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
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
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.
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
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
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.
Men are constantly attracted and deluded by two opposite charms: the charm of competence which is engendered by Mathematics and everything akin to Mathematics, and the charm of humble awe, which is engendered by meditation on the human soul and its experiences. Philosophy is characterized by the gentle, if firm, refusal to succumb to either charm.leo strauss
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
Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.Albert Einstein
Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.
[There is] a delusion that macro-economics is both viableanduseful (a delusionencouraged by its extensive use of Mathematics, which must always impress politicians lacking any mathematical education, and which is really the nearest thing to the practice of magic that occurs among professional economists).
Sexually progressive cultures gave us Mathematics, literature, philosophy, civilization and the rest, while sexually restrictive cultures gave us the Dark Ages and the Holocaust. Not that I’m trying to load my argument, of course.alan moore
Great physics does not automatically imply complicated Mathematics!martinus j. g. veltman
Our future rates of gain will fall far short of those achieved in the past. Berkshire's capital base is now simply too large to allow us to earn truly outsized returns. If you believe otherwise, you should consider a career in sales but avoid one in Mathematics (bearing in mind that there are really only three kinds of people in the world: those who can count and those who can't).warren buffett
It was an All-in-One and One-in-All of limitless being and self not merely a thing of one Space-Time continuum, but allied to the ultimate animating essence of existence's whole unbounded sweep the last, utter sweep which has no confines and which outreaches fancy and Mathematics alike. It was perhaps that which certain secret cults of earth have whispered of as YOG-SOTHOTH, and which has been a deity under other names; that which the crustaceans of Yuggoth worship as the Beyond-One, and which the vaporous brains of the spiral nebulae know by an untranslatable Sign...h. p. lovecraft
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity . The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in Mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.alan turing
God used beautiful Mathematics in creating the world.paul dirac