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.
General Systems Theory is a name which has come into use to describe a level of theoretical model-building which lies somewhere between the highly generalized constructions of pure Mathematics and the specific theories of the specialized disciplines. Mathematics attempts to organize highly general relationships into a coherent system, a system however which does not have any necessary connections with the "real" world around us. It studies all thinkable relationships abstracted from any concrete situation or body of empirical knowledge.Kenneth Boulding (1956) "General systems theory - the skeleton of science" in: Management Science, Vol.2. No. 3. (April 1956) p.197: Opening sentences
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
At present, when the prevailing forms of society have become hindrances to the free expression of human powers, it is precisely the abstract branches of science, Mathematics and theoretical physics, which ... offer a less distorted form of knowledge than other branches of science which are interwoven with the pattern of daily life, and the practicality of which seemingly testifies to their realistic character.max horkheimer
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
It is noteworthy that modern Platonists , almost without exception, are ignorant of Mathematics, in spite of the immense importance that Plato attached to arithmetic and geometry, and the immense influence that they [these studies] had on his philosophy. This is an example of the evils of specialization: a man must not write on Plato unless he has spent so much of his youth on Greek as to have no time for the things that Plato thought important.Book One, Part II, Chapter XV, The Theory of Ideas, p. 132
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
He has made contributions to many areas of science; among them are agronomy , anthropology, astronomy, bacteriology, botany, economics, forestry, meteorology, psychology, public health, and-above all-genetics, in which he is recognized as one of the leaders. Out of this varied scientific research and his skill in Mathematics, he has evolved systematic principles for the interpretation of empirical data; and he has founded a science of experimental design. On the foundations he has laid down, there has been erected a structure of statistical techniques that are used whenever men attempt to learn about nature from experiment and observation.ronald fisher
Science and Mathematics Run parallel to reality , they symbolize it, they squint at it, They never touch it: consider what an explosion Would rock the bones of men into little white fragments and unsky the world If any mind for a moment touch truth .Robinson Jeffers, in "The Silent Shepherds" (1958)
Grosseteste was deeply concerned with the detailed investigation of natural phenomena. It was the inspiration of this attitude of mind, together with Grosseteste's emphasis on the importance of Mathematics, that was perhaps his chief legacy to thinkers in fourteenth-century Oxford who were developing the beginnings of a mathematical physics.Neil Lewis, "Robert Grosseteste" Stanford Encyclopedia of Philosophy (2007, 2013)
We can no more have exact religious thinking without theology, than exact mensuration and astronomy without Mathematics, or exact iron-making without chemistry,John Hall (Presbyterian pastor) (1895) Dictionary of Burning Words of Brilliant Writers p.580.
Math is perfect (in principle), but mathematicians are not (because they are humans), hence the Mathematics that (human) mathematicians do is influenced by the weltanschauung of the people around them.Doron Zeilberger "Computerized Deconstruction". Appeared in Adv. Appl. Math. v. 31 (2003), 532-543.
India was the motherland of our race, and Sanskrit the mother of Europe's languages: she was the mother of our philosophy; mother, through the Arabs, of much of our Mathematics; mother, through the Buddha , of the ideals embodied in Christianity; mother, through the village community, of self-government and democracy. Mother India is in many ways the mother of us all.Will Durant, in The Case for India (1931)
Anyone who cannot cope with Mathematics is not fully human. At best he is a tolerable sub-human who has learned to wear shoes, bathe, and not make messes in the house.Robert Heinlein, Time Enough For Love (1973), and again in The Notebooks of Lazarus Long (1978)
If perchance there should be foolish speakers who, together with those ignorant of all Mathematics , will take it upon themselves to decide concerning these things, and because of some place in the Scriptures wickedly distorted to their purpose, should dare to assail this my work, they are of no importance to me, to such an extent do I despise their judgment as rash .Nicolaus Copernicus, in The metaphysical foundations of modern physical science, p.39
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