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.
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
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.
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
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.
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.
As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.james joseph sylvester
I have often been surprised that Mathematics, the quintessence of Truth, should have found admirers so few and so languid. Frequent consideration and minute scrutiny have at length unravelled the cause: viz . that though Reason is feasted, Imagination is starved; whilst Reason is luxuriating in its proper Paradise, Imagination is wearily travelling on a dreary desert.Samuel Taylor Coleridge
The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of Mathematics consists in the analysis of Symbolic Logic itself.bertrand russell
Beauty isthe first test: there isno permanent place in the world for ugly Mathematics.
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.isa bowman
There is no branch of Mathematics, however abstract, which may not some day be applied to phenomena of the real world.
It is almost as hard to define Mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, “Economics is what economists do,” and say that Mathematics is what mathematicians do. A large part of Mathematics deals with the formal relations of quantities or numbers.kenneth boulding
[W]hen Galileo discovered he could use the tools of Mathematics and mechanics to understand the motion of celestial bodies, he felt, in the words of one imminent researcher, that he had learned the language in which God recreated the universe . Today we are learning the language in which God created life . We are gaining ever more awe for the complexity, the beauty , the wonder of God's most divine and sacred gift.
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 the forces and materials of nature, and since this utilization is accomplished in nearly all cases by machines, or by processes working through machines, it is evident that mechanical engineering is the basis of aU art and industry.
* 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.
One of the most frequently mentioned equations was Euler 's equation, Respondents called it "the most profound mathematical statement ever written"; "uncanny and sublime"; "filled with cosmic beauty "; and " mind -blowing". Another asked: "What could be more mystical than an imaginary number interacting with real numbers to produce nothing ?" The equation contains nine basic concepts of Mathematics once and only once in a single expression. These are: e (the base of natural logarithms); the exponent operation; ?; plus (or minus, depending on how you write it); multiplication; imaginary numbers; equals; one; and zero.
Today's scientists have substituted Mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
The land of easy Mathematics where he who works adds up and he who retires subtracts.