„Mathematics… is the set of all possible self-consistent structures“

—  Michio Kaku, livro Hyperspace, Hyperspace (1995), Context: Mathematics... is the set of all possible self-consistent structures, and there are vastly more logical structures than physical principles. Ch.15 Conclusion<!--p.328-->
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Martin Gardner photo

„Mathematical magic combines the beauty of mathematical structure with the entertainment value of a trick.“

—  Martin Gardner recreational mathematician and philosopher 1914 - 2010
Mathematics, Magic, and Mystery https://books.google.com/books?id=-kOFBQAAQBAJ&pg=PR11#v=onepage&q=%22Mathematical%20magic%20combines%22%23v%3Dsnippet&f=false (1956), p. ix

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Eduardo Torroja photo
Bertrand Russell photo

„The rules of logic are to mathematics what those of structure are to architecture.“

—  Bertrand Russell logician, one of the first analytic philosophers and political activist 1872 - 1970
1900s, "The Study of Mathematics" (November 1907)

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„A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…“

—  Benoît Mandelbrot Polish-born, French and American mathematician 1924 - 2010
As quoted in a review of The Fractal Geometry of Nature by J. W. Cannon in The American Mathematical Monthly, Vol. 91, No. 9 (November 1984), p. 594

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Henri Poincaré photo

„The very possibility of the science of mathematics seems an insoluble contradiction.“

—  Henri Poincaré, livro Science and Hypothesis
Science and Hypothesis (1901), Context: 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 Ch. I: On the Nature of Mathematical Reasoning (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead

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Doron Zeilberger photo

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