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Pencil Quotes (17 quotes)


A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence.
In An Introduction to the History of Mathematics (1953, 1976), 354. This same idea was said much earlier by Ernst Mach (1893). See the quote that begins, “The mathematician who pursues his studies,” on the Ernst Mach Quotes page on this website.
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A theoretical physicist can spend his entire lifetime missing the intellectual challenge of experimental work, experiencing none of the thrills and dangers — the overhead crane with its ten-ton load, the flashing skull and crossbones and danger, radioactivity signs. A theorist’s only real hazard is stabbing himself with a pencil while attacking a bug that crawls out of his calculations.
In Leon Lederman and Dick Teresi, The God Particle: If the Universe is the Answer, What is the Question (1993), 15.
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About the use of language: it is impossible to sharpen a pencil with a blunt axe. It is equally vain to try to do it with ten blunt axes instead.
…...
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Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the answer.
From 'Arithmetic', Harvest Poems, 1910-1960 (1960), 115.
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I became expert at dissecting crayfish. At one point I had a crayfish claw mounted on an apparatus in such a way that I could operate the individual nerves. I could get the several-jointed claw to reach down and pick up a pencil and wave it around. I am not sure that what I was doing had much scientific value, although I did learn which nerve fiber had to be excited to inhibit the effects of another fiber so that the claw would open. And it did get me interested in robotic instrumentation, something that I have now returned to. I am trying to build better micromanipulators for surgery and the like.
In Jeremy Bernstein, 'A.I.', The New Yorker (14 Dec 1981).
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Ideas are elusive, slippery things. Best to keep a pad of paper and a pencil at your bedside, so you can stab them during the night before they get away.
As quoted, without citation, in Cleophus Jackson, Reprogram Your Mind for Success and Happiness (2001), 150.
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It [mathematics] is in the inner world of pure thought, where all entia dwell, where is every type of order and manner of correlation and variety of relationship, it is in this infinite ensemble of eternal verities whence, if there be one cosmos or many of them, each derives its character and mode of being,—it is there that the spirit of mathesis has its home and its life.
Is it a restricted home, a narrow life, static and cold and grey with logic, without artistic interest, devoid of emotion and mood and sentiment? That world, it is true, is not a world of solar light, not clad in the colours that liven and glorify the things of sense, but it is an illuminated world, and over it all and everywhere throughout are hues and tints transcending sense, painted there by radiant pencils of psychic light, the light in which it lies. It is a silent world, and, nevertheless, in respect to the highest principle of art—the interpenetration of content and form, the perfect fusion of mode and meaning—it even surpasses music. In a sense, it is a static world, but so, too, are the worlds of the sculptor and the architect. The figures, however, which reason constructs and the mathematic vision beholds, transcend the temple and the statue, alike in simplicity and in intricacy, in delicacy and in grace, in symmetry and in poise. Not only are this home and this life thus rich in aesthetic interests, really controlled and sustained by motives of a sublimed and supersensuous art, but the religious aspiration, too, finds there, especially in the beautiful doctrine of invariants, the most perfect symbols of what it seeks—the changeless in the midst of change, abiding things hi a world of flux, configurations that remain the same despite the swirl and stress of countless hosts of curious transformations.
In 'The Universe and Beyond', Hibbert Journal (1904-1906), 3, 314.
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Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.
Quoted in 'And Sometimes the Mathematician Wants a Powerful Computer', in Donald J. Albers and Gerald L. Alexanderson (eds.), Mathematical People (1985). In John De Pillis, 777 Mathematical Conversation Starters (2002), 193.
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Once the hatch was opened, I turned the lock handle and bright rays of sunlight burst through it. I opened the hatch and dust from the station flew in like little sparklets, looking like tiny snowflakes on a frosty day. Space, like a giant vacuum cleaner, began to suck everything out. Flying out together with the dust were some little washers and nuts that dad got stuck somewhere; a pencil flew by.
My first impression when I opened the hatch was of a huge Earth and of the sense of unreality concerning everything that was going on. Space is very beautiful. There was the dark velvet of the sky, the blue halo of the Earth and fast-moving lakes, rivers, fields and clouds clusters. It was dead silence all around, nothing whatever to indicate the velocity of the flight… no wind whistling in your ears, no pressure on you. The panorama was very serene and majestic.
…...
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One-sixth gravity on the surface of the moon is just delightful. It’s not like being in zero gravity, you know. You can drop a pencil in zero gravity and look for it for three days. In one-sixth gravity, you just look down and there it is.
In Houston Chronicle (2004) as cited in Will Dunham, 'John Young, “most experienced” U.S. astronaut, dies at 87', on Reuters website (6 Jan 2018).
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The advantage is that mathematics is a field in which one’s blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one’s best moments that count and not one’s worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician’s reputation.
In Ex-Prodigy: My Childhood and Youth (1953), 21.
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The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy. The very existence of this new member of the solar system, and its exact location, were demonstrated with pencil and paper; there was left to observers only the routine task of pointing their telescopes at the spot the mathematicians had marked.
In J.R. Newman (ed.), 'Commentary on John Couch Adams', The World of Mathematics (1956), 820.
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The glimpses of chemical industry's services to man afforded by this book could be presented only by utilizing innumerable chemical products. The first outline of its plan began to take shape on chemically produced notepaper with the aid of a chemically-treated graphite held in a synthetic resin pencil. Early corrections were made with erasers of chemically compounded rubber. In its ultimate haven on the shelves of your bookcase, it will rest on a coating of chemical varnish behind a pane of chemically produced glass. Nowhere has it been separated from that industry's products.
Man in a Chemical World (1937), L'Envoi, 284.
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The mathematician who pursues his studies without clear views of this matter, must often have the uncomfortable feeling that his paper and pencil surpass him in intelligence.
From 'The Economy of Science' in The Science of Mechanics: A Critical and Historical Exposition of its Principles (1893), 489.
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The student of mathematics often finds it hard to throw off the uncomfortable feeling that his science, in the person of his pencil, surpasses him in intelligence,—an impression which the great Euler confessed he often could not get rid of. This feeling finds a sort of justification when we reflect that the majority of the ideas we deal with were conceived by others, often centuries ago. In a great measure it is really the intelligence of other people that confronts us in science.
In Popular Scientific Lectures (1910), 196.
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Thinking is merely the comparing of ideas, discerning relations of likeness and of difference between ideas, and drawing inferences. It is seizing general truths on the basis of clearly apprehended particulars. It is but generalizing and particularizing. Who will deny that a child can deal profitably with sequences of ideas like: How many marbles are 2 marbles and 3 marbles? 2 pencils and 3 pencils? 2 balls and 3 balls? 2 children and 3 children? 2 inches and 3 inches? 2 feet and 3 feet? 2 and 3? Who has not seen the countenance of some little learner light up at the end of such a series of questions with the exclamation, “Why it’s always that way. Isn’t it?” This is the glow of pleasure that the generalizing step always affords him who takes the step himself. This is the genuine life-giving joy which comes from feeling that one can successfully take this step. The reality of such a discovery is as great, and the lasting effect upon the mind of him that makes it is as sure as was that by which the great Newton hit upon the generalization of the law of gravitation. It is through these thrills of discovery that love to learn and intellectual pleasure are begotten and fostered. Good arithmetic teaching abounds in such opportunities.
In Arithmetic in Public Education (1909), 13. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 68.
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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 the pencil on paper, he experiences a feeling of pride, of satisfaction. And justly so, for the fountain of all thought has been opened to him, the difference between the ideal and the real, potentia et actu, has become clear to him; henceforth the philosopher can reveal him nothing new, as a geometrician he has discovered the basis of all thought.
In Sprüche in Reimen. Sprüche in Prosa. Ethisches (1850), Vol. 3, 214. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 67. From the original German, “Wenn der knabe zu begreifen anfängt, daß einem sichtbaren Punkte ein unsichtbarer vorhergehen müsse, daß der nächste Weg zwischen zwei Punkten schon als Linie gedacht werde, ehe sie mit dem Bleistift aufs Papier gezogen wird, so fühlt er einen gewissen Stolz, ein Behagen. Und nicht mit Unrecht; denn ihm ist die Quelle alles Denkens aufgeschlossen, Idee und Verwirklichtes, potentia et actu, ist ihm klargeworden; der Philosoph entdeckt ihm nichts Neues; dem Geometer war von seiner Seite der Grund alles Denkens aufgegangen.” The Latin phrase, “potentia et actu” means “potentiality and actuality”.
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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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- 50 -
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- 40 -
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- 30 -
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- 20 -
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Galileo Galilei
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Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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