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.
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
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
Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [...] The proliferation of programming languages shows no more uniformity than Mathematics. Nevertheless, programming languages do bring a different perspective. [...] Because of their application to a broad range of topics, their strict grammar, and their strict interpretation, programming languages can provide new insights into mathematical notation.kenneth e. iverson
Magic is that which it is; it is by itself, like the Mathematics; for it is the exact and absolute science of Nature and its laws . Magic is the science of the Ancient Magi: and the Christian religion, which has imposed silence on the lying oracles, and put an end to the prestiges of the false Gods , itself reveres those Magi who came from the East, guided by a Star , to adore the Saviour of the world in His cradle.albert pike
The study of Mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.Alfred North Whitehead
It must be owned (...) that all the knowledge, whether of physic, astronomy, philosophy, or Mathematics, which flourished in Europe from the tenth century, was originally derived from them; and that the Spanish Saracens, in a more particular manner, may be looked upon as the fathers of European philosophy.Johann Lorenz von Mosheim, An Ecclesiastical History, Samuel Etheridge, t.2, 1810, p.388
Herbert A. Simon's scientific output goes far beyond the disciplines in which he has held professorships: political science, administration, psychology and information sciences. He has made contributions in the fields of science theory, applied Mathematics, statistics, operations research, economics and business and public administration (and), in all areas in which he has conducted research, Simon has had something of importance to say."The Royal Swedish Academy of Sciences (1978) "Nobel Prize announcement of the Royal Academy of Sciences in Sweden, 16 okt. 1978"
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
For many parts of Nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity , nor accommodated unto use with sufficient dexterity, without the aid and intervening of the Mathematics , of which sort are perspective, music , astronomy , cosmography , architecture , engineery, and divers others.Sir Francis Bacon, in Tom Sorell, et al., Scientia in Early Modern Philosophy: Seventeenth-Century Thinkers on Demonstrative Knowledge from First Principles, Springer, 28 October 2009, p.4
God used beautiful Mathematics in creating the world.Paul Dirac, as quoted in The Cosmic Code : Quantum Physics As The Language Of Nature (1982) by Heinz R. Pagels, p. 295; also in Paul Adrien Maurice Dirac : Reminiscences about a Great Physicist (1990) edited by Behram N. Kursunoglu and Eugene Paul Wigner, p. xv.
A trivial philosophy of Mathematics holds that every well-formed mathematical formula, in any language of Mathematics is true (and its negation is true), and any philosophical sentence about Mathematics is also true.Koji Tanaka, et al., in "Paraconsistency: Logic and Applications: Logic and Applications", p.296
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