„As a science mathematics has been adapted to the description of natural phenomena, and the great practitioners in this field… have never concerned themselves with the logical foundations of mathematics, but have boldly taken a pragmatic view of mathematics as an intellectual machine which works successfully. Description has been verified by further observation, still more strikingly be prediction, and sometimes, more ominously, by control of natural forces. Happily, unresolved problems… still remain as challenges.“

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— George Frederick James Temple

100 Years of Mathematics: a Personal Viewpoint (1981)

Estratto da Wikiquote. Ultimo aggiornamento 03 Giugno 2021.

George Frederick James Temple21

British mathematician 1901 - 1992

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„The 'language theory' is inadequate as a description of the nature of mathematics.“

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— George Frederick James Temple British mathematician 1901 - 1992

100 Years of Mathematics: a Personal Viewpoint (1981)

„So intimate is the union between Mathematics and Physics that probably by far the larger part of the accessions to our mathematical knowledge have been obtained by the efforts of mathematicians to solve the problems set to them by experiment, and to create for each successive class phenomena a new calculus or a new geometry, as the case might be, which might prove not wholly inadequate to the subtlety of nature. Sometimes the mathematician has been before the physicist, and it has happened that when some great and new question has occurred to the experimentalist or the observer, he has found in the armory of the mathematician the weapons which he needed ready made to his hand. But much oftener, the questions proposed by the physicist have transcended the utmost powers of the mathematics of the time, and a fresh mathematical creation has been needed to supply the logical instrument requisite to interpret the new enigma.“

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— Henry John Stephen Smith mathematician 1826 - 1883

As quoted in The Century: A Popular Quarterly (1874) ed. Richard Watson Gilder, Vol. 7, pp. 508-509, https://books.google.com/books?id=ceYGAQAAIAAJ&pg=PA508 "Relations of Mathematics to Physics". Earlier quote without citation in Nature, Volume 8 (1873), page 450.
Also quoted partially in Michael Grossman and Robert Katz, Calculus http://babel.hathitrust.org/cgi/mb?a=listis;c=216746186|Non-Newtonian (1972) p. iv. ISBN 0912938013.

„Mathematics has also been developed as a philosophy, in the sense in which this term is defined by A. N. Whitehead as 'the endeavor to frame a coherent, logical and necessary system of general ideas in terms of which every element of our experience can be interpreted'. Substitute 'mathematics' for 'experience' and we have an admirable description of its speculative and philosophic development…. Philosophy of mathematics… has its paradoxes and antimonies, and also diverse schools of thought…“

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— George Frederick James Temple British mathematician 1901 - 1992

100 Years of Mathematics: a Personal Viewpoint (1981)

„Our mathematical concepts, structures, ideas have been invented as tools to organise the phenomena of the physical, social and mental world. Phenomenology of a mathematical concept, structure, or idea means describing it in its relation to the phenomena for which it was created, and to which it has extended in the learning process of mankind, and, as far as this description is concerned with the learning process of the young generation, it is didactical phenomenology, a way to show the teacher the places where the learner might step into the learning process of mankind.“

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— Hans Freudenthal Dutch mathematician 1905 - 1990

Origine: The Concept and the Role of the Model in Mathematics and Natural and Social Sciences (1961), p. ix

„A model may be pictorial, descriptive, qualitative, or generally approximate in nature, or it may be mathematical and quantitative in nature and reasonably precise.“

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— Harold Chestnut American engineer 1917 - 2001

Origine: Systems Engineering Tools, (1965), p. 108

„The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!“

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— David Hilbert, Mathematical Problems

Mathematical Problems (1900)

„In mathematical quarters, the regular division of the plane has been considered theoretically... Does this mean that it is an exclusively mathematical question? In my opinion, it does not. [Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it.“

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— M. C. Escher Dutch graphic artist 1898 - 1972

Quote of Escher, from his essay on Tessellation 1957; as cited by Tony Thomas, in 'The Strange Worlds of M C Escher' http://www.escapeintolife.com/essays/the-strange-worlds-of-m-c-escher/
1950's

„The great advances in mathematics have not been made by logic but by creative imagination.“

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— George Frederick James Temple British mathematician 1901 - 1992

100 Years of Mathematics: a Personal Viewpoint (1981)
Contesto: Logical analysis is indispensable for an examination of the strength of a mathematical structure, but it is useless for its conception and design. The great advances in mathematics have not been made by logic but by creative imagination.

„In many ways it is true to say that syntax is mathematical logic, semantics is philosophy or philosophy of science, and pragmatics is psychology, but these fields are not really all distinct.“

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— Frank Honywill George British psychologist 1921 - 1997

Origine: The Brain As A Computer (1962), p.42 as cited in: Sica Pettigiani (1996) La comunicazione interumana. p.48

„The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future;“

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— Eric Temple Bell mathematician and science fiction author born in Scotland who lived in the United States for most of his life 1883 - 1960

Origine: The Development of Mathematics (1940), p. 283
Contesto: The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future; and should analysis ever appear to be without or blemish, its perfection might only be that of death.

„So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premisses which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary.“

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— Bertrand Russell logician, one of the first analytic philosophers and political activist 1872 - 1970

Origine: 1910s, Introduction to Mathematical Philosophy (1919), Ch. 18: Mathematics and Logic

„It can have no analogy in fact with the descriptions of those who know nothing of the subject; furthermore, it is not to be represented as this or that by any person whomsoever: it is that which it is, drawing from itself only, even as mathematics do, for it is the exact and absolute science of Nature and her laws.“

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— Eliphas Levi French writer 1810 - 1875

Introduction
The History Of Magic (1860)

„Only an unashamed dogmatist would dare to assert that the issue has finally been resolved now, in favor of the view that, outside logic or mathematics, the method of modern science is the only method to employ in seeking knowledge. The dogmatist who made this assertion would have to be more than ashamed. He would have to blind himself to the fact that his own assertion was not established by the experimental method, nor made as an indisputable conclusion of mathematical reasoning or of purely logical analysis.“

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— Robert Maynard Hutchins philosopher and university president 1899 - 1977

Great Books: The Foundation of a Liberal Education (1954)

„The more advanced the sciences have become, the more they have tended to enter the domain of mathematics, which is a sort of center towards which they converge. We can judge of the perfection to which a science has come by the facility, more or less great, with which it may be approached by calculation.“

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— Adolphe Quetelet Belgian astronomer, mathematician, statistician and sociologist 1796 - 1874

Edward Mailly, Essai sur la vie et les ouv rages de Quetelet in the Annuaire de Vacadimie royale des sciences des lettres et des beaux-arts de Belgique (1875) Vol. xli pp. 109-297 found also in "Conclusions" of Instructions populaires sur le calcul des probabilités p. 230

„Mathematical activity has taken the forms of a science, a philosophy and an art.“

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— George Frederick James Temple British mathematician 1901 - 1992

100 Years of Mathematics: a Personal Viewpoint (1981)

„More than any of his predecessors Plato appreciated the scientific possibilities of geometry... By his teaching he laid the foundations of the science, insisting upon accurate definitions, clear assumptions, and logical proof. His opposition to the materialists, who saw in geometry only what was immediately useful to the artisan and the mechanic is… clear. …That Plato should hold the view… is not a cause for surprise. The world's thinkers have always held it. No man has ever created a mathematical theory for practical purposes alone. The applications of mathematics have generally been an afterthought.“

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— David Eugene Smith American mathematician 1860 - 1944

Origine: History of Mathematics (1923) Vol.1, p. 90

„The last thirty years [1925 to 1955] have seen an enormous improvement in the position of geometry as a branch of mathematics, or, rather, have seen the re-integration of geometry into the main fabric of mathematics. Indeed, one can go further and say that with the restoration of geometry to its rightful place in the mathematical scheme the process of fragmentation which had been doing so much harm to mathematics has been reversed, and we may look forward to the day in which there are no longer analysts, algebraists, geometers and so on, but simply mathematicians. Mathematical research has two aspects, motivation and technique, and when the latter gains control the result is apt to be excessive specialisation. The revolution of geometrical thought, and the reinstatement of geometry as one of the major mathematical disciplines, have helped to bring about a unification of mathematics which we may justly regard as one of the major contributions of the last quarter century to the subject.“

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— W. V. D. Hodge British mathematician 1903 - 1975

W. V. D. Hodge, Changing Views of Geometry. Presidential Address to the Mathematical Association, 14th April, 1955, The Mathematical Gazette 39 (329) (1955), 177-183.

„The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena. The verbal interpretation, on the other hand – i. e., the metaphysics of quantum theory – is on far less solid ground. In fact, in more than forty years physicists have not been able to provide a clear metaphysical model.“

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— Fritjof Capra, libro Il Tao della fisica

Origine: The Tao of Physics (1975), Ch. 10, The Unity of All Things, p. 132.

„There is a mistake into which several have fallen, and have deceived others, and perhaps themselves, by clothing some false reasoning in what they called a mathematical dress, imagining that by the application of mathematical symbols to their subject, they secured mathematical argument. This could not have happened if they had possessed a knowledge of the bounds within which the empire of mathematics is contained. That empire is sufficiently wide, and might have been better known, had the time which has been wasted in aggressions upon the domains of others, been spent in exploring the immense tracts which are yet untrodden.“

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— Augustus De Morgan British mathematician, philosopher and university teacher (1806-1871) 1806 - 1871

Origine: On the Study and Difficulties of Mathematics (1831), Ch. I.

„I discovered the works of Euler and my perception of the nature of mathematics underwent a dramatic transformation. I was de-Bourbakized, stopped believing in sets, and was expelled from the Cantorian paradise. I still believe in abstraction, but now I know that one ends with abstraction, not starts with it. I learned that one has to adapt abstractions to reality and not the other way around. Mathematics stopped being a science of theories but reappeared to me as a science of numbers and shapes.“

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— Alexander Stepanov Russian programmer 1950

Bjarne Stroustrup: Evolving a language in and for the real world: C++ 1991-2006. ACM HOPL-III. June 2007., 2008-04-25, http://web.archive.org/web/20071120015600/http://www.research.att.com/~bs/hopl-almost-final.pdf, 2007-11-20 http://www.research.att.com/~bs/hopl-almost-final.pdf,

George Frederick James Temple21

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