Henri Poincare Quotes & Sayings

#1. It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry; the founders are hampered in their general grasp by third and fourth decimal places.

Henri Poincare

#2. What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?

Henri Poincare

#3. Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.

Henri Poincare

#4. Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so lone as the relations remain unchanged. Content to them is irrelevant; they are interested in form only.

Henri Poincare

#5. 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.

Henri Poincare

#6. Zero is the number of objects that satisfy a condition that is never
satisfied. But as never means "in no case", I do not see that any progress has been made.

Henri Poincare

#7. Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer?

Henri Poincare

#8. If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

Henri Poincare

#9. 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.

Henri Poincare

#10. Mathematics is the art of giving the same name to different things.

Henri Poincare

#11. A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.

Henri Poincare

#12. Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

Henri Poincare

#13. Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.

Henri Poincare

#14. But all of my efforts served only to make me better acquainted with the difficulty, which in itself was something.

Henri Poincare

#15. To invent is to discern, to choose.

Henri Poincare

#16. Einstein does not remain attached to the classical principles, and when presented with a problem in physics he quickly envisages all of its possibilities. This leads immediately in his mind to the prediction of new phenomena which may one day be verified by experiment.

Henri Poincare

#17. Chance ... must be something more than the name we give to our ignorance.

Henri Poincare

#18. To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection.

Henri Poincare

#19. Mathematicians are born, not made.

Henri Poincare

#20. Sociology is the science with the greatest number of methods and the least results.

Henri Poincare

#21. The feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know

Henri Poincare

#22. Thought is only a flash between two long nights, but this flash is everything.

Henri Poincare

#23. The Scientist must set in order. Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.

Henri Poincare

#24. It is not order only, but unexpected order, that has value.

Henri Poincare

#25. One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.

Henri Poincare

#26. It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.

Henri Poincare

#27. 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.

Henri Poincare

#28. For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

Henri Poincare

#29. Mathematical discoveries, small or great are never born of spontaneous generation.

Henri Poincare

#30. Thought must never submit, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, save to the facts themselves, because, for thought, submission would mean ceasing to be.

Henri Poincare

#31. 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.

Henri Poincare

#32. But for harmony beautiful to contemplate, science would not be worth following.

Henri Poincare

#33. To doubt everything and to believe everything are two equally convenient solutions; each saves us from thinking.

Henri Poincare

#34. 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.

Henri Poincare

#35. How is error possible in mathematics?

Henri Poincare

#36. Every good mathematician should also be a good chess player and vice versa.

Henri Poincare

#37. Talk with M. Hermite. He never evokes a concrete image, yet you soon perceive that the more abstract entities are to him like living creatures.

Henri Poincare

#38. Science is facts.

Henri Poincare

#39. Just as houses are made of stones, so is science made of facts.

Henri Poincare

#40. 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.

Henri Poincare

#41. Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.

Henri Poincare

#42. Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.

Henri Poincare

#43. Physicists believe that the Gaussian law has been proved in mathematics while mathematicians think that it was experimentally established in physics.

Henri Poincare

#44. Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority.

Henri Poincare

#45. When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks.

Henri Poincare

#46. It is with logic that one proves; it is with intuition that one invents.

Henri Poincare

#47. Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means ...

Henri Poincare

#48. There are no solved problems; there are only problems that are more or less solved.

Henri Poincare

#49. A cat is witty, he has nerve, he knows how to do precisely the right thing at the right moment.

Henri Poincare

#50. It is by logic we prove. It is by intuition we discover.

Henri Poincare

#51. It may happen that small differences in the initial conditions produce very great ones in the final phenomena.

Henri Poincare

#52. 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.

Henri Poincare

#53. The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.

Henri Poincare

#54. Often when works at a hard question, nothing good is accomplished at the first attack. Then one takes a rest, long or short, and sits down anew to the work. During the first half-hour, as before, nothing is found, and then all of a sudden the decisive idea presents itself to the mind.

Henri Poincare

#55. All that is not thought is pure nothingness; since we can think only thoughts, and all the words we use to speak of things can express only thoughts, to say there is something other than thought is therefore an affirmation which can have no meaning.

Henri Poincare

#56. Hypotheses are what we lack the least.

Henri Poincare

#57. Astronomy is useful because it raises us above ourselves; it is useful because it is grand; ... It shows us how small is man's body, how great his mind, since his intelligence can embrace the whole of this dazzling immensity, where his body is only an obscure point, and enjoy its silent harmony.

Henri Poincare

#58. Thus, they are free to replace some objects by others so long as the relations remain unchanged.

Henri Poincare

#59. Geometry is the art of correct reasoning from incorrectly drawn figures.

Henri Poincare

#60. It is through science that we prove, but through intuition that we discover.

Henri Poincare

#61. Point set topology is a disease from which the human race will soon recover.

Henri Poincare

#62. Doubting everything and believing everything are two equally convenient solutions that guard us from having to think

Henri Poincare

#63. A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.

Henri Poincare

#64. The task of the educator is to make the child's spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppressing none of them. In this regard, the history of science must be our guide.

Henri Poincare

#65. The aim of Mathematical Physics is not only to facilitate for the physicist the numerical calculation of certain constants or the integration of certain differential equations. It is besides, it is above all, to reveal to him the hidden harmony of things in making him see them in a new way.

Henri Poincare

#66. A very small cause, which escapes us, determines a considerable effect which we cannot ignore, and we say that this effect is due to chance.

Henri Poincare

#67. One does not ask whether a scientific theory is true, but only whether it is convenient.

Henri Poincare

#68. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.

Henri Poincare

#69. Analyse data just so far as to obtain simplicity and no further.

Henri Poincare

#70. It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed.

Henri Poincare

#71. 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.

Henri Poincare

#72. A small error in the former will produce an enormous error in the latter.

Henri Poincare

#73. It has adopted the geometry most advantageous to the species or, in other words, the most convenient.

Henri Poincare

#74. Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

Henri Poincare

#75. Mathematicians do not study objects, but relations between objects.

Henri Poincare

#76. The mind uses its faculty for creativity only when experience forces it to do so.

Henri Poincare

#77. Facts do not speak.

Henri Poincare

#78. No more than these machines need the mathematician know what he does.

Henri Poincare

#79. Is is by logic that we prove, but by intuition that we discover.

Henri Poincare

#80. Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose.

Henri Poincare

#81. How is an error possible in mathematics?

Henri Poincare

#82. All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance.

Henri Poincare

#83. What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.

Henri Poincare