The practice of first developing a clear and precise definition of a process without regard for efficiency, and then using it as a guide and a test in exploring equivalent processes possessing other characteristics, such as greater efficiency, is very common in mathematics. It is a very fruitful practice which should not be blighted by premature emphasis on efficiency in computer execution.
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.Richard Courant in: The Australian Mathematics Teacher, Volumes 39-40, Australian Association of Mathematics Teachers, 1983, p.3
Even in Mathematics his whimsical fancy was sometimes suffered to peep out, and little girls who learnt the rudiments of calculation at his knee found the path they had imagined so thorny set about with roses by reason of the delightful fun with which he would turn a task into a joy. But when the fun was over the little girl would find that she had learnt the lesson (all unknowingly) just the same. Happy little girls who had such a master.Page 5 (The Story of Lewis Carroll (1899))
The land of easy Mathematics where he who works adds up and he who retires subtracts.Núria Añó, in the short story 2066. Beginning the age of correction
The subject of management science has evolved for more than 60 years and is now a mature field within the broad category of applied Mathematics. This book will emphasize both the applied and mathematical aspects of management science.Wayne Winston, ?S. Albright (2011) Practical Management Science. p. 3
I have often been surprised that Mathematics, the quintessence of Truth, should have found admirers so few and so languid. Frequent consideration and minute scrutiny have at length unravelled the cause: viz . that though Reason is feasted, Imagination is starved; whilst Reason is luxuriating in its proper Paradise, Imagination is wearily travelling on a dreary desert.Samuel Taylor Coleridge
Mathematics is the language in which God wrote the universe.Attributed to Galileo Galilei in Statistics: Concepts and Applications (1994) by Harry Frank and Steven C. Althoen, p. xxi
Beauty isthe first test: there isno permanent place in the world for ugly Mathematics.1941A Mathematician's Apology.
You need only a sheet of paper and so Mathematics starts.Interview of Guido Beck by John Heilbron on April 22, 1967, Niels Bohr Library & Archives, American Institute of Physics, College Park, MD USA
There are problems to whose solution I would attach an infinitely greater importance than to those of Mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.carl friedrich gauss
Poetry is a sort of inspired Mathematics, which gives us equations, not for abstract figures, triangles, squares, and the like, but for the human emotions. If one has a mind which inclines to magic rather than science, one will prefer to speak of these equations as spells or incantations; it sounds more arcane, mysterious, recondite.ezra pound
It seems to me now that Mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true.bertrand russell
It was, however, from Spain, and not from Arabia, that a knowledge of eastern Mathematics first came into western Europe. The Moors had established their rules in Spain in 747, and by the tenth or eleven century had attained a high degree of civilisation.W. W. Rouse Ball, A Short Account of the History of Mathematics (1888), Courier Dover, 1960, p.164
No one really knew the sciences except the Lord Robert, Bishop of Lincoln, by reason of his length of life and experience, as well as of his studiousness and zeal. He knew Mathematics and perspective, and there was nothing which he was unable to know; and at the same time he was sufficiently acquainted with languages to be able to understand the saints and the philosophers and the wise men of antiquity but his knowledge of languages was not such as to enable him to effect translations until the latter portion of his life...roger bacon
Like all of Mathematics, game theory is a tautology whose conclusions are true because they are contained in the premises.Thomas Flanagan (1998) Game Theory and Canadian Politics Chapter 10, What Have We Learned?, p. 164
Mystical doctrines as to the relation of time to eternity are also reinforced by pure Mathematics, for the mathematical objects, such as numbers, if real at all, are eternal and not in time. Such eternal objects can be conceived as God's thoughts. Hence Plato's doctrine that God is a geometer, and Sir James Jeans' belief that He is addicted to arithmetic.Book One, Part I, Chapter III, Pythagoras, p. 37
Bacon not only despised the syllogism, but undervalued Mathematics, presumably as insufficiently experimental. He was virulently hostile to Aristotle , but he thought very highly of Democritus , Although he did not deny that the course of nature exemplifies a Divine purpose, he objected to any admixture of teleological explanation in the actual investigation of phenomena; everything, he held, should be explained as following necessarily from efficient causes .bertrand russell
Computer science is neither Mathematics nor electrical engineeringAlan Perlis (1968) title of article "Computer Science is neither Mathematics nor Electrical Engineering" in: A. Finerman (Hg.), University Education in Computing Science, New York, London, pp. 69-77
Ever since Plato most philosophers have considered it part of their business to produce ‘proofs’ of immortality and the existence of God . They have found fault with the proofs of their predecessors Saint Thomas rejected Saint Anselm's proofs, and Kant rejected Descartes ' but they have supplied new ones of their own. In order to make their proofs seem valid, they have had to falsify logic , to make Mathematics mystical , and to pretend that deep seated prejudices were heaven-sent intuitions .Bertrand Russell, in Ie – Evaluating “Proofs” of God’s Existence, Zenofzero.net, 30 October 2012
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