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Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
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Return Quotes (55 quotes)


...Furthermore, an inducement must be offered to those who are engaged in the industrial exploitation of natural sources of power, as waterfalls, by guaranteeing greater returns on the capital invested than they can secure by local development of the prop
http://web.archive.org/web/20070109161311/http://www.knowprose.com/node/12961
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All parts of the material universe are in constant motion and though some of the changes may appear to be cyclical, nothing ever exactly returns, so far as human experience extends, to precisely the same condition.
Address (Jul 1874) at the grave of Joseph Priestley, in Joseph Henry and Arthur P. Molella, et al. (eds.), A Scientist in American Life: Essays and Lectures of Joseph Henry (1980), 119.
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An involuntary return to the point of departure is, without doubt, the most disturbing of all journeys.
…...
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Any country that wants to make full use of all its potential scientists and technologists … must not expect to get the women quite so simply as it gets the men. It seems to me that marriage and motherhood are at least as socially important as military service. Government regulations are framed to ensure (in the United Kingdom) that a man returning to work from military service is not penalized by his absence. Is it utopian, then, to suggest that any country that really wants a woman to return to a scientific career when her children no longer need her physical presence should make special arrangements to encourage her to do so?
In Impact of Science on Society (1970), 20 58. Commenting how for men who went to war, their jobs were held for them pending their return.
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Biological evolution is a system of constant divergence without subsequent joining of branches. Lineages, once distinct, are separate forever. In human history, transmission across lineages is, perhaps, the major source of cultural change. Europeans learned about corn and potatoes from Native Americans and gave them smallpox in return.
…...
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Euler was a believer in God, downright and straightforward. The following story is told by Thiebault, in his Souvenirs de vingt ans de séjour à Berlin, … Thiebault says that he has no personal knowledge of the truth of the story, but that it was believed throughout the whole of the north of Europe. Diderot paid a visit to the Russian Court at the invitation of the Empress. He conversed very freely, and gave the younger members of the Court circle a good deal of lively atheism. The Empress was much amused, but some of her counsellors suggested that it might be desirable to check these expositions of doctrine. The Empress did not like to put a direct muzzle on her guest’s tongue, so the following plot was contrived. Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of God, and would give it him before all the Court, if he desired to hear it. Diderot gladly consented: though the name of the mathematician is not given, it was Euler. He advanced toward Diderot, and said gravely, and in a tone of perfect conviction:
Monsieur, (a + bn) / n = x, donc Dieu existe; repondez!

Diderot, to whom algebra was Hebrew, was embarrassed and disconcerted; while peals of laughter rose on all sides. He asked permission to return to France at once, which was granted.
In Budget of Paradoxes (1878), 251. [The declaration in French expresses, “therefore God exists; please answer!” This Euler-Diderot anecdote, as embellished by De Morgan, is generally regarded as entirely fictional. Diderot before he became an encyclopedist was an accomplished mathematician and fully capable of recognizing—and responding to—the absurdity of an algebraic expression in proving the existence of God. See B.H. Brown, 'The Euler-Diderot Anecdote', The American Mathematical Monthly (May 1942), 49, No. 5, 392-303. —Webmaster.]
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Every mathematical book that is worth reading must be read “backwards and forwards”, if I may use the expression. I would modify Lagrange’s advice a little and say, “Go on, but often return to strengthen your faith.” When you come on a hard or dreary passage, pass it over; and come back to it after you have seen its importance or found the need for it further on.
In Algebra, Part 2 (1889), Preface, viii.
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Few people doubt that the Apollo missions to the Moon as well as the precursory Mercury and Gemini missions not only had a valuable role for the United States in its Cold War with the Soviet Union but also lifted the spirits of humankind. In addition, the returned samples of lunar surface material fueled important scientific discoveries.
In 'Is Human Spaceflight Obsolete?', Issues in Science and Technology (Summer 2004).
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Humanity is about to learn that a lunatic (touched by the moon) is not a crazy man but one so sane, well-informed, well-coordinated, self-disciplined, cooperative and fearless as to be the first earthian human to have been ferried to a physical landing upon the moon, and thereafter to have been returned safely to reboard his mother space vehicle earth.
In 'Reactions to Man’s Landing on the Moon Show Broad Variations in Opinions', The New York Times (21 Jul 1969), 6.
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I stand almost with the others. They believe the world was made for man, I believe it likely that it was made for man; they think there is proof, astronomical mainly, that it was made for man, I think there is evidence only, not proof, that it was made for him. It is too early, yet, to arrange the verdict, the returns are not all in. When they are all in, I think that they will show that the world was made for man; but we must not hurry, we must patiently wait till they are all in.
Attributed.
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I want to get back again from Chemistry to Physics as soon as I can. The second-rate men seem to know their place so much better.
R. J. Strutt, John William Strutt, Third Baron Rayleigh (1924), 222.
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I would request that my body in death be buried, not cremated so that the energy content contained within in gets returned to the earth, so that flora and fauna can dine upon it just as I’ve dined upon flora and fauna throughout my life.
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In 1946 [we visited] a rock called Le Veyron, around which sea life swarmed … an undersea paradise.… About thirty years later I returned … to the same depth, to the same caves, at the same time of year. The grotto was empty. Not one single fish lived among the rocks. The verdant gardens were gone.…
When I saw Le Veyron, I believed that the sea’s most monstrous force doesn’t live in Loch Ness. It lives in us.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 40-41.
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It must happen that in some cases the author is not understood, or is very imperfectly understood; and the question is what is to be done. After giving a reasonable amount of attention to the passage, let the student pass on, reserving the obscurity for future efforts. … The natural tendency of solitary students, I believe, is not to hurry away prematurely from a hard passage, but to hang far too long over it; the just pride that does not like to acknowledge defeat, and the strong will that cannot endure to be thwarted, both urge to a continuance of effort even when success seems hopeless. It is only by experience we gain the conviction that when the mind is thoroughly fatigued it has neither the power to continue with advantage its course in .an assigned direction, nor elasticity to strike out a new path; but that, on the other hand, after being withdrawn for a time from the pursuit, it may return and gain the desired end.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 68.
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It would be rash to say that nothing remains for discovery or improvement even in elementary mathematics, but it may be safely asserted that the ground has been so long and so thoroughly explored as to hold out little hope of profitable return for a casual adventurer.
In 'Private Study of Mathematics', Conflict of Studies and other Essays (1873), 73.
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Just go on ... and faith will soon return.
[To a friend hesitant with respect to infinitestimals].
As expressed in P. J. Davis and R. Hersh, The Mathematical Experience (1981, 1995), 277.
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Men always fool themselves when they give up experience for systems born of the imagination. Man is the work of nature, he exists in nature, he is subject to its laws, he can not break free, he can not leave even in thought; it is in vain that his spirit wants to soar beyond the bounds of the visible world, he is always forced to return.
Opening statement of first chapter of Système de la Nature (1770), Vol. 1, 1. Translation by Webmaster using Google Translate. From the original French, “Les hommes se tromperont toujours, quand ils abandonneront l'expérience pour des systèmes enfantés par l’imagination. L’homme est l’ouvrage de la nature, il existe dans la nature, il est soumis à ses lois, il ne peut s’en affranchir, il ne peut même par la pensée en sortir; c’est en vain que son esprit veut s’élancer au delà des bornes du monde visible, il est toujours forcé d’y rentrer.” In the English edition (1820-21), Samuel Wilkinson gives this as “Man has always deceived himself when he abandoned experience to follow imaginary systems.—He is the work of nature.—He exists in Nature.—He is submitted to the laws of Nature.—He cannot deliver himself from them:—cannot step beyond them even in thought. It is in vain his mind would spring forward beyond the visible world: direful and imperious necessity ever compels his return.”
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Misuse of reason might yet return the world to pre-technological night; plenty of religious zealots hunger for just such a result, and are happy to use the latest technology to effect it.
The Heart of Things: Applying Philosophy to the 21st Century (2006).
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Most manufacturers take resources out of the ground and convert them to products that are designed to be thrown away or incinerated within months. We call these “cradle to grave” product flows. Our answer to that is “cradle to cradle” design. Everything is reused—either returned to the soil as nontoxic “biological nutrients” that will biodegrade safely, or returned to industry as “technical nutrients” that can be infinitely recycled.
In interview article, 'Designing For The Future', Newsweek (15 May 2005).
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Newton lectured now and then to the few students who chose to hear him; and it is recorded that very frequently he came to the lecture-room and found it empty. On such occasions he would remain fifteen minutes, and then, if no one came, return to his apartments.
In 'Sir Isaac Newton', People’s Book of Biography: Or, Short Lives of the Most Interesting Persons of All Ages and Countries (1868), 250.
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Not marble graven with public records, whereby breath and life return to goodly heroes after death.
Horace
In Ode 8, 'In Praise of Poesy', Horace, The Odes and Epodes (1921), 315.
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On Tuesday evening at Museum, at a ball in the gardens. The night was chill, I dropped too suddenly from Differential Calculus into ladies’ society, and could not give myself freely to the change. After an hour’s attempt so to do, I returned, cursing the mode of life I was pursuing; next morning I had already shaken hands, however, with Diff. Calculus, and forgot the ladies….
From his diary for 10 Aug 1851, as quoted in J. Helen Gardner and Robin J. Wilson, 'Thomas Archer Hirst—Mathematician Xtravagant II: Student Days in Germany', The American Mathematical Monthly (Jun-Jul 1993), 6, No. 100, 534.
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Our federal income tax law defines the tax y to be paid in terms of the income x; it does so in a clumsy enough way by pasting several linear functions together, each valid in another interval or bracket of income. An archaeologist who, five thousand years from now, shall unearth some of our income tax returns together with relics of engineering works and mathematical books, will probably date them a couple of centuries earlier, certainly before Galileo and Vieta.
From Address (1940), given at the Bicentennial Conference at the University of Pennsylvania, 'The Mathematical Way of Thinking'. Collected in Hermann Weyl and Peter Pesic (ed.), Levels of Infinity: Selected Writings on Mathematics and Philosophy (2012), 67.
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Relativity
There was a young lady named Bright,
Whose speed was far faster than light;
She set out one day
In a relative way,
And returned on the previous night.
Published without attribution in Punch (19 Dec 1923), 165, 591. He was later identified as the author, based his claim to have written it, in a letter to The Observer (1937).
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Returning now to the Malay Archipelago, we find that all the wide expanse of sea which divides Java, Sumatra, and Borneo from each other, and from Malacca and Siam, is so shallow that ships can anchor in any part of it, since it rarely exceeds forty fathoms in depth; and if we go as far as the line of a hundred fathoms, we shall include the Philippine Islands and Bali, east of Java. If, therefore, these islands have been separated from each other and the continent by subsidence of the intervening tracts of land, we should conclude that the separation has been comparatively recent, since the depth to which the land has subsided is so small. It is also to be remarked that the great chain of active volcanoes in Sumatra and Java furnishes us with a sufficient cause for such subsidence, since the enormous masses of matter they have thrown out would take away the foundations of the surrounding district; and this may be the true explanation of the often-noticed fact that volcanoes and volcanic chains are always near the sea. The subsidence they produce around them will, in time, make a sea, if one does not already exist.
Malay Archipelago
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Returning to the moon is an important step for our space program. Establishing an extended human presence on the moon could vastly reduce the costs of further space exploration, making possible ever more ambitious missions. Lifting heavy spacecraft and fuel out of the Earth’s gravity is expensive. Spacecraft assembled and provisioned on the moon could escape its far lower gravity using far less energy, and thus, far less cost. Also, the moon is home to abundant resources. Its soil contains raw materials that might be harvested and processed into rocket fuel or breathable air. We can use our time on the moon to develop and test new approaches and technologies and systems that will allow us to function in other, more challenging environments. The moon is a logical step toward further progress and achievement.
Speech, NASA Headquarters (14 Jan 2004). In Office of the Federal Register (U.S.) Staff (eds.), Public Papers of the Presidents of the United States, George W. Bush (2007), 58.
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The bones of Descartes were returned to France (all except those of the right hand, which were retained by the French Treasurer-General as a souvenir for his skill in engineering the transaction) and were re-entombed in what is now the Pantheon. There was to have been a public oration, but this was hastily forbidden by order of the crown, as the doctrines of Descartes were deemed to be still too hot for handling before the people.
In Men of Mathematics (1937), 51-52. The remains of Descartes were returned to his native France, seventeen years after he died in Stockholm, Sweden.
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The brain is waking and with it the mind is returning. It is as if the Milky Way entered upon some cosmic dance. Swiftly the head-mass becomes an enchanted loom where millions of flashing shuttles weave a dissolving pattern, always a meaningful pattern though never an abiding one.
Man on His Nature (1940), 225.
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The crew of the shuttle Columbia did not return safely to Earth; yet we can pray that all are safely home.
Address to the Nation on the Space Shuttle Columbia tragedy, from the Cabinet Room (1 Feb 2003). In William J. Federer, A Treasury of Presidential Quotations (2004), 438.
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The Dark Ages may return—the Stone Age may return on the gleaming wings of Science; and what might now shower immeasureable material blessings upon mankind may even bring about its total destruction. Beware! I say. Time may be short.
Referring to the discovery of atomic energy.
“Iron Curtain” speech at Fulton, Missouri (5 Mar 1946). Maxims and Reflections (1947), 164.
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The earth holds a silver treasure, cupped between ocean bed and tenting sky. Forever the heavens spend it, in the showers that refresh our temperate lands, the torrents that sluice the tropics. Every suckling root absorbs it, the very soil drains it down; the rivers run unceasing to the sea, the mountains yield it endlessly… Yet none is lost; in vast convection our water is returned, from soil to sky, and sky to soil, and back gain, to fall as pure as blessing. There was never less; there could never be more. A mighty mercy on which life depends, for all its glittering shifts, water is constant.
In A Cup of Sky (1950), 41.
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The edge of the sea is a strange and beautiful place. All through the long history of Earth it has been an area of unrest where waves have broken heavily against the land, where the tides have pressed forward over the continents, receded, and then returned. For no two suc-cessive days is the shore line precisely the same. Not only do the tides advance and retreat in their eternal rhythms, but the level of the sea itself is never at rest. It rises or falls as the glaciers melt or grow, as the floor of the deep ocean basins shifts under its increasing load of sediments, or as the Earth’s crust along the continental margins warps up or down in adjustment to strain and tension. Today a little more land may belong to the sea, tomorrow a little less. Always the edge of the sea remains an elusive and indefinable boundary.
The Edge of the Sea
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The explosive component in the contemporary scene is not the clamor of the masses but the self-righteous claims of a multitude of graduates from schools and universities. This army of scribes is clamoring for a society in which planning, regulation, and supervision are paramount and the prerogative of the educated. They hanker for the scribe’s golden age, for a return to something like the scribe-dominated societies of ancient Egypt, China, and Europe of the Middle Ages. There is little doubt that the present trend in the new and renovated countries toward social regimentation stems partly from the need to create adequate employment for a large number of scribes. And since the tempo of the production of the literate is continually increasing, the prospect is of ever-swelling bureaucracies.
In 'Scribe, Writer, and Rebel', The Ordeal of Change (1963), 109.
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The future of humanity is uncertain, even in the most prosperous countries, and the quality of life deteriorates; and yet I believe that what is being discovered about the infinitely large and the infinitely small is sufficient to absolve this end of the century and millennium. What a very few are acquiring in knowledge of the physical world will perhaps cause this period not to be judged as a pure return to barbarism.
In 'News from the Sky', Other People’s Trades (1989), 23-24.
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The law of diminishing returns means that even the most beneficial principle will become harmful if carried far enough.
'Penetrating the Rhetoric', The Vision of the Anointed (1996), 102.
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The powers which tend to preserve, and those which tend to change the condition of the earth's surface, are never in equilibrio; the latter are, in all cases, the most powerful, and, in respect of the former, are like living in comparison of dead forces. Hence the law of decay is one which suffers no exception: The elements of all bodies were once loose and unconnected, and to the same state nature has appointed that they should all return... TIME performs the office of integrating the infinitesimal parts of which this progression is made up; it collects them into one sum, and produces from them an amount greater than any that can be assigned.
Illustrations of the Huttonian Theory of the Earth (1802), 116-7.
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The search for extraterrestrial intelligence (SETI, to us insiders) has so far only proved that no matter what you beam up—the Pythagorean theorem, pictures of attractive nude people, etc.—the big 800 number in the sky does not return calls.
From essay 'First Person Secular: Blocking the Gates to Heaven', Mother Jones Magazine (Jun 1986), 48. Collected in The Worst Years of our Lives: Irreverent Notes from a Decade of Greed (1995), 267.
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The various branches of knowledge always tend as a whole to stray away from life, and return thither only by a roundabout way.
In The Maxims and Reflections of Goethe (1906), 189.
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There came in February the issue of Life saying on the cover “Dr. Teller Refutes 9000 Scientists”… I wrote to Life and said first that Teller hadn’t refuted 9000 scientists and second I felt that they should publish the article that I had written… They sent the article back and said that they didn’t want it and then I offered it to Look. The editor of Look called me and said they couldn’t get into a controversy with Life. Then I offered it to the Saturday Evening Post and the Ladies Home Journal and Readers Digest and none of them were interested in it. And then I thought, “What shall I do? I’ll have to write a book and see if I can’t get it published.”’
As quoted in Ted Goertzel, et al., Linus Pauling: A Life in Science and Politics (1965, 1995), 46.
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There is no doubt that human survival will continue to depend more and more on human intellect and technology. It is idle to argue whether this is good or bad. The point of no return was passed long ago, before anyone knew it was happening.
…...
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There is nothing mysterious, as some have tried to maintain, about the applicability of mathematics. What we get by abstraction from something can be returned.
In Introduction to the Foundations of Mathematics (1952), 175.
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This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 19.
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Thus I learned the single essential to qualify a dive as successful: a return.
In Jacques Cousteau and Susan Schiefelbein, The Human, the Orchid, and the Octopus: Exploring and Conserving Our Natural World (2007), 38.
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Tobacco, in its various forms, is one of the most mischievous of all drugs. There is perhaps no other drug which injures the body in so many ways and so universally as does tobacco. Some drugs offer a small degree of compensation for the evil effects which they produce; but tobacco has not a single redeeming feature and gives nothing in return.
In Tobaccoism: or, How Tobacco Kills (1922), Preface, 7.
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We had various kinds of tape-recorded concerts and popular music. But by the end of the flight what we listened to most was Russian folk songs. We also had recordings of nature sounds: thunder, rain, the singing of birds. We switched them on most frequently of all, and we never grew tired of them. It was as if they returned us to Earth.
…...
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We have before us the restoration of that ancient land whose name was a synonym for abundance, prosperity, and grandeur for many generations. Records as old as those of Egypt and as well attested tell of fertile lands and teeming populations, mighty kings and warriors, sages and wise men, over periods of thousands of years. ... A land such as this is worth resuscitating. Once we have apprehended the true cause of its present desolate and abandoned condition, we are on our way to restoring it to its ancient fertility. A land which so readily responded to ancient science, and gave a return which sufficed for the maintenance of a Persian Court in all its splendor, will surely respond to the efforts of modern science and return manifold the money and talent spent on its regeneration.
From The Restoration of the Ancient Irrigation Works on the Tigris: or, The Re-creation of Chaldea (1903), 30.
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What marvel is this? We begged you for drinkable springs,
O earth, and what is your lap sending forth?
Is there life in the deeps as well? A race yet unknown
Hiding under the lava? Are they who had fled returning?
Come and see, Greeks; Romans, come! Ancient Pompeii Is found again, the city of Hercules rises!
Translation as given, without citation, as epigraph in C.W. Ceram, Gods, Graves, and Scholars: The Story of Archaeology (1986), 1. There are other translations of the Schiller’s original German, for example, in 'Pompeii and Herculaneum', Life of Schiller: Poetical Works (1902), 249.
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What strange wonder is this? Our prayer to thee was for water,
Earth! What is this that thou now send’st from thy womb in reply?
In the abyss is there life ? Or hidden under the lava
Dwelleth some race now unknown? Does what hath fled e’er return?
Greeks and Romans, oh come! Oh, see the ancient Pompeii
Here is discover’d again,—Hercules’ town is rebuilt!
Beginning lines of poem, 'Pompeii and Herculaneum', in Edgar A. Bowring (trans.), The Poems of Schiller (1875), 237.
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When autumn returns with its long anticipated holidays, and preparations are made for a scamper in some distant locality, hammer and notebook will not occupy much room in the portmanteau, and will certainly be found most entertaining company.
In The Story of a Boulder: or, Gleanings from the Note-book of a Field Geologist (1858), viii.
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When I read some forty years ago that shells from Syria were found in the Alpes, I said, I admit, in a rather joking way, that these shells had apparently been carried by pilgrims on their return from Jerusalem. Mr. Buffon reprimanded me rather sharply in his Theory of the Earth, p. 28 I. I did not want to lose his friendship for peanuts; however, I am still of the same opinion because the impossibility of the formation of mountains by the sea is demonstrated to me.
Les Singularites de la Nature (1768), in Oeuvres Completes de Voltaire (1877-1885), Vol. 26, 408. Trans. Albert V. and Marguerite Carozzi.
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When the president said, “We’re going to send a man to the moon and return him safely,” the safe part sounded pretty good. But they were using hydrogen, and the only thing I knew about hydrogen was that they used it with the Hindenburg, and that didn’t work out too good.
Interview (30 Sep 2004) with Morley Safer at luncheon after official reopening of Rocket Park. As quoted in Corey Kilgannon, 'The Rocket Park Reopens, And Cronkite Reminisces', New York Times (1 Oct 2004), B6.
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You will die but the carbon will not; its career does not end with you. It will return to the soil, and there a plant may take it up again in time, sending it once more on a cycle of plant and animal life.
…...
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[In the Royal Society, there] has been, a constant Resolution, to reject all the amplifications, digressions, and swellings of style: to return back to the primitive purity, and shortness, when men deliver'd so many things, almost in an equal number of words. They have exacted from all their members, a close, naked, natural way of speaking; positive expressions; clear senses; a native easiness: bringing all things as near the Mathematical plainness, as they can: and preferring the language of Artizans, Countrymen, and Merchants, before that, of Wits, or Scholars.
The History of the Royal Society (1667), 113.
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~~[No known source]~~ Once you have flown, you will walk the earth with your eyes turned skyward, for there you have been, there you long return.
Best attributed simply to “Anonymous” because there seems to be no known reliable primary source. Another example of a feral quote that is almost certainly not authentic, yet spreads virally like a lexicographic plague. It must be centuries old, but does not show up in major 19th-century quote collections. It is simply too good to be true. Included here to attach this caution.
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’Tis late; the astronomer in his lonely height
Exploring all the dark, descries from far
Orbs that like distant isles of splendor are,
And mornings whitening in the infinite.…
He summons one disheveled, wandering star,—
Return ten centuries hence on such a night.
That star will come. It dare not by one hour
Cheat science, or falsify her calculation;
Men will have passed, but watchful in the tower
Man shall remain in sleepless contemplation;
And should all men have perished there in turn,
Truth in their stead would watch that star’s return.
From poem, 'The Appointment', as translated by Arthur O’Shaughnessy, collected in Samuel Waddington (ed.), The Sonnets of Europe (1886), 154.
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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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- 90 -
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- 80 -
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- 70 -
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- 60 -
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- 40 -
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- 30 -
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