Popular quotes about Mathematics! Wisdom and inspiration are here! | page 17
Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.
Richard AskeyWhat, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?
David Eugene SmithThe proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself.
Barry MazurIt has been a fortunate fact in the modern history of physical science that the scientist constructing a new theoretical system has nearly always found that the mathematics. . . required. . . had already been worked out by pure mathematicians for their own amusement. . . . The moral for statesmen would seem to be that, for proper scientific "planning", pure mathematics should be endowed fifty years ahead of scientists.
R. B. BraithwaiteI think mathematics is a vast territory. The outskirts of mathematics are the outskirts of mathematical civilization. There are certain subjects that people learn about and gather together. Then there is a sort of inevitable development in those fields. You get to the point where a certain theorem is bound to be proved, independent of any particular individual, because it is just in the path of development.
William ThurstonSo 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 ChaitinThe calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
John von NeumannMathematics 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 is the surest way to immortality. If you make a big discovery in mathematics, you will be remembered after everyone else will be forgotten
Paul ErdosOur teaching of mathematics revolves around a fundamental conflict. Rightly or wrongly, students are required to master a series of mathematical concepts and techniques, and anything that might divert them from doing so is deemed unnecessary. Putting mathematics into its cultural context, explaining what is has done for humanity, telling the story of its historical development, or pointing out the wealth of unsolved problems or even the existence of topics that do not make it into school textbooks leaves less time to prepare for the exam. So most of these things aren't discussed.
Ian StewartMathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.
Deepak ChopraThe totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience.
Willard Van Orman QuineTaking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half.
Gottfried LeibnizAll the sciences have a relation, greater or less, to human nature; and...however wide any of them may seem to run from it, they still return back by one passage or another. Even Mathematics, Natural Philosophy, and Natural Religion, are in some measure dependent on the science of MAN; since they lie under the cognizance of men, and are judged of by their powers and faculties.
David HumeI 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 LockeMathematics-a wonderful science, but it hasn't yet come up with a way to divide one tricycle between three small boys.
Earl WilsonMathematics is the art of accurate reasoning on inaccurately-drawn figures... let that be our motto.
Arthur MattuckOne would normally define a "religion" as a system of ideas that contain statements that cannot be logically or observationally demonstrated... Gรถdels theorem not only demonstrates that meathematics is a religion, but shows that mathematics is the only religion that proves itself to be one!
John D. BarrowI 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. ThompsonThe word "mathematics" is a Greek word and, by origin, it means "something that has been learned or understood," or perhaps "acquired knowledge," or perhaps even, somewhat against grammar, "acquirable knowledge," that is, "learnable knowledge," that is, "knowledge acquirable by learning."
Salomon Bochner... we should not be disappointed that everyday language does not work any longer at the apex of our little theory. It is natural; like poetry, the very reason for the existence of mathematics is that it expresses thoughts and feelings which we cannot express in mundane everyday language.
Alexandre BorovikI merely say that all reading for pleasure is escape, whether it be Greek, mathematics, astronomy, Benedetto Croce, or The Diary of the Forgotten Man. To say otherwise is to be an intellectual snob, and a juvenile at the art of living.
Raymond ChandlerThere 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 WienerOf the properties of mathematics, as a language, the most peculiar one is that by playing formal games with an input mathematical text, one can get an output text which seemingly carries new knowledge. The basic examples are furnished by scientific or technological calculations: general laws plus initial conditions produce predictions, often only after time-consuming and computer-aided work. One can say that the input contains an implicit knowledge which is thereby made explicit.
IU?. I. ManinIf people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
John von NeumannMathematics is concerned only with the enumeration and comparison of relations.
Carl Friedrich GaussThus 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 EulerMy occupation is an open question. I was once an assistant professor of mathematics. Since then, I have spent time living in the woods of Montana.
Theodore KaczynskiWe have these amazing gifts of music and mathematics and painting and Olympic running. I mean, we're the animal that is best of all the animals at long-distance running. Why? It is quite amazing. Superfluous gifts you don't really need to survive.
Freeman DysonThere was a transition going on - Baghdad being the intellectual capital of the world where major advances were made in agriculture and mathematics and engineering and medicine and astronomy, and then that all sort of collapsed. And I was trying to understand how such a intellectually fertile environment can lose its compass bearing. Because I think about the creative centers today - countries, or even regions. Will Silicon Valley always be as innovative? Will the United States be innovative, or will we become complacent?
Neil deGrasse TysonThe economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.
Paul KrugmanThe truth is that you can divide your heart in all sorts of interesting ways - a little here, a little there, most banked at home, some of it coined out for a flutter. But love cleaves through the mind's mathematics. Love's lengthways splits the heart in two - the heart where you are, the heart where you want to be. How will you heal your heart when love has split it in two?
Jeanette WintersonThe true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
Bertrand RussellPure mathematics is, in its way, the poetry of logical ideas. ... [By seeking] logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.
Albert EinsteinMost of the arts, as painting, sculpture, and music, have emotional appeal to the general public. This is because these arts can be experienced by some one or more of our senses. Such is not true of the art of mathematics; this art can be appreciated only by mathematicians, and to become a mathematician requires a long period of intensive training. The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose.
Cornelius LanczosOur faith in Mathematics is not likely to wane if we openly acknowledge that the personalities of even the greatest mathematicians may be as flawed as those of anyone else.
Gian-Carlo RotaIf you learn music, you'll learn history. If you learn music, you'll learn mathematics. If you learn music, you'll learn most all there is to learn.
Edgar CaycePerhaps there will be prattlers who, although completely ignorant of mathematics, nevertheless take it upon themselves to pass judgment on mathematical questions, and on account of some passage in Scripture, badly distorted to their purpose, will dare to censure and assail what I have presented here.
Nicolaus CopernicusQuestions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.
Giuseppe Peano