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.
It is now quite lawful for a Catholic woman to avoid pregnancy by a resort to Mathematics, though she is still forbidden to resort to physics and chemistry.h. l. mencken
Origami helps in the study of Mathematics and science in many ways. ... Using origami anyone can become a scientific experimenter with no fuss.Martin Kruskal
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
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 is the gate and key of the sciences... Neglect of Mathematics works injury to all knowledge , since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus Ignorant are unable to perceive their own ignorance and so do not seek a remedy.roger bacon
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.
Like all of Mathematics, game theory is a tautology whose conclusions are true because they are contained in the premises.thomas flanagan
Three principles — the conformability of nature to herself, the applicability of the criterion of simplicity, and the "unreasonable effectiveness" of certain parts of Mathematics in describing physical reality — are thus consequences of the underlying law of the elementary particles and their interactions. Those three principles need not be assumed as separate metaphysical postulates. Instead, they are emergent properties of the fundamental laws of physics.murray gell-mann
Thanks to my memory, which enabled me to quote Latin and to discuss Greek and Roman civilization, it became obvious to some of my colleagues in other fields that I was interested in things outside Mathematics. This lead quickly to very pleasant relationships.stanislaw ulam
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.
The land of easy Mathematics where he who works adds up and he who retires subtracts.Núria Añó
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.
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.
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.
Mathematics my foot! Algorithms are Mathematics too, and often more interesting and definitely more useful.doron zeilberger
Wherever Mathematics is mixed up with anything, which is outside its field, you will find attempts to demonstrate these merely conventional propositions a priori, and it will be your task to find out the false deduction in each case.carl gustav jacob jacobi
[Mathematics is] the science that draws necessary conclusions.
The new art must be based upon science — in particular, upon Mathematics, as the most exact, logical, and graphically constructive of the sciences.albrecht dürer
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
Let me also remind you that zero, like all of Mathematics, is fictional and an idealization. It is impossible to reach absolute zero temperature or to get perfect vacuum. Luckily, Mathematics is a fairyland where ideal and fictional objects are possible.doron zeilberger
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.
Like all of Mathematics, game theory is a tautology whose conclusions are true because they are contained in the premises.
Mystical doctrines as to the relation of time to eternity are also reinforced by pure Mathematics, for the mathematical objects, such as numbers, if real at all, are eternal and not in time. Such eternal objects can be conceived as God's thoughts. Hence Plato's doctrine that God is a geometer, and Sir James Jeans' belief that He is addicted to arithmetic.
Computer science is neither Mathematics nor electrical engineering
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.