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 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
When I came back from Munich, it was September, and I was Professor of Mathematics at the Eindhoven University of Technology. Later I learned that I had been the Department's third choice, after two numerical analysts had turned the invitation down; the decision to invite me had not been an easy one, on the one hand because I had not really studied Mathematics, and on the other hand because of my sandals, my beard and my "arrogance" (whatever that may be).edsger w. dijkstra
Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.Friedrich Nietzsche, as quoted in The Puzzle Instinct : The Meaning of Puzzles in Human Life? (2004) by Marcel Danesi, p. 71.
Mathematics is good for the soul, getting things right enlivens a sense of truth, efforts to understand automatically purify desires.Iris Murdoch, Metaphysics As A Guide To Morals, p. 178
Grattan-Guiness's uniformly interesting and valuable account of the interwoven development of logic and related fields of Mathematics . . . between 1870 and 1940 presents a significantly revised analysis of the history of the period. . . . [His] book is important because it supplies what has been lacking: a full account of the period from a primary mathematical perspective.ivor grattan-guinness
Discovery in Mathematics is not a matter of logic. It is rather the result of mysterious powers which no one understands, and in which unconscious recognition of beauty must play an important part. Out of an infinity of designs, a mathematician chooses one pattern for beauty's sake and pulls it down to earth.marston morse
When we ask what ought to be the relative remunerations of a nurse or a butcher, or a coal miner and a judge at a high court, of the deep sea diver of the cleaner of sewers, of the organiser of a new industry and a jockey, of the inspector of taxes and the inventor of a life-saving drug, of the jet-pilot or the professor of Mathematics, the appeal to 'social justice' does not give us the slightest help in deciding…friedrich hayek
Mechanical Engineering may be defined as being the application of Mathematics to Science, with particular reference to the design and fabrication of all forms of machinery. Since engineering is the combined science and art of utilizing theUnited States. Congress. Senate (1898) Senate Documents, Otherwise Publ. as Public Documents and Executive Documents: 14th Congress, 1st Session-48th Congress, 2nd Session and Special Session. p. 245
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.Kenneth E. Iverson (1979) Notation as a Tool of Thought. §5.4
But one will say, 'What is the principal behind these scales, and what, if not acoustic phenomena and the laws of Mathematics, has set the order of their tones?' I respond that this principle is purely metaphysical [anthropological]. We conceive this order and the melodic and harmonic phenomena that spring from it out of our conformation and education. (p.249)Hugo Riemann, cited in Gurlitt, W. (1950). "Hugo Riemann (1849-1919)".
The terms synthesis and analysis are used in Mathematics in a more special sense than in logic. In ancient Mathematics they had a different meaning from what they now have. The oldest definition of mathematical analysis as opposed to synthesis is that given in Euclid , XIII. 5, which in all probability was framed by Eudoxus: "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it."Florian Cajori, A History of Mathematics (1893). p. 30
The land of easy Mathematics where he who works adds up and he who retires subtracts.Núria Añó, 2066. Beginning the age of correction
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