„There are two general Methods made use of in the Mathematicks, viz. Synthesis and Analysis, which we shall explain, after having acquainted the Reader, that the Method we make use of to resolve a Mathematical Problem, is called Zetetick; and that that Method which determines when, and by what way, and how many different ways a Problem may be resolved, is called Poristick. But in treating of Methods, we will first premise, that in general, a Method is the Art of disposing a Train of Arguments or Consequences in a right Order, either to discover the Truth of a Theorem, which we would find out, or to demonstrate it to others, when found.“

Quelle: A Mathematical Dictionary: Or; A Compendious Explication of All Mathematical Terms, 1702, p. 26

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Jacques Ozanam Foto
Jacques Ozanam
französischer Mathematiker 1640 - 1718

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„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

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„The method of viewing things which proceeds in accordance with the principle of sufficient reason is the rational method, and it alone is valid and of use in practical life and in science. The method which looks away from the content of this principle is the method of genius, which is only valid and of use in art.“

—  Arthur Schopenhauer, buch Die Welt als Wille und Vorstellung

Die dem Satz vom Grunde nachgehende ist die vernünftige Betrachtungsart, welche im praktischen Leben, wie in der Wissenschaft, allein gilt und hilft: die vom Inhalt jenes Satzes wegsehende ist die geniale Betrachtungsart, welche in der Kunst allein gilt und hilft.
Die Welt als Wille und Vorstellung, Zweiter Band, Ergänzungen zum dritten Buch, para. 36 (1859)
The World as Will and Representation (1819; 1844; 1859)

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„The entire method consists in the order and arrangement of the things to which the mind’s eye must turn so that we can discover some truth.“

—  René Descartes, buch Rules for the Direction of the Mind

Rules for the Direction of the Mind: X.379
As quoted in [Clarke, Desmond M., 2006, Descartes : a Biography, Cambridge Press, 67, ISBN 978-0-521-82301-2]

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„Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive? …If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.“

—  Henri Poincaré, buch Wissenschaft und Hypothese

Quelle: Science and Hypothesis (1901), Ch. I: On the Nature of Mathematical Reasoning (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Kontext: The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A!... Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive?... If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.<!--pp.5-6

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„The right method in any particular case must be largely determined by the nature of the problem.“

—  Arnold Toynbee British economic historian 1852 - 1883

Quelle: Lectures on The Industrial Revolution in England (1884), p. 29

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„The truth is that other systems of geometry are possible, yet after all, these other systems are not spaces but other methods of space measurements. There is one space only, though we may conceive of many different manifolds, which are contrivances or ideal constructions invented for the purpose of determining space.“

—  Paul Carus American philosopher 1852 - 1919

Science, Vol. 18 (1903), p. 106, as reported in Memorabilia Mathematica; or, The Philomath's Quotation-Book https://archive.org/stream/memorabiliamathe00moriiala#page/81/mode/2up, (1914), by Robert Edouard Moritz, p. 352

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