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
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
Mathematics is the queen of the sciences and number theory is the queen of Mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.Carl Friedrich Gauss, in Gauss zum Gedächtniss (1856) by Wolfgang Sartorius von Waltershausen, as translated in Memorabilia Mathematica; or, The Philomath's Quotation-Book (1914) by Robert Édouard Moritz, p. 271
The principles of logic and Mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and Mathematics are analytic propositions or tautologies.alfred jules ayer
We had principles in Mathematics that were granted to be absolute in Mathematics for over 800 years, but new science has gotten rid of those absolutism, gotten forward other different logics of looking at Mathematics, and sort of turned the way we look at it as a science altogether after 800 years.mahmoud ahmadinejad
As soon as a thought or word becomes a tool, one can dispense with actually ‘thinking’ it, that is, with going through the logical acts involved in verbal formulation of it. As has been pointed out, often and correctly, the advantage of Mathematics the model of all neo-positivistic thinking lies in just this ‘intellectual economy.’ Complicated logical operations are carried out without actual performance of the intellectual acts upon which the mathematical and logical symbols are based. … Reason … becomes a fetish, a magic entity that is accepted rather than intellectually experienced.max horkheimer
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
In Mathematics the art of asking questions is more valuable than solving problems.Georg Cantor (1867) Doctoral thesis
Questions that pertain to the foundations of Mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.Giuseppe Peano (1889) Arithmetices Principia, nova methodo exposita [The Principles of Arithmetic, presented by a new method]
Tantra is a very very poetic approach, not arithmetical. And tantra believes in love, not in Mathematics. It believes in sudden enlightenment.Osho in P.125 (Tantra: The Supreme Understanding: Discourses on the Tantric Way of Tilopa's Song of Mahamudra)
The land of easy Mathematics where he who works adds up and he who retires subtracts.Núria Añó, 2066. Beginning the age of correction
... one of the basic principles of higher Mathematics is the contradiction that in certain circumstances straight lines and curves may be the same.... But even lower Mathematics teems with contradictions.Engels, in "Selected Works of Mao Tse-tung On Contradiction".
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