Popular quotes about Mathematics! Wisdom and inspiration are here! | page 26
Statistics is, or should be, about scientific investigation and how to do it better, but many statisticians believe it is a branch of mathematics. Now I agree that the physicist, the chemist, the engineer, and the statistician can never know too much mathematics, but their objectives should be better physics, better chemistry, better engineering, and in the case of statistics, better scientific investigation. Whether in any given study this implies more or less mathematics is incidental.
George E. P. BoxThis is a wonderful book, unique and engaging. Diaconis and Graham manage to convey the awe and marvels of mathematics, and of magic tricks, especially those that depend fundamentally on mathematical ideas. They range over many delicious topics, giving us an enchanting personal view of the history and practice of magic, of mathematics, and of the fascinating connection between the two cultures. Magical Mathematics will have an utterly devoted readership.
Barry MazurI don't think that everyone should become a mathematician, but I do believe that many students don't give mathematics a real chance. I did poorly in math for a couple of years in middle school; I was just not interested in thinking about it. I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers.
Maryam MirzakhaniOne of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.
Benoit MandelbrotMathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
David HilbertOnly dead mathematics can be taught where the attitude of competition prevails: living mathematics must always be a communal possession.
Mary Everest BoolePure mathematics is on the whole distinctly more useful than applied... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.
G. H. HardyThe propositions of mathematics have, therefore, the same unquestionable certainty which is typical of such propositions as "All bachelors are unmarried," but they also share the complete lack of empirical content which is associated with that certainty: The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter.
Carl Gustav HempelThough the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.
Keith DevlinFor me, rhythm is a type of divine mathematics in a way. No matter where you're from, we can all understand the mathematics of rhythm. I try to apply this mathematical thinking to my playing.
John McLaughlinIt seems that every practitioner of physics has had to wonder at some point why mathematics and physics have come to be so closely entwined. Opinions vary on the answer. ..Bertrand Russell acknowledged..'Physics is mathematical not because we know so much about the physical world, but because we know so little.' ..Mathematics may be indispensable to physics, but it obviously does not constitute physics.
Etienne KleinVery few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languanges of the world than to master all mathematics at present known.
W. W. SawyerMathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself.
Paul LockhartMathematics without natural history is sterile, but natural history without mathematics is muddled.
John Maynard SmithA Noah's Ark of mathematicians, their lives, loves, hard times, and madnesses, Loving and Hating Mathematics shows our community with all its warts as well as its triumphs. I especially liked the chapter on much-hated school mathematics, 'Almost All Children Left Behind.'
David MumfordMathematics, in the common lay view, is a static discipline based on formulas...But outside the public view, mathematics continues to grow at a rapid rate...the guid to this growth is not calculation and formulas, but an open ended search for pattern.
Lynn SteenMathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.
Vladimir ArnoldThe principles of logic and mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.
A.J. AyerWhere mathematics and spirit join, where proof of the existence of mystery-salvific mystery-shimmers just below the surfaces of human perception, experience and the linguistic veil itself, Killarney Clary's new book-her best to date-dwells, plumbs, persuades and thrills.
Jorie GrahamMathematics may be the only exception in the sciences that leaves no room for skepicism. But, if mathematical results are exact as no empirical law can ever be, philosophers have discovered that they are not absolutely novel - instead, they are tautological.
Luigi Luca Cavalli-SforzaThat is, you can have nothingness, absolute nothingness for maybe a tiny fraction of a second, if a second can be defined in that arena, but then it falls apart into a something and an anti-something. And that something is then what we call the universe. But can we really understand that or put rigorous mathematics or testable experiments against that? Not yet. So one of the big holy grail of physics is to understand why there is something rather than nothing.
Brian GreeneAll mathematicians share... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics.
Martin GardnerIn short, if we adhere to the standard of perfection in all our endeavors, we are left with nothing but mathematics and the White Album.
Daniel GilbertMuch of what we know about mathematics and trade comes from the Arabs. Then came stagnation, and now they're the West's whipping boy. This is a problem that cannot be solved overnight, and certainly not militarily.
Brent ScowcroftEducation is like a diamond with many facets: It includes the basic mastery of numbers and letters that give us access to the treasury of human knowledge, accumulated and refined through the ages; it includes technical and vocational training as well as instruction in science, higher mathematics, and humane letters.
Ronald ReaganMost people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.
G. H. HardyI doubt not, but from self-evident Propositions, by necessary Consequences, as incontestable as those in Mathematics, the measures of right and wrong might be made out.
John LockeThe development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.
Kurt GรถdelIn mathematics, two angles that are said to coincide fit together perfectly. The word "coincidence" does not describe luck or mistakes. It describes that which fits together perfectly.
Wayne DyerThe power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us.
Ian StewartDoing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.
Paul LockhartIn our civilization, there are permanent forms which are part of every epoch and every culture. They are not especially difficult to detect. A minimal knowledge of physics, astrophysics, and perhaps mathematics, brings to light certain patterns that make these subjects easier to understand. It is striking to see the extreme similarity between these scientific propositions and the forms that recur in all times, places and civilizations.
Philippe StarckMathematical study and research are very suggestive of mountaineering. Whymper made several efforts before he climbed the Matterhorn in the 1860's and even then it cost the life of four of his party. Now, however, any tourist can be hauled up for a small cost, and perhaps does not appreciate the difficulty of the original ascent. So in mathematics, it may be found hard to realise the great initial difficulty of making a little step which now seems so natural and obvious, and it may not be surprising if such a step has been found and lost again.
Louis J. MordellI have long admired Ron Whitehead. He is crazy as nine loons, and his poetry is a dazzling mix of folk wisdom and pure mathematics
Hunter S. ThompsonBut I simply can't stand a view limited to this earth, I feel life is so small unless it has windows into other worlds...I like mathematics largely because it is not human.
Bertrand RussellThinking - in particular abstract thinking, which most of us are introduced to through the study of mathematics and literature - helps us learn that we can become problem solvers.
Kathryn LaskyThere are fields of scientific work...which have been explored from the different sides of pure mathematics, statistics, electrical engineering, and neurophysiology...in which every single notion receives a separate and different name from each group, and in which important work has been triplicated or quadruplicated, while still other important work is delayed by the unavailability in one field of results that may have already become classical in the next field.
Norbert WienerBy simple mathematics giving is key to the world you seek to live in. If I take I alone gain. If I give or share then two at least are enriched.
Rasheed OgunlaruThus you see, most noble Sir, how this type of solution to the Kรถnigsberg bridge problem bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle.
Leonhard EulerCombinatorics is an honest subject. No adรจles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven't. You get the feeling that the result you have discovered is forever, because it's concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing; you don't get a feeling of having done an honest day's work. Don't get the wrong idea - combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.
Gian-Carlo RotaRemote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos [mathematics], where pure thought can dwell in its natural home.
Bertrand RussellAnd as for Mixed Mathematics, I may only make this prediction, that there cannot fail to be more kinds of them, as nature grows further disclosed.
Francis Bacon