometric content. At the research level geometry has become not more than a specialized branch of algebra and analysis. | |
| Branko Grunbaum and G.C. Shephard, from Tilings and Patterns, p. vii. | 1783 |
| The essence of mathematics is not to make simple things complicated but to make complicated things simple. | |
| S. Gudder, | 144 |
| Education is learning more than it is being taught. It's the chemistry of curiosity exposed to information. In that sense all of life is potentially school. And even I can pass that. | |
| Bob Guiccione, Jr., from Spin Magazine. | 145 |
| Unlike scientists, who observe nature with all five senses, mathematicians observe nature with the sense of imagination almost exclusively. That is, mathematicians are as specialized, and therefore as well practiced, with this sixth sense as musicians are with sound, gourmets are with tastes and smells, and photographers and filmmakers are with sights. This comparison also suggests that mathematicians are artists of the imagination just as surely as musicians, gourmets, photographers and filmmakers are of their respective sensory domains. | |
| Michael Guillen, from Bridges to Infinity. | 532 |
| A mathematicians ultimate concern is that his or her inventions be logical, not realistic. | |
| Michael Guillen, from Bridges to Infinity. | 531 |
| I aint a communist necessarily, but I sure been in the red all my life. | |
| Woody Guthrie, | 146 |
| Yes, as through this world I've wandered I've seen lots of funny men. Some will rob you with a six-gun, and some with a fountain pen. | |
| Woody Guthrie, | 1691 |
| If you play more than two chords, you're showing off. | |
| Woody Guthrie, | 1794 |
| It's round the world I've traveled; it's round the world I've roamed; but I've yet to see an outlaw drive a family from its home. | |
| Woody Guthrie, | 1795 |
| Was a great high wall there that tried to stop me. A sign was painted said: 'Private Property.' But on the backside, it didn't say nothing. That side was made for you and me. | |
| Woody Guthrie, | 1800 |
| I am out to sing songs that will prove to you that this is your world and that if it has hit you pretty hard and knocked you for a dozen loops, no matter what color, what size you are, how you are built, I am out to sing the songs that make you take pride in yourself and in your work. And the songs that I sing are made up for the most part by all sorts of folks just about like you. | |
| Woody Guthrie, | 1776 |
| There aren't enough small numbers to meet the many demands made of them. | |
| Richard K. Guy, quoted in "Tangent sequences, world records, pi, and the meaning of life..." by Ira Rosenholtz, Mathematics Magazine, Dec. 1999 | 974 |
106 quotes found and displayed.