„Classification is thought of by many librarians as either a fearful complication of a very simply act, or an outmoded, almost prehistoric, method of doing a very complex mathematical task.“

—  Douglas John Foskett, p. 138
Douglas John Foskett24
1918 - 2004
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„[The books of Euclid pass on to us] something admirable and very necessary to see and to read, namely the order in the method of writing on mathematics in that aforementioned time of the wise age.“

—  Simon Stevin Flemish scientist, mathematician and military engineer 1548 - 1620
Géographie, in Les Oeuvres Mathématiques de Simon Stevin de Bruges (1634) ed. Girard, p. 109, as quoted by Jacob Klein]], Greek Mathematical Thought and the Origin of Algebra (1968)

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„If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.“

—  John Von Neumann Hungarian-American mathematician and polymath 1903 - 1957
Remark made by von Neumann as keynote speaker at the first national meeting of the Association for Computing Machinery in 1947, as mentioned by Franz L. Alt at the end of "Archaeology of computers: Reminiscences, 1945--1947", Communications of the ACM, volume 15, issue 7, July 1972, special issue: Twenty-fifth anniversary of the Association for Computing Machinery, p. 694.

Henri Poincaré photo

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

—  Henri Poincaré French mathematician, physicist, engineer, and philosopher of science 1854 - 1912
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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„I believe that no one who is familiar, either with mathematical advances in other fields, or with the range of special biological conditions to be considered, would ever conceive that everything could be summed up in a single mathematical formula, however complex.“

—  Ronald Fisher English statistician, evolutionary biologist, geneticist, and eugenicist 1890 - 1962
The evolutionary modification of genetic phenomena. Proceedings of the 6th International Congress of Genetics 1, 165-72, 1932.

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„Without continuous mathematics, the study of discrete mathematics soon becomes trivial and very limited. ...The two topics“

—  Richard Hamming American mathematician and information theorist 1915 - 1998
Context: Increasingly... the application of mathematics to the real world involves discrete mathematics... the nature of the discrete is often most clearly revealed through the continuous models of both calculus and probability. Without continuous mathematics, the study of discrete mathematics soon becomes trivial and very limited.... The two topics, discrete and continuous mathematics, are both ill served by being rigidly separated.

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„Contrary to popular opinion, mathematics is about simplifying life, not complicating it.“

—  Benoît Mandelbrot Polish-born, French and American mathematician 1924 - 2010
Context: Contrary to popular opinion, mathematics is about simplifying life, not complicating it. A child learns a bag of candies can be shared fairly by counting them out: That is numeracy. She abstracts that notion to dividing a candy bar into equal pieces: arithmetic. Then, she learns how to calculate how much cocoa and sugar she will need to make enough chocolate for fifteen friends: algebra. Ch. 7, p. 125

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„One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.“

—  Paul Dirac theoretical physicist 1902 - 1984
Context: It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.

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