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Mathematics quotes (68)
We lay down a fundamental principle of generalization by abstraction: The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features.... Eliakim Hastings Moore Category: Mathematics
A mathematician is a device for turning coffee into theorems. Paul Erdos Category: Mathematics
The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face the blackboard and to turn his back to the class. He writes a he says b he means c; but it should be d. Some of his sayings are handed down from generation to generation. In order to solve this differential equation you look at it till a solution occurs to you. This principle is so perfectly general that no particular application of it is possible. Geometry is the science of correct reasoning on incorrect figures. My method to overcome a difficulty is to go round it. What is the difference between method and device? A method is a device which you used twice. George Polyá Category: Mathematics
... it is interesting to note that the original problem that started my research is still outstanding  namely the problem of planning or scheduling dynamically over time particularly planning dynamically under uncertainty. If such a problem could be successfully solved it could eventually through better planning contribute to the wellbeing and stability of the world. George Dantzig Category: Mathematics
Since you are now studying geometry and trigonometry I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken the cabin boy is on deck there are 12 passengers aboard the wind is blowing EastNorthEast the clock points to a quarter past three in the afternoon. It is the month of May. How old is the captain? Gustave Flaubert Category: Mathematics
About Thomas Hobbes: He was 40 years old before he looked on geometry; which happened accidentally. Being in a gentlemans library Euclids Elements lay open and twas the 47 El. libri I [Pythagoras Theorem]. He read the proposition By God sayd he this is impossible: So he reads the demonstration of it which referred him back to such a proposition; which proposition he read. That referred him back to another which he also read. Et sic deinceps that at last he was demonstratively convinced of that truth. This made him in love with geometry. John Aubrey Category: Mathematics
I think youre begging the question said Haydock and I can see looming ahead one of those terrible exercises in probability where six men have white hats and six men have black hats and you have to work it out by mathematics how likely it is that the hats will get mixed up and in what proportion. If you start thinking about things like that you would go round the bend. Let me assure you of that! Agatha Christie Category: Mathematics
Mathematics is not a careful march down a wellcleared 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. W. S. Anglin Category: Mathematics
When I am violently beset with temptations or cannot rid myself of evil thoughts [I resolve] to do some Arithmetic or Geometry or some other study which necessarily engages all my thoughts and unavoidably keeps them from wandering. Jonathon Edwards Category: Mathematics
Einstein is an analytical mathematician seeking to give a physical interpretation to the conclusions of his mathematical process. In this he is hampered by a load of contradictory and absurd assumptions of the school that he follows which throws him in to all manner of difficulty. Einstein has such a faculty for embracing both sides of a contradiction that one would have to be of the same frame of mind to follow his thought it is so peculiarly his own. The whole Relativity theory is as easy to follow as the path of a bat in the air at night. Father Jeremiah Joseph Callahan Category: Mathematics
One is hard pressed to think of universal customs that man has successfully established on earth. There is one however of which he can boast the universal adoption of the HinduArabic numerals to record numbers. In this we perhaps have mans unique worldwide victory of an idea. Howard W. Eves Category: Mathematics
Mathematicians are like lovers. Grant a mathematician the least principle and he will draw from it a consequence which you must also grant him and from this consequence another. Bernard Le Bovier de Fontenelle Category: Mathematics
It is India that gave us the ingenious method of expressing all numbers by means of ten symbols each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius two of the greatest men produced by antiquity. Pierre Simon de Laplace Category: Mathematics
The union of the mathematician with the poet fervor with measure passion with correctness this surely is the ideal. William James Category: Mathematics
Mathematics may be defined as the subject in which we never know what we are talking about nor whether what we are saying is true. Bertrand Russell Category: Mathematics
For the things of this world cannot be made known without a knowledge of mathematics. Roger Bacon Category: Mathematics
... Newton was an unquestioning believer in an allwise creator of the universe and in his own inability like the boy on the seashore to fathom the entire ocean in all its depths. He therefore believed that there were not only many things in heaven beyond his philosophy but plenty on earth as well and he made it his business to understand for himself what the majority of intelligent men of his time accepted without dispute (to them it was as natural as common sense) the traditional account of the creation. Sir Isaac Newton Category: Mathematics
God exists since mathematics is consistent and the Devil exists since we cannot prove it. Andre Weil Category: Mathematics
I have hardly ever known a mathematician who was capable of reasoning. Plato Category: Mathematics
There are no sects in geometry. Francois Voltaire Category: Mathematics
Blaise Pascal Category: Mathematics
Mathematics seems to endow one with something like a new sense. Charles Robert Darwin Category: Mathematics
The most painful thing about mathematics is how far away you are from being able to use it after you have learned it. James R. Newman Category: Mathematics
You know we all became mathematicians for the same reason: we were lazy. Max Rosenlicht Category: Mathematics
I don't believe in mathematics. Albert Einstein Category: Mathematics
A mathematician is a blind man in a dark room looking for a black cat which isnt there. Charles Robert Category: Mathematics
[The works of Archimedes] are without exception monuments of mathematical exposition; the gradual revelation of the plan of attack the masterly ordering of the propositions the stern elimination of everything not immediately relevant to the purpose the finish of the whole are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader. Sir Thomas Heath Category: Mathematics
Proof is the idol before whom the pure mathematician tortures himself. Sir Arthur Stanley Eddington Category: Mathematics
Time was when all the parts of the subject were dissevered when algebra geometry and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties and we may confidently look forward to a time when they shall form but one body with one soul. J.J. Sylvester Category: Mathematics
Mathematicians boast of their exacting achievements but in reality they are absorbed in mental acrobatics and contribute nothing to society. Sorai Ogyu Category: Mathematics
Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers and we have reason to believe that it is a mystery into which the human mind will never penetrate. Leonhard Euler Category: Mathematics
In the World of Reality there is no self There is no otherthanself. Category: Mathematics
... the science of calculation also is indispensable as far as the extraction of the square and cube roots: Algebra as far as the quadratic equation and the use of logarithms are often of value in ordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; but not to be in indulged in by one who is to have a profession to follow for his subsistence. Thomas Jefferson Category: Mathematics
We come finally however to the relation of the ideal theory to real world or real probability. If he is consistent a man of the mathematical school washes his hands of applications. To someone who wants them he would say that the ideal system runs parallel to the usual theory: If this is what you want try it: it is not my business to justify application of the system; that can only be done by philosophizing; I am a mathematician. In practice he is apt to say: try this; if it works that will justify it. But now he is not merely philosophizing; he is committing the characteristic fallacy. Inductive experience that the system works is not evidence. J. E. Littlewood Category: Mathematics
On Ramanujan: I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one and that I hoped it was not an unfavorable omen. No he replied it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways. Godfrey H. Hardy Category: Mathematics
Medicine makes people ill mathematics makes them sad and theology makes them sinful. Martin Luther Category: Mathematics
In mathematics you don't understand things. You just get used to them. John Louis von Neumann Category: Mathematics
Mathematics has beauties of its own a symmetry and proportion in its results a lack of superfluity an exact adaptation of means to ends which is exceedingly remarkable and to be found only in the works of the greatest beauty. When this subject is properly ... presented the mental emotion should be that of enjoyment of beauty not that of repulsion from the ugly and the unpleasant. J. W. A. Young Category: Mathematics
Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesnt make any sense since things follow from each other and in principle whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form arent they? Alfred Renyi Category: Mathematics
Most 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 Lanczos Category: Mathematics
The mathematical life of a mathematician is short. Work rarely improves after the age of twentyfive or thirty. If little has been accomplished by then little will ever be accomplished. Alfred Adler Category: Mathematics
Without the concepts methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or achievements of mathematics in the last 50 years. [Said in 1950] Hermann Weyl Category: Mathematics
The fraction of life can be increased in value not so much By increasing your numerator as by lessening your denominator. Nay unless my Algebra deceives me unity itself divided by zero will give infinity. Thomas Carlyle Category: Mathematics
Mathematicians do not study objects but relations between objects. Thus they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only. Jules Henri Poincare Category: Mathematics
Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes bathe and not make messes in the house. Robert Anson Heinlein Category: Mathematics
What is algebra exactly; is it those threecornered things? Sir James Matthew Barrie Category: Mathematics
In my opinion a mathematician in so far as he is a mathematician need not preoccupy himself with philosophy  an opinion moreover which has been expressed by many philosophers. Henri Lebesgue Category: Mathematics
When you have mastered numbers you will in fact no longer be reading numbers any more than you read words when reading books. You will be reading meanings. Harold Geneen Category: Mathematics
This seems to be one of the many cases in which the admitted accuracy of mathematical processes is allowed to throw a wholly inadmissible appearance of authority over the results obtained by them. Mathematics may be compared to a mill of exquisite workmanship which grinds your stuff to any degree of fineness; but nevertheless what you get out depends on what you put in; and as the grandest mill in the world will not extract wheat flour from peascods so pages of formulae will not get a definite result out of loose data. Thomas Henry Huxley Category: Mathematics
We often hear that mathematics consists mainly of proving theorems. Is a writers job mainly that of writing sentences? Giancarlo Rota Category: Mathematics
The errors of definitions multiply themselves according as the reckoning proceeds; and lead men into absurdities which at last they see but cannot avoid without reckoning anew from the beginning. Thomas Hobbes Category: Mathematics
To be a scholar of mathematics you must be born with talent insight concentration taste luck drive and the ability to visualize and guess. Paul R. Halmos Category: Mathematics
Don't talk to me of your Archimedes lever. He was an absentminded person with a mathematical imagination. Mathematics commands all my respect, but I have no use for engines. Give me the right word and the right accent and I will move the world. Joseph Conrad Category: Mathematics
A mathematician of the first rank Laplace quickly revealed himself as only a mediocre administrator; from his first work we saw that we had been deceived. Laplace saw no question from its true point of view; he sought subtleties everywhere; had only doubtful ideas and finally carried the spirit of the infinitely small into administration. Napoleon Bonaparte Category: Mathematics
If the entire Mandelbrot set were placed on an ordinary sheet of paper the tiny sections of boundary we examine would not fill the width of a hydrogen atom. Physicists think about such tiny objects; only mathematicians have microscopes fine enough to actually observe them. John Ewing Category: Mathematics
For a smart material to be able to send out a more complex signal it needs to be nonlinear. If you hit a tuning fork twice as hard it will ring twice as loud but still at the same frequency. Thats a linear response. If you hit a person twice as hard theyre unlikely just to shout twice as loud. That property lets you learn more about the person than the tuning fork. Neil Gershenfeld Category: Mathematics
Study reveals that 5 out of 4 Americans have trouble with fractions. Unknown Category: Mathematics
I had a feeling once about Mathematics that I saw it all. Depth beyond depth was revealed to me the Byss and Abyss. I saw as one might see the transit of Venus or even the Lord Mayors Show a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go. Sir Winston Churchill Category: Mathematics
Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable but it is impossible to foresee their consequences. These have only been found out by long study extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton Euler Gauss or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature since it is independent of language. E. C. Titchmarsh Category: Mathematics
There is nothing mysterious as some have tried to maintain about the applicability of mathematics. What we get by abstraction from something can be returned. R. L. Wilder Category: Mathematics
How happy the lot of the mathematician. He is judged solely by his peers and the standard is so high that no colleague or rival can ever win a reputation he does not deserve. Wystan Hugh Auden Category: Mathematics
A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator the smaller the fraction. Count Leo Nikolaevich Tolstoy Category: Mathematics
If others would but reflect on mathematical truths as deeply and as continuously as I have they would make my discoveries. Karl Friedrich Gauss Category: Mathematics
Mathematics the nonempirical science par excellence ... the science of sciences delivering the key to those laws of nature and the universe which are concealed by appearances. Hannah Arendt Category: Mathematics
The different branches of Arithmetic Ambition Distraction Uglification and Derision. Lewis Carroll Category: Mathematics
To be an abstraction does not mean that an entity is nothing. It merely means that its existence is only a factor of a more concrete element of nature. Alfred North Whitehead Category: Mathematics
Life is good for only two things discovering mathematics and teaching mathematics. Simeon Poisson Category: Mathematics
The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell. Saint Augustine of Hippo Category: Mathematics
