Mathematics Quotes

 All the mathematical sciences are founded on relations between physical laws and laws of numbers. 
Author: James Clerk Maxwell
Nationality: Scottish
b. 13 June 1931  - d. 05 November 1879
  
 Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin. 
Author: John von Neumann
Nationality: American
b. 28 December 1903  - d. 08 February 1957
  
 I think of lotteries as a tax on the mathematically challenged. 
Author: Roger Jones
Nationality: American   
 In things to be seen at once, much variety makes confusion, another vice of beauty. In things that are not seen at once, and have no respect one to another, great variety is commendable, provided this variety transgress not the rules of optics and geometry. 
Author: Sir Christopher Wren
Nationality: English
b. 20 October 1632  - d. 25 February 1723
  
 In mathematics you don't understand things. You just get used to them. 
Author: John von Neumann
Nationality: American
b. 28 December 1903  - d. 08 February 1957
  
 Mathematics is a game played according to certain simple rules with meaningless marks on paper. 
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 Mathematics is the art of giving the same name to different things. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 Mathematics is the language with which God has written the universe. 
Author: Galileo Galilei
Nationality: Italian
b. 15 February 1564  - d. 8 January 1642
  
 Science is facts; just as houses are made of stones, so is science made of facts; but a pile of stones is not a house and a collection of facts is not necessarily science. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra. 
Author: Fran Lebowitz
Nationality: American
b. 27 October 1950
  
 The most important thing in a programming language is the name. A language will not succeed without a good name. I have recently invented a very good name and now I am looking for a suitable language. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.  
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 Before beginning I should put in three years of intensive study, and I haven't that much time to squander on a probable failure. 
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.  
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 Galileo was no idiot. Only an idiot could believe that science requires martyrdom - that may be necessary in religion, but in time a scientific result will establish itself.  
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 He who seeks for methods without having a definite problem in mind seeks in the most part in vain. 
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.  
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations. 
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?  
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in existence, they would not be able to discover anything so stupid as astrology.  
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.  
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country. 
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 No one shall expel us from the paradise that Cantor has created for us. 
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. 
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.  
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 Physics is becoming too difficult for the physicists.  
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 The art of doing mathematics consists in finding that special case which contains all the germs of generality. 
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.  
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 The infinite! No other question has ever moved so profoundly the spirit of man. 
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 We must know. We will know.  
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 There's no sense in being precise when you don't even know what you're talking about. 
Author: John von Neumann
Nationality: American
b. 28 December 1903  - d. 08 February 1957
  
 It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in 5 years. 
Author: John von Neumann
Nationality: American
b. 28 December 1903  - d. 08 February 1957
  
 The manuals we got from IBM would show examples of programs and I knew I could do a heck of a lot better than that. So I thought I might have some talent. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 The most important thing in the kitchen is the waste paper basket and it needs to be centrally located. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 The most important thing in the programming language is the name. A language will not succeed without a good name. I have recently invented a very good name and now I am looking for a suitable language 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 We're competeing against ignorance. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 There's ways to amuse yourself while doing things and thats how I look at efficency. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 The hardest thing is to go to sleep at night, when there are so many urgent things needing to be done. A huge gap exists between what we know is possible with today's machines and what we have so far been able to finish. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 People think that computer science is the art of geniuses but the actual reality is the opposite, just many people doing things that build on each other, like a wall of mini stones. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 Premature optimization is the root of all evil - or at least most of it - in programming. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 Let us change our traditional attitude to the construction of programs. Instead of imagining that our main task is to instruct a computer what to do, let us concentrate rather on explaining to human beings what we want a computer to do. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 Science is what we understand well enough to explain to a computer. Art is everything else we do. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 If you find that you're spending almost all your time on theory, start turning some attention to practical things; it will improve your theories. If you find that you're spending almost all your time on practice, start turning some attention to theoretical things; it will improve your practice. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 In fact what I would like to see is thousands of computer scientists let loose to do whatever they want. That's what really advances the field. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 If you optimize everything, you will always be unhappy. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 I decry the current tendency to seek patents on algorithms. There are better ways to earn a living than to prevent other people from making use of one's contributions to computer science. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 Beware of bugs in the above code; I have only proved it correct, not tried it. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 God is a challenge because there is no proof of his existence and therefore the search must continue. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 Any inaccuracies in this index may be explained by the fact that it has been sorted with the help of a computer. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 An algorithm must be seen to be believed. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 A list is only as strong as its weakest link. 
Author: Donald Knuth
Nationality: American
b. 10 January 1938
  
 Who among us would not be happy to lift the veil behind which is hidden the future; to gaze at the coming developments of our science and at the secrets of its development in the centuries to come? What will be the ends toward which the spirit of future generations of mathematicians will tend? What methods, what new facts will the new century reveal in the vast and rich field of mathematical thought? 
Author: David Hilbert
Nationality: German
b. 23 January 1862  - d. 14 February 1943
  
 It has become almost a cliche to remark that nobody boasts of ignorance of literature, but it is socially acceptable to boast ignorance of science and proudly claim incompetence in mathematics. 
Author: Richard Dawkins
Nationality: British
b. 26 March 1941
  
 Philosophy is written in this grand book - I mean the universe - which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth. 
Author: Galileo Galilei
Nationality: Italian
b. 15 February 1564  - d. 8 January 1642
  
 The great book of nature is written in mathematical symbols. 
Author: Galileo Galilei
Nationality: Italian
b. 15 February 1564  - d. 8 January 1642
  
 The number of syllables in the English names of finite integers tends to increase as the integers grow larger, and must gradually increase indefinitely, since only a finite number of names can be made with a given finite number of syllables. Hence the names of some integers must consist of at least nineteen syllables, and among these there must be a least. Hence "the least integer not nameable in fewer than nineteen syllables" must denote a definite integer; in fact, it denotes 111, 777. But "the least integer not nameable in fewer than nineteen syllables" is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables, which is a contradiction. This contradiction was suggested to us by Mr. G. G. Berry of the Bodleian Library. 
Author: Bertrand Russell
Nationality: British
b. 18 May 1872  - d. 2 February 1970
  
 In the revolt against idealism, the ambiguities of the word “experience” have been perceived, with the result that realists have more and more avoided the word. It is to be feared, however, that if the word is avoided the confusions of thought with which it has been associated may persist. 
Author: Bertrand Russell
Nationality: British
b. 18 May 1872  - d. 2 February 1970
  
 Equations are the devil's sentences. 
Author: Stephen Colbert
Nationality: American
b. 13 May 1964
  
 Submission to the experimental data is the golden rule that dominates any scientific discipline. 
Author: Maurice Allais
Nationality: French
b. 31 May 1911  - d. 09 October 2010
  
 Any author who uses mathematics should always express in ordinary language the meaning of the assumptions he admits, as well as the significance of the results obtained. The more abstract his theory, the more imperative this obligation. In fact, mathematics are and can only be a tool to explore reality. In this exploration, mathematics do not constitute an end in itself, they are and can only be a means. 
Author: Maurice Allais
Nationality: French
b. 31 May 1911  - d. 09 October 2010
  
 Anyone who dares to speak about an aether is regarded as an ignorant and backward mind and he can only lose his credibility in scientific circles, although in reality those who criticize him use the same concept of intermediate medium in other words, whether it be fields, an associated fluid, a probability fluid, a pilot fluid, a quantum fluid, etc. 
Author: Maurice Allais
Nationality: French
b. 31 May 1911  - d. 09 October 2010
  
 Too many theorists have a tendency to ignore facts that contradict their convictions. 
Author: Maurice Allais
Nationality: French
b. 31 May 1911  - d. 09 October 2010
  
 In fact, without any exaggeration, the current mechanism of money creation through credit is certainly the "cancer" that's irretrievably eroding market economies of private property. 
Author: Maurice Allais
Nationality: French
b. 31 May 1911  - d. 09 October 2010
  
 In essence, the present creation of money, out of nothing by the banking system, is similar - I do not hesitate to say it in order to make people clearly realize what is at stake here - to the creation of money by counterfeiters, so rightly condemned by law. 
Author: Maurice Allais
Nationality: French
b. 31 May 1911  - d. 09 October 2010
  
 If you are truly serious abut preparing your child for the future, don't teach him to subtract, teach him to deduct. 
Author: Fran Lebowitz
Nationality: American
b. 27 October 1950
  
 Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra. 
Author: Fran Lebowitz
Nationality: American
b. 27 October 1950
  
 Most were beginning to feel they had learned enough to last for the rest of their lives. They remained mathematicians, but largely went their own way. 
Author: Benoît Mandelbrot
Nationality: American
b. 20 November 1924  - d. 14 October 2010
  
 My fate has been that what I undertook was fully understood only after the fact. 
Author: Benoît Mandelbrot
Nationality: American
b. 20 November 1924  - d. 14 October 2010
  
 Nobody will deny that there is at least some roughness everywhere. 
Author: Benoît Mandelbrot
Nationality: American
b. 20 November 1924  - d. 14 October 2010
  
 Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time. 
Author: Benoît Mandelbrot
Nationality: American
b. 20 November 1924  - d. 14 October 2010
  
 Order doesn't come by itself. 
Author: Benoît Mandelbrot
Nationality: American
b. 20 November 1924  - d. 14 October 2010
  
 Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory. 
Author: Benoît Mandelbrot
Nationality: American
b. 20 November 1924  - d. 14 October 2010
  
 The techniques I developed for studying turbulence, like weather, also apply to the stock market. 
Author: Benoît Mandelbrot
Nationality: American
b. 20 November 1924  - d. 14 October 2010
  
 There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable. 
Author: Benoît Mandelbrot
Nationality: American
b. 20 November 1924  - d. 14 October 2010
  
 There is a saying that every nice piece of work needs the right person in the right place at the right time 
Author: Benoît Mandelbrot
Nationality: American
b. 20 November 1924  - d. 14 October 2010
  
 Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics. 
Author: Benoît Mandelbrot
Nationality: American
b. 20 November 1924  - d. 14 October 2010
  
 When the weather changes, nobody believes the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed. 
Author: Benoît Mandelbrot
Nationality: American
b. 20 November 1924  - d. 14 October 2010
  
 One of my conjectures was solved in six months, a second in five years, a third in 10. But the basic conjecture remains-the Mandelbrot Set. 
Author: Benoît Mandelbrot
Nationality: American
b. 20 November 1924  - d. 14 October 2010
  
 It is certain that the combinations which present themselves to the mind in a kind of sudden illumination after a somewhat prolonged period of unconscious work are generally useful and fruitful combinations, all the combinations are formed as a result of the automatic action of the subliminal ego, but those only which are interesting find their way into the field of consciousness. A few only are harmonious, and consequently at once useful and beautiful, and they will be capable of affecting the geometrician's special sensibility I have been speaking of; which, once aroused, will direct our attention upon them, and will thus give them the opportunity of becoming conscious. In the subliminal ego, on the contrary, there reigns what I would call liberty, if one could give this name to the mere absence of discipline and to disorder born of chance. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 A small error in the former will produce an enormous error in the latter. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 Facts do not speak. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 Geometry is not true, it is advantageous. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 How is an error possible in mathematics? 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 Hypotheses are what we lack the least. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by the laws. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 In the old days when people invented a new function they had something useful in mind. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 It has adopted the geometry most advantageous to the species or, in other words, the most convenient. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 It is far better to foresee even without certainty than not to foresee at all. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 It is through science that we prove, but through intuition that we discover. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 Mathematical discoveries, small or great are never born of spontaneous generation. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 Mathematicians do not study objects, but relations between objects.  
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 Science is facts. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 The mind uses its faculty for creativity only when experience forces it to do so. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 They are free to replace some objects by others so long as the relations remain unchanged. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 To invent is to discern, to choose. 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  
 What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? 
Author: Henri Poincaré
Nationality: French
b. 29 April 1854  - d. 17 July 1912
  




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