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
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
Do not lose your faith. A mighty fortress is our Mathematics. Mathematics will rise to the challenge, as it always has.stanislaw ulam
Hungary, severed from half of the population and most of the natural resources that it had once claimed, had now to practice a sort of economic acupuncture, striving to know the magic nodes in the global energy flow where a pinprick could alter the workings of a major organ. Mathematics was one of the few disciplines where it was possible to exert that degree of leverage, and so the Hungarians had become phenomenally good at teaching it to their children.neal stephenson
Mathematics is not something that you find lying around in your back yard. It’s produced by the human mind. Yet if we ask where Mathematics works best, it is in areas like particle physics and astrophysics, areas of fundamental science that are very, very far removed from everyday affairs.
Grattan-Guinness has achieved a synthesis here of remarkable historical and mathematical scope and sensitivity. His book is a 'must read' for historians of science and Mathematics, as well as mathematicians.ivor grattan-guinness
Angling may be said to be so like the Mathematics that it can never be fully learnt.Izaak Walton
Being a language, Mathematics may be used not only to inform but also, among other things, to seduce.benoît mandelbrot
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.
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.
The terms synthesis and analysis are used in Mathematics in a more special sense than in logic. In ancient Mathematics they had a different meaning from what they now have. The oldest definition of mathematical analysis as opposed to synthesis is that given in Euclid , XIII. 5, which in all probability was framed by Eudoxus: "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it."