„Anyone who understands algebraic notation, reads at a glance in an equation results reached arithmetically only with great labour and pains.“

—  Antoine Augustin Cournot, Researches into the Mathematical Principles of the Theory of Wealth

Origine: Researches into the Mathematical Principles of the Theory of Wealth, 1897, p. 4; Cited in: Moritz (1914, 197): About mathematics as language

Estratto da Wikiquote. Ultimo aggiornamento 03 Giugno 2021. Storia
Antoine Augustin Cournot photo
Antoine Augustin Cournot
filosofo, matematico e economista francese 1801 - 1877

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„Remember that algebra, with all its deep and intricate problems, is nothing but a development of the four fundamental operations of arithmetic. Everyone who understands the meaning of addition, subtraction, multiplication, and division holds the key to all algebraic problems.“

—  Richard von Mises Austrian physicist and mathematician 1883 - 1953

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„Arithmetic is the science of the Evaluation of Functions, Algebra is the science of the Transformation of Functions.“

—  George Holmes Howison American philosopher 1834 - 1916

Journal of Speculative Philosophy, Vol. 5, p. 175. Reported in: Memorabilia mathematica or, The philomath's quotation-book, by Robert Edouard Moritz. Published 1914
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„Anyone who reads a book with a sense of obligation does not understand the art of reading.“

—  Lin Yutang, libro The Importance of Living

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„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?“

—  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)
Contesto: 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.

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„Anyone who votes Labour ought to be locked up.“

—  Bernard Montgomery, 1st Viscount Montgomery of Alamein British Army officer, Commander of Allied forces at the Battle of El Alamein 1887 - 1976

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„The equation which always holds in the case of a normal exchange is an equation not of labour, but of abstract utility, significantly called worth.“

—  Philip Wicksteed English economist 1844 - 1927

Pages 713–714.
"The Marxian Theory of Value: Das Kapital: A Criticism" (1884)
Contesto: It is true also that Marx elsewhere virtually defines value so as to make it essentially dependent upon human labour (p. 81 [43a]). But for all that his analysis is based on the bare fact of exchangeability. This fact alone establishes Verschiedenkeit and Ghichheit, heterogeneity and homogeneity. Any two things which normally exchange for each other, whether products of labour or not, whether they have, or have not, what we choose to call value, must have that "common something" in virtue of which things exchange and can be equated with each other; and all legitimate inferences as to wares which are drawn from the bare fact of exchange must be equally legitimate when applied to other exchangeable things. Now the "common something," which all exchangeable things contain, is neither more nor less than abstract utility, i. e. power of satisfying human desires. The exchanged articles differ from each other in the specific desires which they satisfy, they resemble each other in the degree of satisfaction which they confer. The Verschiedenheit is qualitative, the Gleichheit is quantitative.It cannot be urged that there is no common measure to which we can reduce the satisfaction derived from such different articles as Bibles and brandy, for instance (to take an illustration suggested by Marx), for as a matter of fact we are all of us making such reductions every day. If I am willing to give the same sum of money for a family Bible and for a dozen of brandy, it is because I have reduced the respective satisfactions their possession will afford me to a common measure, and have found them equivalent. In economic phrase, the two things have equal abstract utility for me. In popular (and highly significant) phrase, each of the two things is worth as much to me as the other.Marx is, therefore, wrong in saying that when we pass from that in which the exchangeable wares differ (value in use) to that in which they are identical (value in exchange), we must put their utility out of consideration, leaving only jellies of abstract labour. What we really have to do is to put out of consideration the concrete and specific qualitative utilities in which they differ, leaving only the abstract and general quantitative utility in which they are identical.This formula applies to all exchangeable commodities, whether producible in indefinite quantities, like family Bibles and brandy, or strictly limited in quantity, like the "Raphaels," one of which has just been purchased for the nation. The equation which always holds in the case of a normal exchange is an equation not of labour, but of abstract utility, significantly called worth. … A coat is made specifically useful by the tailor's work, but it is specifically useful (has a value in use) because it protects us. In the same way, it is made valuable by abstractly useful work, but it is valuable because it has abstract utility.

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„Through algebra you easily arrive at equations, but always to pass therefrom to the elegant constructions and demonstrations which usually result by means of the method of porisms is not so easy, nor is one's ingenuity and power of invention so greatly exercised and refined in this analysis.“

—  Isaac Newton British physicist and mathematician and founder of modern classical physics 1643 - 1727

The Mathematical Papers of Isaac Newton (edited by Whiteside), Volume 7; Volumes 1691-1695 / pg. 261. http://books.google.com.br/books?id=YDEP1XgmknEC&printsec=frontcover
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„In 1673 he wrote his great work De Algebra Tractatus; Historicus & Practicus, of which an English edition appeared in 1685. In this there is seen the first serious attempt in England to write on the history of mathematics, and the result shows a wide range of reading of classical literature of the science.“

—  David Eugene Smith American mathematician 1860 - 1944

This work is also noteworthy because it contains the first of an effort to represent the imaginary number graphically by the method now used. The effort stopped short of success but was an ingenious beginning.
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„It may be in some measure due to the defects of notation in his time that Diophantos will have in his solutions no numbers whatever except rational numbers, in [the non-numbers of] which, in addition to surds and imaginary quantities, he includes negative quantities. …Such equations then as lead to surd, imaginary, or negative roots he regards as useless for his purpose: the solution is in these cases ὰδοπος, impossible. So we find him describing the equation 4=4x+20 as ᾰτοπος because it would give x=-4. Diophantos makes it throughout his object to obtain solutions in rational numbers, and we find him frequently giving, as a preliminary, conditions which must be satisfied, which are the conditions of a result rational in Diophantos' sense. In the great majority of cases when Diophantos arrives in the course of a solution at an equation which would give an irrational result he retraces his steps and finds out how his equation has arisen, and how he may by altering the previous work substitute for it another which shall give a rational result. This gives rise, in general, to a subsidiary problem the solution of which ensures a rational result for the problem itself. Though, however, Diophantos has no notation for a surd, and does not admit surd results, it is scarcely true to say that he makes no use of quadratic equations which lead to such results. Thus, for example, in v. 33 he solves such an equation so far as to be able to see to what integers the solution would approximate most nearly.“

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