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Home > Category Index for Science Quotations > Category Index I > Category: Invent

Invent Quotes (51 quotes)

Pour inventor il faut penser à côté.
To invent you must think aside
In Calyampudi Radhakrishna Rao, Statistics and Truth (1997), 31.
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A man who is master of himself can end a sorrow as easily as he can invent a pleasure.
In 'Dorian Gray', The Writings of Oscar Wilde: Epigrams, Phrases and Philosophies For the Use of the Young (1907), 49.
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An essential [of an inventor] is a logical mind that sees analogies. No! No! not mathematical. No man of a mathematical habit of mind ever invented anything that amounted to much. He hasn’t the imagination to do it. He sticks too close to the rules, and to the things he is mathematically sure he knows, to create anything new.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 187.
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As the nineteenth century drew to a close, scientists could reflect with satisfaction that they had pinned down most of the mysteries of the physical world: electricity, magnetism, gases, optics, acoustics, kinetics and statistical mechanics ... all had fallen into order before the. They had discovered the X ray, the cathode ray, the electron, and radioactivity, invented the ohm, the watt, the Kelvin, the joule, the amp, and the little erg.
A Short History of Nearly Everything. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 172.
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But we shall not satisfy ourselves simply with improving steam and explosive engines or inventing new batteries; we have something much better to work for, a greater task to fulfill. We have to evolve means for obtaining energy from stores which are forev
http://web.archive.org/web/20070109161311/http://www.knowprose.com/node/12961
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Chaos theory is a new theory invented by scientists panicked by the thought that the public were beginning to understand the old ones.
John Mitchinson and John Lloyd, If Ignorance Is Bliss, Why Aren't There More Happy People?: Smart Quotes for Dumb Times (2009), 273.
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Commenting on Archimedes, for whom he also had a boundless admiration, Gauss remarked that he could not understand how Archimedes failed to invent the decimal system of numeration or its equivalent (with some base other than 10). … This oversight Gauss regarded as the greatest calamity in the history of science.
In Men of Mathematics (1937), 256.
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Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best which is geometrically most simple.
In 'On the Linear Construction of Equations', Universal Arithmetic (1769), Vol. 2, 470.
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Everything that can be invented, has been invented. [A myth, attributed - almost certainly falsely - to Duell.]
A classic example of a zombie-type quote. It should be long dead, but keeps living on as a myth, impossible to extirpate. For example, it is glibly recited and attributed (as always, without a valid primary source), to a Commissioner ("Director") of U.S. Patent Office, urging President McKinley to abolish his office, in Chris Morgan and David Langford, Facts and Fallacies (1981). (Duell held the office 1898-1901.) It has a long history of being debunked, for example, see Eber Jeffery, Journal of the Patent Office Society (July 1940), and Samuel Sass, 'A Patently False Patent Myth', Skeptical Inquirer (Spring 1989), 13, 310-313.
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His Majesty has, with great skill, constructed a cart, containing a corn mill, which is worked by the motion of the carriage. He has also contrived a carriage of such a magnitude as to contain several apartments, with a hot bath; and it is drawn by a single elephant. This movable bath is extremely useful, and refreshing on a journey. … He has also invented several hydraulic machines, which are worked by oxen. The pulleys and wheels of some of them are so adjusted that a single ox will at once draw water out of two wells, and at the same time turn a millstone.
From Ain-i-Akbery (c.1590). As translated from the original Persian, by Francis Gladwin in 'Akbar’s Conduct and Administrative Rules', 'Of Machines', Ayeen Akbery: Or, The Institutes of the Emperor Akber (1783), Vol. 1, 284. Note: Akbar (Akber) was a great ruler and enlightened statesman.
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I believe no woman could have invented calculus.
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I believe that the useful methods of mathematics are easily to be learned by quite young persons, just as languages are easily learned in youth. What a wondrous philosophy and history underlie the use of almost every word in every language—yet the child learns to use the word unconsciously. No doubt when such a word was first invented it was studied over and lectured upon, just as one might lecture now upon the idea of a rate, or the use of Cartesian co-ordinates, and we may depend upon it that children of the future will use the idea of the calculus, and use squared paper as readily as they now cipher. … When Egyptian and Chaldean philosophers spent years in difficult calculations, which would now be thought easy by young children, doubtless they had the same notions of the depth of their knowledge that Sir William Thomson might now have of his. How is it, then, that Thomson gained his immense knowledge in the time taken by a Chaldean philosopher to acquire a simple knowledge of arithmetic? The reason is plain. Thomson, when a child, was taught in a few years more than all that was known three thousand years ago of the properties of numbers. When it is found essential to a boy’s future that machinery should be given to his brain, it is given to him; he is taught to use it, and his bright memory makes the use of it a second nature to him; but it is not till after-life that he makes a close investigation of what there actually is in his brain which has enabled him to do so much. It is taken because the child has much faith. In after years he will accept nothing without careful consideration. The machinery given to the brain of children is getting more and more complicated as time goes on; but there is really no reason why it should not be taken in as early, and used as readily, as were the axioms of childish education in ancient Chaldea.
In Teaching of Mathematics (1902), 14.
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I find out what the world needs, then I proceed to invent. My main purpose in life is to make money so that I can afford to go on creating more inventions.
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I never pick up an item without thinking of how I might improve it. I never perfected an invention that I did not think about in terms of the service it might give others. I want to save and advance human life, not destroy it. I am proud of the fact that I never invented weapons to kill. The dove is my emblem.
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I should like to draw attention to the inexhaustible variety of the problems and exercises which it [mathematics] furnishes; these may be graduated to precisely the amount of attainment which may be possessed, while yet retaining an interest and value. It seems to me that no other branch of study at all compares with mathematics in this. When we propose a deduction to a beginner we give him an exercise in many cases that would have been admired in the vigorous days of Greek geometry. Although grammatical exercises are well suited to insure the great benefits connected with the study of languages, yet these exercises seem to me stiff and artificial in comparison with the problems of mathematics. It is not absurd to maintain that Euclid and Apollonius would have regarded with interest many of the elegant deductions which are invented for the use of our students in geometry; but it seems scarcely conceivable that the great masters in any other line of study could condescend to give a moment’s attention to the elementary books of the beginner.
In Conflict of Studies (1873), 10-11.
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If you ask a person, “What were you thinking?” you may get an answer that is richer and more revealing of the human condition than any stream of thoughts a novelist could invent. I try to see through people’s faces into their minds and listen through their words into their lives, and what I find there is beyond imagining.
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In any conceivable method ever invented by man, an automaton which produces an object by copying a pattern, will go first from the pattern to a description to the object. It first abstracts what the thing is like, and then carries it out. It’s therefore simpler not to extract from a real object its definition, but to start from the definition.
From lecture series on self-replicating machines at the University of Illinois, Lecture 5 (Dec 1949), 'Re-evaluation of the Problems of Complicated Automata—Problems of Hierarchy and Evolution', Theory of Self-Reproducing Automata (1966).
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In some remote corner of the universe, poured out and glittering in innumerable solar systems, there once was a star on which clever animals invented knowledge. That was the haughtiest and most mendacious minute of ‘world history’—yet only a minute. After nature had drawn a few breaths the star grew cold, and the clever animals had to die. ... There have been eternities when [human intellect] did not exist; and when it is done for again, nothing will have happened.
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In the summer of 1937, … I told Banach about an expression Johnny [von Neumann] had once used in conversation with me in Princeton before stating some non-Jewish mathematician’s result, “Die Goim haben den folgendenSatzbewiesen” (The goys have proved the following theorem). Banach, who was pure goy, thought it was one of the funniest sayings he had ever heard. He was enchanted by its implication that if the goys could do it, Johnny and I ought to be able to do it better. Johnny did not invent this joke, but he liked it and we started using it.
In Adventures of a Mathematician (1976, 1991), 107. Von Neumann, who was raised in Budapest by a Jewish family, knew the Yiddish word “goy” was equivalent to “gentile” or a non-Jew. Stefan Banach, a Polish mathematician, was raised in a Catholic family, hence “pure goy”. Ulam thus gives us the saying so often elsewhere seen attributed to von Neumann without the context: “The goys have proved the following theorem.” It is seen anecdotally as stated by von Neumann to begin a classroom lecture.
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Inventing is the intellectual bicycle that he rides each day.
Reported without quotation marks, describing James West, by Timothy L. O’Brien, in 'Not Invented here: Are U.S. Innovators Losing Their Competitive Edge?', New York Times (13 Nov 2005), B6.
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It frequently happens that two persons, reasoning right on a mechanical subject, think alike and invent the same thing without any communication with each other.
As quoted by Coleman Sellers, Jr., in his Lecture (20 Nov 1885) delivered at the Franklin Institute. Printed in Coleman Sellers, Jr., 'Oliver Evans and his Inventions', Journal of the Franklin Institute (Jul 1886), 122, No. 1, 15.
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It is quite possible that mathematics was invented in the ancient Middle East to keep track of tax receipts and grain stores. How odd that out of this should come a subtle scientific language that can effectively describe and predict the most arcane aspects of the Universe.
Epigraph in Isaac Asimov’s Book of Science and Nature Quotations (1988), 265.
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It was necessary to invent everything. Dynamos, regulators, meters, switches, fuses, fixtures, underground conductors with their necessary connecting boxes, and a host of other detail parts, even down to insulating tape.
Concerning the electrical system to power his customers’ electric lights.
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It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.
In Presidential Address British Association for the Advancement of Science, Section A., (1890), Nature, 42, 466.
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Junior high school seemed like a fine idea when we invented it but it turned out to be an invention of the devil. We’re catching our boys in a net in which they’re socially unprepared. We put them in junior high school with girls who are two years ahead of them. There isn’t a thing they should have to do with girls at this age except growl at them.
As quoted in Frances Glennon, 'Student and Teacher of Human Ways', Life (14 Sep 1959), 147.
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Last night I invented a new pleasure, and as I was giving it the first trial an angel and a devil came rushing toward my house. They met at my door and fought with each other over my newly created pleasure; the one crying, “It is a sin!” - the other, “It is a virtue!”
In Kahlil Gibran: The Collected Works (207), 21.
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Learning how to access a continuity of common sense can be one of your most efficient accomplishments in this decade. Can you imagine common sense surpassing science and technology in the quest to unravel the human stress mess? In time, society will have a new measure for confirming truth. It’s inside the people-not at the mercy of current scientific methodology. Let scientists facilitate discovery, but not invent your inner truth.
…...
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Let me arrest thy thoughts; wonder with me, why plowing, building, ruling and the rest, or most of those arts, whence our lives are blest, by cursed Cain’s race invented be, and blest Seth vexed us with Astronomy.
…...
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Metals are the great agents by which we can examine the recesses of nature; and their uses are so multiplied, that they have become of the greatest importance in every occupation of life. They are the instruments of all our improvements, of civilization itself, and are even subservient to the progress of the human mind towards perfection. They differ so much from each other, that nature seems to have had in view all the necessities of man, in order that she might suit every possible purpose his ingenuity can invent or his wants require.
From 'Artist and Mechanic', The artist & Tradesman’s Guide: embracing some leading facts & principles of science, and a variety of matter adapted to the wants of the artist, mechanic, manufacturer, and mercantile community (1827), 16.
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Of all the sciences that pertain to reason, Metaphysics and Geometry are those in which imagination plays the greatest part. … Imagination acts no less in a geometer who creates than in a poet who invents. It is true that they operate differently on their object. The first shears it down and analyzes it, the second puts it together and embellishes it. … Of all the great men of antiquity, Archimedes is perhaps the one who most deserves to be placed beside Homer.
From the original French: “La Métaphysique & la Géométrie sont de toutes les Sciences qui appartiennent à la raison, celles où l’imagination à le plus de part. … L’imagination dans un Géometre qui crée, n’agit pas moins que dans un Poëte qui invente. Il est vrai qu’ils operent différemment sur leur objet; le premier le dépouille & l’analyse, le second le compose & l’embellit. … De tous les grands hommes de l’antiquité, Archimede est peut-être celui qui mérite le plus d’être placé à côté d’Homere.” In Discours Preliminaire de L'Encyclopedie (1751), xvi. As translated by Richard N. Schwab and Walter E. Rex, Preliminary Discourse to the Encyclopedia of Diderot (1963, 1995), xxxvi. A footnote states “Note that ‘geometer’ in d’Alembert’s definition is a term that includes all mathematicians and is not strictly limited to practitioners of geometry alone.” Also seen in a variant extract and translation: “Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this …. The imagination in a mathematician who creates makes no less difference than in a poet who invents…. Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer.” This latter translation may be from The Plan of the French Encyclopædia: Or Universal Dictionary of Arts, Sciences, Trades and Manufactures (1751). Webmaster has not yet been able to check for a verified citation for this translation. Can you help?
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One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.
In The Works of Archimedes (1897), Preface, vi.
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Pure mathematics and physics are becoming ever more closely connected, though their methods remain different. One may describe the situation by saying that the mathematician plays a game in which he himself invents the rules while the while the physicist plays a game in which the rules are provided by Nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen. … Possibly, the two subjects will ultimately unify, every branch of pure mathematics then having its physical application, its importance in physics being proportional to its interest in mathematics.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 124.
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Pure mathematics is much more than an armoury of tools and techniques for the applied mathematician. On the other hand, the pure mathematician has ever been grateful to applied mathematics for stimulus and inspiration. From the vibrations of the violin string they have drawn enchanting harmonies of Fourier Series, and to study the triode valve they have invented a whole theory of non-linear oscillations.
In 100 Years of Mathematics: a Personal Viewpoint (1981), 3.
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Some of my youthful readers are developing wonderful imaginations. This pleases me. Imagination has brought mankind through the Dark Ages to its present state of civilization. Imagination led Columbus to discover America. Imagination led Franklin to discover electricity. Imagination has given us the steam engine, the telephone, the talking-machine and the automobile, for these things had to be dreamed of before they became realities. So I believe that dreams—day dreams, you know, with your eyes wide open and your brain-machinery whizzing—are likely to lead to the betterment of the world. The imaginative child will become the imaginative man or woman most apt to create, to invent, and therefore to foster civilization. A prominent educator tells me that fairy tales are of untold value in developing imagination in the young. I believe it.
Opening paragraph of preface, 'To My Readers', The Lost Princess of Oz (1917), 13.
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Someone poring over the old files in the United States Patent Office at Washington the other day found a letter written in 1833 that illustrates the limitations of the human imagination. It was from an old employee of the Patent Office, offering his resignation to the head of the department His reason was that as everything inventable had been invented the Patent Office would soon be discontinued and there would be no further need of his services or the services of any of his fellow clerks. He, therefore, decided to leave before the blow fell.
Magazine
Written jokingly, to contrast with the burgeoning of American inventions in the new century. In 'Nothing More to Invent?', Scientific American (16 Oct 1915), 334. Compare that idea, expressed in 1915, with the classic myth still in endless recirculation today, “Everything that can be invented, has been invented,” for example, in Chris Morgan and David Langford, Facts and Fallacies (1981), on the Charles Duell Quotations page on this website, which includes references debunking the myth.
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Sometimes I wonder whether there is any such thing as biology. The word was invented rather late—in 1809—and other words like botany, zoology, physiology, anatomy, have much longer histories and in general cover more coherent and unified subject matters. … I would like to see the words removed from dictionaries and college catalogues. I think they do more harm than good because they separate things that should not be separated…
In The Forest and the Sea (1960), 6-7.
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Symbolism is useful because it makes things difficult. Now in the beginning everything is self-evident, and it is hard to see whether one self-evident proposition follows from another or not. Obviousness is always the enemy to correctness. Hence we must invent a new and difficult symbolism in which nothing is obvious. … Thus the whole of Arithmetic and Algebra has been shown to require three indefinable notions and five indemonstrable propositions.
In International Monthly (1901), 4, 85-86.
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The distinctive Western character begins with the Greeks, who invented the habit of deductive reasoning and the science of geometry.
In 'Western Civilization', collected in In Praise of Idleness and Other Essays (1935), 161.
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The importance of a result is largely relative, is judged differently by different men, and changes with the times and circumstances. It has often happened that great importance has been attached to a problem merely on account of the difficulties which it presented; and indeed if for its solution it has been necessary to invent new methods, noteworthy artifices, etc., the science has gained more perhaps through these than through the final result. In general we may call important all investigations relating to things which in themselves are important; all those which have a large degree of generality, or which unite under a single point of view subjects apparently distinct, simplifying and elucidating them; all those which lead to results that promise to be the source of numerous consequences; etc.
From 'On Some Recent Tendencies in Geometric Investigations', Rivista di Matematica (1891), 44. In Bulletin American Mathematical Society (1904), 444.
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The most technologically efficient machine that man has invented is the book.
Quoted, without citation as epigraph in Claus Grupen, Astroparticle Physics (2005), ix. Need primary source. Can you help?
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The only way to get rid of the [football] combats of gorillas which now bring millions to the colleges will be to invent some imbecility which brings in even more. To that enterprise, I regret to have to report, I find myself unequal.
From American Mercury (Jun 1931). Collected in A Mencken Chrestomathy (1949, 1956), 372.
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The radical invents the views. When he has worn them out, the conservative adopts them.
In Albert Bigelow Paine (ed.), Mark Twain's Notebook (1935, 1971), Chap. 31, 344, (1898 entry).
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The significant thing about the Darbys and coke-iron is not that the first Abraham Darby “invented” a new process but that five generations of the Darby connection were able to perfect it and develop most of its applications.
In Essays on Culture Change (2003), Vol. 2, 200.
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There is a noble vision of the great Castle of Mathematics, towering somewhere in the Platonic World of Ideas, which we humbly and devotedly discover (rather than invent). The greatest mathematicians manage to grasp outlines of the Grand Design, but even those to whom only a pattern on a small kitchen tile is revealed, can be blissfully happy. … Mathematics is a proto-text whose existence is only postulated but which nevertheless underlies all corrupted and fragmentary copies we are bound to deal with. The identity of the writer of this proto-text (or of the builder of the Castle) is anybody’s guess. …
In 'Mathematical Knowledge: Internal, Social, and Cultural Aspects', Mathematics As Metaphor: Selected Essays (2007), 4.
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This [the fact that the pursuit of mathematics brings into harmonious action all the faculties of the human mind] accounts for the extraordinary longevity of all the greatest masters of the Analytic art, the Dii Majores of the mathematical Pantheon. Leibnitz lived to the age of 70; Euler to 76; Lagrange to 77; Laplace to 78; Gauss to 78; Plato, the supposed inventor of the conic sections, who made mathematics his study and delight, who called them the handles or aids to philosophy, the medicine of the soul, and is said never to have let a day go by without inventing some new theorems, lived to 82; Newton, the crown and glory of his race, to 85; Archimedes, the nearest akin, probably, to Newton in genius, was 75, and might have lived on to be 100, for aught we can guess to the contrary, when he was slain by the impatient and ill mannered sergeant, sent to bring him before the Roman general, in the full vigour of his faculties, and in the very act of working out a problem; Pythagoras, in whose school, I believe, the word mathematician (used, however, in a somewhat wider than its present sense) originated, the second founder of geometry, the inventor of the matchless theorem which goes by his name, the pre-cognizer of the undoubtedly mis-called Copernican theory, the discoverer of the regular solids and the musical canon who stands at the very apex of this pyramid of fame, (if we may credit the tradition) after spending 22 years studying in Egypt, and 12 in Babylon, opened school when 56 or 57 years old in Magna Græcia, married a young wife when past 60, and died, carrying on his work with energy unspent to the last, at the age of 99. The mathematician lives long and lives young; the wings of his soul do not early drop off, nor do its pores become clogged with the earthy particles blown from the dusty highways of vulgar life.
In Presidential Address to the British Association, Collected Mathematical Papers, Vol. 2 (1908), 658.
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To learn is to incur surprise—I mean really learning, not just refreshing our memory or adding a new fact. And to invent is to bestow surprise—I mean really inventing, not just innovating what others have done.
In How Invention Begins: Echoes of Old Voices in the Rise of New Machines (2006), 217.
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Two extreme views have always been held as to the use of mathematics. To some, mathematics is only measuring and calculating instruments, and their interest ceases as soon as discussions arise which cannot benefit those who use the instruments for the purposes of application in mechanics, astronomy, physics, statistics, and other sciences. At the other extreme we have those who are animated exclusively by the love of pure science. To them pure mathematics, with the theory of numbers at the head, is the only real and genuine science, and the applications have only an interest in so far as they contain or suggest problems in pure mathematics.
Of the two greatest mathematicians of modern tunes, Newton and Gauss, the former can be considered as a representative of the first, the latter of the second class; neither of them was exclusively so, and Newton’s inventions in the science of pure mathematics were probably equal to Gauss’s work in applied mathematics. Newton’s reluctance to publish the method of fluxions invented and used by him may perhaps be attributed to the fact that he was not satisfied with the logical foundations of the Calculus; and Gauss is known to have abandoned his electro-dynamic speculations, as he could not find a satisfying physical basis. …
Newton’s greatest work, the Principia, laid the foundation of mathematical physics; Gauss’s greatest work, the Disquisitiones Arithmeticae, that of higher arithmetic as distinguished from algebra. Both works, written in the synthetic style of the ancients, are difficult, if not deterrent, in their form, neither of them leading the reader by easy steps to the results. It took twenty or more years before either of these works received due recognition; neither found favour at once before that great tribunal of mathematical thought, the Paris Academy of Sciences. …
The country of Newton is still pre-eminent for its culture of mathematical physics, that of Gauss for the most abstract work in mathematics.
In History of European Thought in the Nineteenth Century (1903), 630.
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We have become a people unable to comprehend the technology we invent.
Report, Integrity in the College Curriculum (Feb 1985).
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What is mathematics? What is it for? What are mathematicians doing nowadays? Wasn't it all finished long ago? How many new numbers can you invent anyway? Is today’s mathematics just a matter of huge calculations, with the mathematician as a kind of zookeeper, making sure the precious computers are fed and watered? If it’s not, what is it other than the incomprehensible outpourings of superpowered brainboxes with their heads in the clouds and their feet dangling from the lofty balconies of their ivory towers?
Mathematics is all of these, and none. Mostly, it’s just different. It’s not what you expect it to be, you turn your back for a moment and it's changed. It's certainly not just a fixed body of knowledge, its growth is not confined to inventing new numbers, and its hidden tendrils pervade every aspect of modern life.
Opening paragraphs of 'Preface', From Here to Infinity (1996), vii.
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When all the discoveries [relating to the necessities and some to the pastimes of life] were fully developed, the sciences which relate neither to pleasure nor yet to the necessities of life were invented, and first in those places where men had leisure. Thus the mathematical sciences originated in the neighborhood of Egypt, because there the priestly class was allowed leisure.
Aristotle
In Metaphysics, 1-981b, as translated by Hugh Tredennick (1933). Also seen translated as “Now that practical skills have developed enough to provide adequately for material needs, one of these sciences which are not devoted to utilitarian ends [mathematics] has been able to arise in Egypt, the priestly caste there having the leisure necessary for disinterested research.”
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When I needed an apparatus to help me linger below the surface of the sea, Émile Gagnan and I used well-known scientific principles about compressed gases to invent the Aqualung; we applied science. The Aqualung is only a tool. The point of the Aqualung—of the computer, the CAT scan, the vaccine, radar, the rocket, the bomb, and all other applied science—is utility.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 181.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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Carl Gauss
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- 90 -
Antoine Lavoisier
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Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
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Andre Ampere
Winston Churchill
- 80 -
John Locke
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Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
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Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
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Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
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Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
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- 30 -
Andreas Vesalius
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- 20 -
Carl Sagan
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- 10 -
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