„I thought fit to… explain in detail in the same book the peculiarity of a certain method, by which it will be possible… to investigate some of the problems in mathematics by means of mechanics. This procedure is… no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards… But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.“

—  Archimedes, buch The Method of Mechanical Theorems

The Method of Mechanical Theorems

Letzte Aktualisierung 22. Mai 2020. Geschichte
Archimedes Foto
Archimedes4
antiker griechischer Mathematiker, Physiker und Ingenieur -287 - -212 v.Chr

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Archimedes Foto
Archimedes Foto
Pierre de Fermat Foto

„I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof“

—  Pierre de Fermat French mathematician and lawyer 1601 - 1665

Letter to Frénicle (1657) Oeuvres de Fermat Vol.II as quoted by Edward Everett Whitford, The Pell Equation http://books.google.com/books?id=L6QKAAAAYAAJ (1912)
Kontext: There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically? This certainly is indicated by many works ancient and modern. Diophantus himself also indicates this. But he has freed himself from geometry a little more than others have, in that he limits his analysis to rational numbers only; nevertheless the Zetcica of Vieta, in which the methods of Diophantus are extended to continuous magnitude and therefore to geometry, witness the insufficient separation of arithmetic from geometry. Now arithmetic has a special domain of its own, the theory of numbers. This was touched upon but only to a slight degree by Euclid in his Elements, and by those who followed him it has not been sufficiently extended, unless perchance it lies hid in those books of Diophantus which the ravages of time have destroyed. Arithmeticians have now to develop or restore it. To these, that I may lead the way, I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof: Given any number which is not a square, there also exists an infinite number of squares such that when multiplied into the given number and unity is added to the product, the result is a square.

David Hilbert Foto
Maimónides Foto

„These sublime and profound themes admit of no proof whatever… In all questions that cannot be demonstrated, we must adopt the method which we have adopted in this question about God's Omniscience. Note it.“

—  Maimónides, buch The Guide for the Perplexed

Quelle: Guide for the Perplexed (c. 1190), Part III, Ch.21
Kontext: He fully knows His unchangeable essence, and has thus a knowledge of all that results from any of His acts. If we were to try to understand in what manner this is done, it would be the same as if we tried to be the same as God, and to make our knowledge identical with His knowledge. Those who seek the truth, and admit what is true, must believe that nothing is hidden from God; that everything is revealed to His knowledge, which is identical with His essence; that this kind of knowledge cannot be comprehended by us; for if we knew its method, we would possess that intellect by which such knowledge could be acquired.... Note this well, for I think that this is an excellent idea, and leads to correct views; no error will be found in it; no dialectical argument; it does not lead to any absurd conclusion, nor to ascribing any defect to God. These sublime and profound themes admit of no proof whatever... In all questions that cannot be demonstrated, we must adopt the method which we have adopted in this question about God's Omniscience. Note it.

Salvador Dalí Foto
Eduard Jan Dijksterhuis Foto

„Mechanics… was an axiomatic construction; and… its problem could be solved quantitatively by algebraic methods.“

—  Eduard Jan Dijksterhuis Dutch historian 1892 - 1965

Robert Jacobus Forbes and E. J. Dijksterhuis (1963) A History of Science and Technology, vol. I: Ancient Times to the Seventeenth Century, Baltimore.

David Eugene Smith Foto
Ronald Fisher Foto

„The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.“

—  Ronald Fisher English statistician, evolutionary biologist, geneticist, and eugenicist 1890 - 1962

Discussion to ‘Statistics in agricultural research’ by J.Wishart, Journal of the Royal Statistical Society, Supplement, 1, 26-61, 1934.
1930s

Henry John Stephen Smith Foto
Eduard Jan Dijksterhuis Foto
David Chalmers Foto

„The easy problems of consciousness are those that seem directly susceptible to the standard methods of cognitive science, whereby a phenomenon is explained in terms of computational or neural mechanisms. The hard problems are those that seem to resist those methods. …The really hard problem of consciousness is the problem of experience.“

—  David Chalmers Australian philosopher and cognitive scientist 1966

When we think and perceive, there is a whir of information-processing, but there is also a subjective aspect. ...When we see, for example, we experience visual sensations: the felt quality of redness, the experience of dark and light, the quality of depth in a visual field. Other experiences go along with perception in different modalities: the sound of a clarinet, the smell of mothballs. Then there are bodily sensations, from pains to orgasms; mental images that are conjured up internally; the felt quality of emotion, and the experience of a stream of conscious thought.
"Facing Up to the Problem of Consciousness," 1995

J. J. Thomson Foto
Joseph Louis Lagrange Foto

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“