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
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
As a mathematician, von Neumann was quick, brilliant, efficient, and enormously broad in scientific interests beyond Mathematics itself. He knew his technical abilities; his virtuosity in following complicated reasoning and his insights were supreme; yet he lacked absolute self confidence.stanislaw ulam
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
The idea of an isolated American painting , so popular in this country during the thirties, seems absurd to me, just as the idea of a purely American Mathematics or physics would seem absurd... And in another sense, the problem doesn’t exist at all; or, if it did, would solve itself: An American is an American and his painting would naturally be qualified by the fact, whether he wills or not. But the basic problems of contemporary painting are independent of any one country.jackson pollock
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
(Econometrics is) the unification of economic theory, statistics and Mathematics .Ragnar Frisch, quoted in: Warren Page (2013) Applications of Mathematics in Economics. p. 75
If in other sciences we should arrive at certainty without doubt and truth without error , it behooves us to place the foundations of knowledge in Mathematics...Bk. 1, ch. 4. Translated by Robert B. Burke, in: Edward Grant (1974) Source Book in Medieval Science. Harvard University Press. p. 93
If scientific reasoning were limited to the logical processes of arithmetic, we should not get far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the Mathematics of probability. The abacus, with its beads strung on parallel wires, led the Arabs to positional numeration and the concept of zero many centuries before the rest of the world; and it was a useful tool so useful that it still exists.Vannevar Bush (1945) As We May Think
Lateral thinking... is the process of using information to bring about creativity and insight restructuring. Lateral thinking can be learned, practised and used. It is possible to acquire skill in it just as it is possible to acquire skill in Mathematics .Edward de Bono (1970) Lateral thinking: creativity step by step p. 5
I cannot recall a period when I did not draw; and at school, the studies that were distasteful to me, Mathematics and grammar , were retarded by the indulgence of teachers who were proud of my drawing faculties, and passed over my neglect of uncongenial subjects.Jacob Epstein in: Milton Hindus The Jewish East Side: 1881 – 1924, Transaction Publishers, p.6
If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in Mathematics.Roger Bacon Opus Majus, Book 1, Chapter 4.
Trivialism arises from the idea that Mathematics is classical and there is contradiction in Mathematics, and therefore (under our old classical reasoning), all of Mathematics is true , we then get to the meaninglessness of any particular mathematical statement and wallow in our degenerate theory .Koji Tanaka, et al., in "Paraconsistency: Logic and Applications: Logic and Applications", p.296
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