Selected mathematics quotes

1. Quaternions came from Hamilton after his really good work had been done, and though beautifully ingenious, have been an unmixed evil to those who have touched them in any way.

2. Symmetrical equations are good in their place, but 'vector' is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.

3. Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

4. Without mathematics, we are blind.

5. Instruction tables will have to be made up by mathematicians with computing experience and perhaps a certain puzzle-solving ability. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself.

6. Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.

7. God does not care about our mathematical difficulties. He integrates empirically.

8. I don't believe in mathematics.

9. We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made.

10. I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days.

11. I loved doing problems in school.

12. I realized that anything to do with Fermat's Last Theorem generates too much interest.

13. I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.

14. I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.

15. Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.

16. The rules of logic are to mathematics what those of structure are to architecture.

17. The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length... Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.

18. We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.

19. I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.

20. A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.

21. I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.

22. Mathematicians stand on each other's shoulders.

23. Mathematics seems to endow one with something like a new sense.

24. A mathematician is a blind man in a dark room looking for a black cat which isn't there.

25. Bear in mind the simple rule, X squared to the power of two minus five over the seven point eight three times nineteen is approximately equal to the cube root of MCC squared divided by X minus a quarter of a third percent. Keep that in mind, and you can't go very far wrong.

26. I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce.

27. The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

28. It is with children that we have the best chance of studying the development of logical knowledge, mathematical knowledge, physical knowledge, and so forth.

29. Do you think Arabs are dumb? They gave us our numbers. Try doing long division with Roman numerals.

30. Quaternions came from Hamilton after his really good work had been done, and though beautifully ingenious, have been an unmixed evil to those who have touched them in any way.

31. Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

32. Differential equations won't help you much in the design of aeroplanes - not yet, anyhow.

33. I have hardly ever known a mathematician who was capable of reasoning.

34. Evolution has ensured that our brains just aren't equipped to visualise 11 dimensions directly. However, from a purely mathematical point of view it's just as easy to think in 11 dimensions, as it is to think in three or four.

35. Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.

36. I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.

37. Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.

38. Equations are more important to me, because politics is for the present, but an equation is something for eternity.

39. As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

40. I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal.

41. The great book of nature is written in mathematical symbols.

42. Mathematics is the language with which God has written the universe.

43. -1 x -1 = +1 is stupid and evil.

44. God created everything by number, weight and measure.

45. Mathematicians are [like] a sort of Frenchmen; if you talk to them, they translate it into their own language, and then it is immediately something quite different.

46. By keenly confronting the enigmas that surround us, and by considering and analysing the observations that I have made, I ended up in the domain of mathematics, Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.

47. The regular division of the plane into congruent figures evoking an association in the observer with a familiar natural object is one of these hobbies or problems...I have embarked on this geometric problem again and again over the years, trying to throw light on different aspects each time. I cannot imagine what my life would be like if this problem had never occurred to me; one might say that I am head over heels in love with it, and I still don't know why.

48. It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further development of the theory.

49. God used beautiful mathematics in creating the world.

50. A mathematician is a device for turning coffee into theorems.

51. God may not play dice with the universe, but something strange is going on with the prime numbers.

52. This one's from the Book!

53. God has a Book where he maintains the best proofs of all mathematical theorems, proofs that are elegant and perfect... You don't have to believe in God, but you should believe in the Book.

54. Another roof, another proof.

55. I hope we'll be able to solve these problems before we leave. And when I say 'before we leave', I mean 'before we die'.

56. If we possessed a thorough knowledge of all the parts of the seed of any animal (e.g. man), we could from that alone, by reasons entirely mathematical and certain, deduce the whole conformation and figure of each of its members, and, conversely if we knew several peculiarities of this conformation, we would from those deduce the nature of its seed.

57. Omnia apud me mathematica fiunt.

58. Perfect numbers like perfect men are very rare.

59. The long concatenations of simple and easy reasoning which geometricians use in achieving their most difficult demonstrations gave me occasion to imagine that all matters which may enter the human mind were interrelated in the same fashion.

60. I started clipping and filing by categories on trends as early as 1930 and my 'youngest' file was started in 1945. Span of time is important; the 3-legged stool of understanding is held up by history, languages, and mathematics. Equipped with these three you can learn anything you want to learn. But if you lack any one of them you are just another ignorant peasant with dung on your boots.

61. 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.

62. We produce these representations in and from ourselves with the same necessity with which the spider spins. If we are forced to comprehend all things only under these forms, then it ceases to be amazing that in all things we actually comprehend nothing but these forms. For they must all bear within themselves the laws of number, and it is precisely number which is most astonishing in things. All that conformity to law, which impresses us so much in the movement of the stars and in chemical processes, coincides at bottom with those properties which we bring to things. Thus it is we who impress ourselves in this way

63. My brain is open.

64. Let n be an integer.