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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Home > Dictionary of Science Quotations > Scientist Names Index A > Archimedes Quotes

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(c. 287 B.C. - c. 212 B.C.)

Greek mathematician and engineer who developed useful inventions and theories in mechanics and hydrostatics, including Archimedes principle, the Archimedean screw, and levers.

Science Quotes by Archimedes (5 quotes)

δος μοι που στω και κινω την γην — Dos moi pou sto kai kino taen gaen (in epigram form, as given by Pappus, classical Greek).
δος μοι πα στω και τα γαν κινάσω — Dos moi pa sto kai tan gan kinaso (Doric Greek).
Give me a place to stand on and I can move the Earth.
About four centuries before Pappas, but about three centuries after Archimedes lived, Plutarch had written of Archimedes' understanding of the lever:
Archimedes, a kinsman and friend of King Hiero, wrote to him that with a given force, it was possible to move any given weight; and emboldened, as it is said, by the strength of the proof, he asserted that, if there were another world and he could go to it, he would move this one.
A commonly-seen expanded variation of the aphorism is:
Give me a lever long enough and a place to stand, and I can move the earth.
— Archimedes
As attributed to Pappus (4th century A.D.) and Plutarch (c. 46-120 A.D.), in Sherman K. Stein, Archimedes: What Did He Do Besides Cry Eureka? (1999), 5, where it is also stated that Archimedes knew that ropes and pulley exploit “the principle of the lever, where distance is traded for force.” Eduard Jan Dijksterhuis, in his book, Archimedes (1956), Vol. 12., 15. writes that Hiero invited Archimedes to demonstrate his claim on a ship from the royal fleet, drawn up onto land and there loaded with a large crew and freight, and Archimedes easily succeeded. Thomas Little Heath in The Works of Archimedes (1897), xix-xx, states according to Athenaeus, the mechanical contrivance used was not pulleys as given by Plutarch, but a helix., Heath provides cites for Pappus Synagoge, Book VIII, 1060; Plutarch, Marcellus, 14; and Athenaeus v. 207 a-b. What all this boils down to, in the opinion of the Webmaster, is the last-stated aphorism would seem to be not the actual words of Archimedes (c. 287 – 212 B.C.), but restatements of the principle attributed to him, formed by other writers centuries after his lifetime.
Science quotes on:  |  Earth (582)  |  Lever (9)  |  Move (75)  |  Stand (85)

Eureka! Eureka!
I have found it!
— Archimedes
Attributed. Supposed to have been his cry, jumping naked from his bath and running in the streets, excited by a discovery about water displacement that solved a problem about the purity of a gold crown. Archimedes probably never uttered the phrase in that way. We have no written record by Archimedes about the Eureka! story. The earliest reference is by Vitruvius, a Roman writer, in the introduction of his ninth book of architecture, c. 1st Century B.C. Being nearly 200 years after the presumed event, his story of Archimedes is likely exaggerated. See the Vitruvius quote here.
Science quotes on:  |  Discovery (601)  |  Eureka (5)

Give me a place to stand, and I will move the earth.
— Archimedes
F. Hultsch (ed.) Pappus Alexandrinus: Collectio (1876-8), Vol. 3, book 8, section 10, ix.
Science quotes on:  |  Lever (9)  |  Mechanics (44)  |  French Saying (61)

Having been the discoverer of many splendid things, he is said to have asked his friends and relations that, after his death, they should place on his tomb a cylinder enclosing a sphere, writing on it the proportion of the containing solid to that which is contained.
— Archimedes
Plutarch, Life of Marcellus, 17.12. Trans. R. W. Sharples.
Science quotes on:  |  Geometry (100)  |  Mathematics (597)

If thou art able, O stranger, to find out all these things and gather them together in your mind, giving all the relations, thou shalt depart crowned with glory and knowing that thou hast been adjudged perfect in this species of wisdom.
— Archimedes
From a letter to Eratosthenes, the chief librarian at Alexandria, containing the Cattle Problem, an exceedingly difficult calculation involving huge numbers (which was not solved exactly until the use of a supercomputer in 1981). In David J. Darling, The Universal Book of Mathematics (2004), 23. The debate by scholars regarding whether Archimedes is the true author is in T. L. Heath (ed.), The Works of Archimedes (1897), xxxiv.
Science quotes on:  |  Glory (48)  |  Problem (382)  |  Solution (175)  |  Wisdom (161)

Quotes by others about Archimedes (17)

Hieron asked Archimedes to discover, without damaging it, whether a certain crown or wreath was made of pure gold, or if the goldsmith had fraudulently alloyed it with some baser metal. While Archimedes was turning the problem over in his mind, he chanced to be in the bath house. There, as he was sitting in the bath, he noticed that the amount of water that was flowing over the top of it was equal in volume to that part of his body that was immersed. He saw at once a way of solving the problem. He did not delay, but in his joy leaped out of the bath. Rushing naked through the streets towards his home, he cried out in a loud voice that he had found what he sought. For, as he ran, he repeatedly shouted in Greek; “Eureka! Eurekal I’ve found it! I’ve found it!”
Vitrivius Pollio, De Architectura, ix, prologue, section 10.
Science quotes on:  |  Research (530)

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.
In A Mathematician's Apology (1940, reprint with Foreward by C.P. Snow 1992), 81.
Science quotes on:  |  Aeschylus (4)  |  Mathematics (597)

Referring to the decimal system of numeration or its equivalent (with some base other than 10): To what heights would science now be raised if Archimedes had made that discovery!
Gauss regarded this oversight as the greatest calamity in the history of science.
Quoted in James Roy Newman, The World of Mathematics, 328.
Science quotes on:  |  Decimal (11)  |  Number (188)

There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein.
Science quotes on:  |  Mathematician (178)  |  Sir Isaac Newton (261)

It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
Quoted in Return to Mathematical Circles H. Eves (Boston 1988).
Science quotes on:  |  Arithmetic (70)

ARCHIMEDES. On hearing his name, shout “Eureka!” Or else: “Give me a fulcrum and I will move the world”. There is also Archimedes’ screw, but you are not expected to know what that is.
The Dictionary of Accepted Ideas (1881), trans. Jaques Barzun (1968), 15.
Science quotes on:  |  Quip (76)

One day at Fenner's (the university cricket ground at Cambridge), just before the last war, G. H. Hardy and I were talking about Einstein. Hardy had met him several times, and I had recently returned from visiting him. Hardy was saying that in his lifetime there had only been two men in the world, in all the fields of human achievement, science, literature, politics, anything you like, who qualified for the Bradman class. For those not familiar with cricket, or with Hardy's personal idiom, I ought to mention that “the Bradman class” denoted the highest kind of excellence: it would include Shakespeare, Tolstoi, Newton, Archimedes, and maybe a dozen others. Well, said Hardy, there had only been two additions in his lifetime. One was Lenin and the other Einstein.
Variety of Men (1966), 87.
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There is an astonishing imagination, even in the science of mathematics. … We repeat, there was far more imagination in the head of Archimedes than in that of Homer.
In A Philosophical Dictionary: from the French (1824), 126.
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Archimedes said Eureka,
Cos in English he weren't too aversed in,
when he discovered that the volume of a body in the bath,
is equal to the stuff it is immersed in,
That is the law of displacement,
Thats why ships don't sink,
Its a shame he weren't around in 1912,
The Titanic would have made him think.
From lyrics of song Sod’s Law.
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We have all heard of the puzzle given to Archimedes…. His finding that the crown was of gold was a discovery; but he invented the method of determining the density of solids. Indeed, discoverers must generally be inventors; though inventors are not necessarily discoverers.
From 'How Discoveries Are Made', Cassell's Magazine, Illustrated (May 1908), 629.
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The reason I cannot really say that I positively enjoy nature is that I do not quite realize what it is that I enjoy. A work of art, on the other hand, I can grasp. I can — if I may put it this way — find that Archimedian point, and as soon as I have found it, everything is readily clear for me. Then I am able to pursue this one main idea and see how all the details serve to illuminate it.
Søren Kierkegaard, translation by Howard Vincent Hong and Edna Hatlestad Hong Søren Kierkegaard’s Journal and Papers (1834), 50.
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[King Hiero II] requested Archimedes to consider [whether a crown was pure gold or alloyed with silver]. The latter, while the case was still on his mind, happened to go to the bath, and on getting into a tub observed that the more his body sank into it the more water ran out over the tub. As this pointed out the way to explain the case in question, without a moment’s delay, and transported with joy, he jumped out of the tub and rushed home naked, crying with a loud voice that he had found what he was seeking; for as he ran he shouted repeatedly in Greek, “Eὕρηκα, εὕρηκα.”
This famous anecdote, being written about two centuries after Archimedes, is of questionable authenticity, but Vitruvius provided the origin of the story as we know it. In De Architectura, Book 9, Introduction, Sec. 10. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 254. Also seen translated as “While Archimedes was turning the problem over, he chanced to come to the place of bathing, and there, as he was sitting down in the tub, he noticed that the amount of water which flowed over the tub was equal to the amount by which his body was immersed. This showed him a means of solving the problem. … In his joy, he leapt out of the tub and, rushing naked towards his home, he cried out with a loud voice that he had found what he sought.” In Ivor Bulmer-Thomas, Selections Illustrating the History of Greek Mathematics (1939), 37.
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Archimedes [indicates] that there can be no true levelling by means of water, because he holds that water has not a level surface, but is of a spherical form, having its centre at the centre of the earth.
In De Architectura, Book 8, Chap 5, Sec. 3. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 243.
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One can argue that mathematics is a human activity deeply rooted in reality, and permanently returning to reality. From counting on one’s fingers to moon-landing to Google, we are doing mathematics in order to understand, create, and handle things, … Mathematicians are thus more or less responsible actors of human history, like Archimedes helping to defend Syracuse (and to save a local tyrant), Alan Turing cryptanalyzing Marshal Rommel’s intercepted military dispatches to Berlin, or John von Neumann suggesting high altitude detonation as an efficient tactic of bombing.
In 'Mathematical Knowledge: Internal, Social and Cultural Aspects', Mathematics As Metaphor: Selected Essays (2007), 3.
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Once a mathematical result is proven to the satisfaction of the discipline, it doesn’t need to be re-evaluated in the light of new evidence or refuted, unless it contains a mistake. If it was true for Archimedes, then it is true today.
In 'The Unplanned Impact of Mathematics', Nature (14 Jul 2011), 475, No. 7355, 166.
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My interest in Science had many roots. Some came from my mother … while I was in my early teens. She fell in love with science,… [from] classes on the Foundations of Physical Science. … I was infected by [her] professor second hand, through hundreds of hours of conversations at my mother’s knees. It was from my mother that I first learned of Archimedes, Leonardo da Vinci, Galileo, Kepler, Newton, and Darwin. We spent hours together collecting single-celled organisms from a local pond and watching them with a microscope.
From 'Richard E. Smalley: Biographical', collected in Tore Frängsmyr (ed.), Les Prix Nobel: The Nobel Prizes 1996 (1997).
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In a manner which matches the fortuity, if not the consequence, of Archimedes’ bath and Newton’s apple, the [3.6 million year old] fossil footprints were eventually noticed one evening in September 1976 by the paleontologist Andrew Hill, who fell while avoiding a ball of elephant dung hurled at him by the ecologist David Western.
Missing Links: The Hunt for Earliest Man
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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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