Popular quotes about Mathematics! Wisdom and inspiration are here! | page 34
May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.
James Joseph Sylvester. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories -- specifically, on the category of all functions. Now much of Mathematics is dynamic, in that it deals with morphisms of an object into another object of the same kind. Such morphisms (like functions) form categories, and so the approach via categories fits well with the objective of organizing and understanding Mathematics. That, in truth, should be the goal of a proper philosophy of Mathematics.
Saunders Mac LaneThere is no thing as a man who does not create mathematics and yet is a fine mathematics teacher. Textbooks, course material-these do not approach in importance the communication of what mathematics is really about, of where it is going, and of where it currently stands with respect to the specific branch of it being taught. What really matters is the communication of the spirit of mathematics. It is a spirit that is active rather than contemplative-a spirit of disciplined search for adventures of the intellect. Only as adventurer can really tell of adventures.
Alfred AdlerAll our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is"... and so we find that we have adapted a religion strikingly similar to many traditional faiths. Change "mathematics" to "God" and little else might seem to change. The problem of human contact with some spiritual realm, of timelessness, of our inability to capture all with language and symbol-all have their counterparts in the quest for the nature of Platonic mathematics.
John D. BarrowIt is impossible to overstate the imporance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps... Every new discovery in mathematics, results from an attempt to solve some problem.
Howard Whitley EvesMathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional. In E. T. Bell Men of Mathematics, New York: Simona and Schuster, 1937.
Charles Proteus SteinmetzA chess problem is genuine mathematics, but it is in some way "trivial" mathematics. However, ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful-"important" if you like, but the word is very ambiguous, and "serious" expresses what I mean much better.
G. H. HardyMathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.
Ludwig WittgensteinI 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 MirzakhaniMen 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 StraussGel'fand amazed me by talking of mathematics as though it were poetry. He once said about a long paper bristling with formulas that it contained the vague beginnings of an idea which could only hint at and which he had never managed to bring out more clearly. I had always thought of mathematics as being much more straightforward: a formula is a formula, and an algebra is an algebra, but Gel'fand found hedgehogs lurking in the rows of his spectral sequences!
Dusa McDuffThough determinants and matrices received a great deal of attention in the nineteenth century and thousands of papers were written on these subjects, they do not constitute great innovations in mathematics.... Neither determinants nor matrices have influenced deeply the course of mathematics despite their utility as compact expressions and despite the suggestiveness of matrices as concrete groups for the discernment of general theorems of group theory.
Morris KlineThe 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 HempelIs mathematics doomed to suffer the same fate as other sciences that have split into separate branches?... Mathematics is, in my opinion, an indivisible whole... May the new century bring with it ingenious champions and many zealous and enthusiastic disciples.
David HilbertThe tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms.
David HilbertWe can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.
Hans ReichenbachMathematics was born and nurtured in a cultural environment. Without the perspective which the cultural background affords, a proper appreciation of the content and state of present-day mathematics is hardly possible.
Raymond Louis WilderWe sometimes think of being good at mathematics as an innate ability. You either have "it" or you don't. But to Schoenfeld, it's not so much ability as attitude. You master mathematics if you are willing to try.
Malcolm GladwellSo in the end it wasn't Gรถdel, it wasn't Turing, and it wasn't my results that are making mathematics go into an experimental mathematics direction, in a quasi-empirical direction. The reason why mathematicians are changing their working habits is the computer. I think that this is an excellent joke!
Gregory ChaitinThers is this wonderful iconoclast at Rutgers, Doron Zeilberger, who says that our mathematics is the result of a random walk, by which he means what WE call mathematics. Likewise, I think, for the sciences.
Ian HackingMathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems-general and specific statements-can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.
Christopher ZeemanMathematics 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 ArnoldTo many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples.
John B. ConwayMathematics 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-SforzaMathematics is a dangerous profession; an appreciable proportion of us go mad.
John Edensor LittlewoodThe idea here, of course, is, you know, mathematics is the language of science, it's the way that we understand the natural world. And there's definitely been a push to sort of study advanced math and kind of reawaken the love of advanced math.
Anya KamenetzFew realize that the world of modern mathematics is rich with vivid images and provocative ideas.
Ivars PetersonMathematics-a wonderful science, but it hasn't yet come up with a way to divide one tricycle between three small boys.
Earl WilsonOne of my colleagues likes to say that, mathematics is the - he thinks about the only subject that he knows in academia or in the real world where if two people disagree about something - if people are studying some mathematical object and there's supposed to be a proof and they disagree about whether this proof or not, the will go into a room, sit down and talk about it and fairly quickly or at the end of the day one of them will admit they're wrong.
Peter Woit... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It's not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I'm able to avoid or manipulate or process pain.
Louise BourgeoisI have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science; most of the few pupils who go a step further, and usually to keep the metaphor, remain in the process of gathering information, become only Halbwisser [one who has superficial knowledge of the subject], for the rarer talents do not want to have themselves educated by lecture courses, but train themselves. And with this thankless work the professor loses his precious time.
Carl Friedrich GaussJournalists say that when a dog bites a man, that is not news, but when a man bites a dog, that is news ... Thanks to the mathematics of combinatorics, we will never run out of news.
Steven PinkerModern bodybuilding is ritual, religion, sport, art, and science, awash in Western chemistry and mathematics. Defying nature, it surpasses it.
Camille PagliaI suppose you are two fathoms deep in mathematics, and if you are, then God help you. For so am I, only with this difference: I stick fast in the mud at the bottom, and there I shall remain.
Charles DarwinI found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total.
Louise BourgeoisMathematics is a vast adventure; its history reflects some of the noblest thoughts of countless generations.
Dirk Jan StruikThings like the financial markets - a proper grounding in mathematics could help the common man. I believe that if people are more familiar with mathematical concepts... it can help deal with modern life, which is increasingly complex.
Viswanathan AnandIt is generally recognised that women are better than men at languages, personal relations and multi-tasking, but less good at map-reading and spatial awareness. It is therefore not unreasonable to suppose that women might be less good at mathematics and physics.
Stephen HawkingMathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms.
Alfred AdlerMathematics had never had more than a secondary interest for him ; and even logic he cared for chiefly as a means of clearing the ground of doctrines imagined to be proved, by showing that the evidence on which they were supposed to rest had no tendency to prove them. But he had been endeavouring to give a more active and positive help than this to the cause of what he deemed pure religion.
Mary Everest Boole