Top 70 Henri Poincaré Quotes (2024 Update)

1. “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.”

— Henri Poincaré

Featured in: Math Quotes

2. “It is through science that we prove, but through intuition that we discover.”

— Henri Poincaré

Featured in: Intuition Quotes

3. “Geometry is the art of correct reasoning from incorrectly drawn figures.”

— Henri Poincaré

4. “Mathematics is the art of giving the same name to different things.”

— Henri Poincaré

5. “Science is built up of 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 Poincaré

6. “It is far better to foresee even without certainty than not to foresee at all.”

— Henri Poincaré

7. “Mathematicians are born, not made.”

— Henri Poincaré

8. “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 Poincaré

9. “Doubting everything and believing everything are two equally convenient solutions that guard us from having to think.”

— Henri Poincaré

10. “Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don’t change. Matter is not important, only form interests them.”

— Henri Poincaré

11. “Thought is only a flash between two long nights, but this flash is everything.”

— Henri Poincaré

12. “If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.”

— Henri Poincaré

13. “How is error possible in mathematics?”

— Henri Poincaré

14. “Intuition is more important to discovery than logic.”

— Henri Poincaré

15. “There are no solved problems; there are only problems that are more or less solved.”

— Henri Poincaré

16. “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 Poincaré

17. “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 Poincaré

18. “Point set topology is a disease from which the human race will soon recover.”

— Henri Poincaré

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

— Henri Poincaré

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

— Henri Poincaré

21. “Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.”

— Henri Poincaré

22. “Guessing before proving! Need I remind you that it is so that all important discoveries have been made?”

— Henri Poincaré

23. “Geometry is not true, it is advantageous.”

— Henri Poincaré

24. “Experiment is the sole source of truth.”

— Henri Poincaré

25. “What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?”

— Henri Poincaré

26. “Every good mathematician should also be a good chess player and vice versa.”

— Henri Poincaré

27. “All of mathematics is a tale about groups.”

— Henri Poincaré

28. “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 Poincaré

29. “One geometry cannot be more true than another; it can only be more convenient.”

— Henri Poincaré

30. “It may happen that small differences in the initial conditions produce very great ones in the final phenomena.”

— Henri Poincaré

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

— Henri Poincaré

32. “A small error in the former will produce an enormous error in the latter.”

— Henri Poincaré

33. “Mathematical discoveries, small or great are never born of spontaneous generation.”

— Henri Poincaré

34. “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 Poincaré

35. “Mathematicians do not study objects, but relations between objects.”

— Henri Poincaré

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

— Henri Poincaré

37. “The mind uses its faculty for creativity only when experience forces it to do so.”

— Henri Poincaré

38. “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 Poincaré

39. “To invent is to discern, to choose.”

— Henri Poincaré

40. “Analyse data just so far as to obtain simplicity and no further.”

— Henri Poincaré

41. “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. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.”

— Henri Poincaré

42. “It is not order only, but unexpected order, that has value.”

— Henri Poincaré

43. “We also know how cruel the truth often is, and we wonder whether delusion is not more consoling.”

— Henri Poincaré

44. “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 Poincaré

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

— Henri Poincaré

46. “The subliminal self is in no way inferior to the conscious self. It knows how to choose and to divine.”

— Henri Poincaré

47. “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 Poincaré

48. “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 Poincaré

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

— Henri Poincaré

50. “Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.”

— Henri Poincaré