87 Mathematics Quotes

Mathematics, often seen as a mere collection of numbers and equations, holds a profound and universal beauty that transcends cultural and linguistic boundaries. Its principles underpin the very fabric of the natural world, influencing everything from the smallest particles to the vastness of the cosmos. In this blog post, we've curated a selection of the top 87 mathematics quotes that capture the elegance, mystery, and significance of this timeless discipline. Whether you're a seasoned mathematician, a student, or simply someone who appreciates the wonder of numbers, these quotes are sure to inspire, provoke thought, and deepen your appreciation for the mathematical universe. Join us as we explore the words of great thinkers, mathematicians, and philosophers who have eloquently expressed the essence of mathematics.

1. “[When asked why are numbers beautiful?]It’s like asking why is Ludwig van Beethoven’s Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is.” - Paul Erdos

2. “In real life, I assure you, there is no such thing as algebra. ” - Fran Lebowitz

3. “Every formula which expresses a law of nature is a hymn of praise to God.” - Maria Mitchell

4. “I tell them that if they will occupy themselves with the study of mathematics they will find in it the best remedy against the lusts of the flesh.” - Thomas Mann

5. “I know that two and two make four - and should be glad to prove it too if I could - though I must say if by any sort of process I could convert 2 and 2 into five it would give me much greater pleasure.” - Lord George Gordon Byron

6. “The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.” - G.K. Chesterton

7. “I would say, if you like, that the party is like an out-moded mathematics...that is to say, the mathematics of Euclid. We need to invent a non-Euclidian mathematics with respect to political discipline.” - Alain Badiou

8. “Soon after I began working for the Professor, I realized that he talked about numbers whenever he was unsure of what to say or do. Numbers were also his way of reaching out to the world. They were safe, a source of comfort.” - Yoko Ogawa

9. “When the time is ripe for certain things, these things appear in different places in the manner of violets coming to light in early spring.” - Farkas Bolyai

10. “My first feeling was that there was no way to continue. Writing isn't like math;in math, two plus two always equals four no matter what your mood is like. With writing, the way you feel changes everything.” - Stephenie Meyer

11. “Its a mathematical fact that two negatives make a positive so even under adverse circumstances think positively.” - Dr. Amit Abraham

12. “Your Excellency, I have no need of this hypothesis.” - Pierre Laplace

13. “The ‘Muse’ is not an artistic mystery, but a mathematical equation. The gift are those ideas you think of as you drift to sleep. The giver is that one you think of when you first awake.” - Roman Payne

14. “The calculative exactness of practical life which the money economy has brought about corresponds to the ideal of natural science: to transform the world by mathematical formulas. Only money economy has filled the days of so many people with weighing, calculating, with numerical determinations, with a reduction of qualitative values to quantitative ones.” - Georg Simmel

15. “My beautiful proof lies all in ruins.” - Georg Cantor

16. “In every department of physical science there is only so much science, properly so-called, as there is mathematics.” - Immanuel Kant

17. “Nothing takes place in the world whose meaning is not that of some maximum or minimum.” - Leonhard Euler

18. “Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.” - Lord Kelvin

19. “Infinite is a meaningless word: except – it states / The mind is capable of performing / an endless process of addition.” - Louis Zukofsky

20. “Too large a proportion of recent "mathematical" economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols.” - John Maynard Keynes

21. “He could not believe that any of them might actually hit somebody. If one did, what a nowhere way to go: killed by accident; slain not as an individual but by sheer statistical probability, by the calculated chance of searching fire, even as he himself might be at any moment. Mathematics! Mathematics! Algebra! Geometry! When 1st and 3d Squads came diving and tumbling back over the tiny crest, Bell was content to throw himself prone, press his cheek to the earth, shut his eyes, and lie there. God, oh, God! Why am I here? Why am I here? After a moment's thought, he decided he better change it to: why are we here. That way, no agency of retribution could exact payment from him for being selfish.” - James Jones

22. “Neglect of mathematics work injury to all knowledge, since he who is ignorant of it cannot know the other sciences or things of this world. And what is worst, those who are thus ignorant are unable to perceive their own ignorance, and so do not seek a remedy.” - Roger Bacon

23. “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.” - Werner Heisenberg

24. “I guess I think of lotteries as a tax on the mathematically challenged.” - Roger Jones

25. “Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.” - Johannes Kepler

26. “Mathemata mathematicis scribuntur.” - Nicolaus Copernicus

27. “I had a polynomial once. My doctor removed it.” - Michael Grant

28. “The mathematicians are the priests of the modern world.” - Bill Gaede

29. “A mathematician is an individual who constructs space with 0D particles and then places a bowling ball on this invisible canvas to explain how gravity works.” - Bill Gaede

30. “A relativist is an individual who doesn't know the difference between an adjective and an adverb.” - Bill Gaede

31. “The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.” - Alfred North Whitehead

32. “Increasingly, the mathematics will demand the courage to face its implications.” - Michael Crichton

33. “I couldn't claim that I was smarter than sixty-five other guys--but the average of sixty-five other guys, certainly!” - Richard P. Feynman

34. “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 Mayor's 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.” - Winston S. Churchill

35. “I could never have gone far in any science because on the path of every science the lion Mathematics lies in wait for you.” - C. S. Lewis

36. “Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.” - Deepak Chopra

37. “[The Old Astronomer to His Pupil]Reach me down my Tycho Brahe, I would know him when we meet,When I share my later science, sitting humbly at his feet;He may know the law of all things, yet be ignorant of howWe are working to completion, working on from then to now.Pray remember that I leave you all my theory complete,Lacking only certain data for your adding, as is meet,And remember men will scorn it, 'tis original and true,And the obloquy of newness may fall bitterly on you.But, my pupil, as my pupil you have learned the worth of scorn,You have laughed with me at pity, we have joyed to be forlorn,What for us are all distractions of men's fellowship and smiles;What for us the Goddess Pleasure with her meretricious smiles.You may tell that German College that their honor comes too late,But they must not waste repentance on the grizzly savant's fate.Though my soul may set in darkness, it will rise in perfect light;I have loved the stars too fondly to be fearful of the night.What, my boy, you are not weeping? You should save your eyes for sight;You will need them, mine observer, yet for many another night.I leave none but you, my pupil, unto whom my plans are known.You 'have none but me,' you murmur, and I 'leave you quite alone'?Well then, kiss me, -- since my mother left her blessing on my brow,There has been a something wanting in my nature until now;I can dimly comprehend it, -- that I might have been more kind,Might have cherished you more wisely, as the one I leave behind.I 'have never failed in kindness'? No, we lived too high for strife,--Calmest coldness was the error which has crept into our life;But your spirit is untainted, I can dedicate you stillTo the service of our science: you will further it? you will!There are certain calculations I should like to make with you,To be sure that your deductions will be logical and true;And remember, 'Patience, Patience,' is the watchword of a sage,Not to-day nor yet to-morrow can complete a perfect age.I have sown, like Tycho Brahe, that a greater man may reap;But if none should do my reaping, 'twill disturb me in my sleepSo be careful and be faithful, though, like me, you leave no name;See, my boy, that nothing turn you to the mere pursuit of fame.I must say Good-bye, my pupil, for I cannot longer speak;Draw the curtain back for Venus, ere my vision grows too weak:It is strange the pearly planet should look red as fiery Mars,--God will mercifully guide me on my way amongst the stars.” - Sarah Williams

38. “Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world.” - Robert Langlands

39. “Real mathematics must be justified as art if it can be justified at all.” - G.H. Hardy

40. “When we are young, we spend much time and pains in filling our note-books with all definitions of Religion, Love, Poetry, Politics, Art, in the hope that, in the course of a few years, we shall have condensed into our encyclopaedia the net value of all the theories at which the world has yet arrived. But year after year our tables get no completeness, and at last we discover that our curve is a parabola, whose arcs will never meet.” - Ralph Waldo Emerson

41. “Some people believe in imaginary friends. I believe in imaginary numbers.” - R.M. ArceJaeger

42. “Women have a passion for mathematics. They divide their age in half, double the price of their clothes, and always add at least five years to the age of their best friend.” - Marcel Achard

43. “...The pages and pages of complex, impenetrable calculations might have contained the secrets of the universe, copied out of God's notebook. In my imagination, I saw the creator of the universe sitting in some distant corner of the sky, weaving a pattern of delicate lace so fine that that even the faintest light would shine through it. The lace stretches out infinitely in every direction, billowing gently in the cosmic breeze. You want desperately to touch it, hold it up to the light, rub it against your cheek. And all we ask is to be able to re-create the pattern, weave it again with numbers, somehow, in our own language; to make the tiniest fragment our own, to bring it back to eart.” - Yoko Ogawa

44. “A mathematician tells you that the wall of warped space prevents the Moon from flying out of its orbit yet can't tell you why an astronaut can go back and forth across that same space.” - Bill Gaede

45. “We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it.” - Roger Penrose

46. “Düşün! Bize, matematik dünyasının kurgusal ve sonsuz olduğu öğretildi. Bunu kabul ederim, 1'den sonra 2 gelir dendi. Bunu da kabul ederim. Ama sonra, 1 ile 2 arasındaki sonsuzluğu düşündüm. Peki o nereye gitti? İrrasyonel sayılar varken bir sayıdan sonra diğer bir tam sayı nasıl gelebilir? Eğer 1'den sonra virgül konursa ve bunun da kıçına sonsuz sayı konabiliyorsa 2 nasıl gelir? İşte! Soru bu! Yanıtsız bir soru. Ve işte matematiğin hatası! Dolayısıyla matematik yok. Onun üzerine kurulmuş dünya düzeni de yok... Ama ben anlayabilirim. Anlayabilirim bu sorunu. Ve o zaman ortaya yaklaşık sayılar çıkar. Yani hiçbir sayı tam değildir. Hepsi tama yaklaşır. Ama varamaz. Demektir ki, 1,999...9'u bize 2 diye yutturmaya çalışan bir dünyanın çocuklarıyız. Ve dünya da aslında tam gibi görünürken, aslmda bir irrasyonellik harikası. İşte bunun için hayat yoktur. Olsa dahi o da irrasyoneldir! Yani anlamsızdır. Ne bir başlama nedeni, ne de bir oluş nedeni vardır. Evrende uçuşan kocaman bir irrasyonellik. Tabiî ki dünyanın bir anlamı olması gerekmiyor. Belki de onu anlamlandıran üzerinde yaşayan akıl sahibi yaratıklardır. Ama onların da bizi getirdiği nokta ortada!” - Hakan Günday

47. “Why don't we want our children to learn to do mathematics? Is it that we don't trust them, that we think it's too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon. Why not about triangles?” - Paul Lockhart

48. “Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.” - Paul Lockhart

49. “It is the story that matters not just the ending.” - Paul Lockhart

50. “So how does one go about proving something like this? It's not like being a lawyer, where the goal is to persuade other people; nor is it like a scientist testing a theory. This is a unique art form within the world of rational science. We are trying to craft a "poem of reason" that explains fully and clearly and satisfies the pickiest demands of logic, while at the same time giving us goosebumps.” - Paul Lockhart

51. “99 percent of all statistics only tell 49 percent of the story.” - Ron DeLegge II

52. “Most people would have probably lost count around seven. This was, Harry knewfrom his extensive reading on logic and arithmetic, the largest number that most peoplecould visually appreciate. Put seven dots on a page, and most people can take a quickglance and declare, “Seven.” Switch to eight, and the majority of humanity was lost.” - Julia Quinn

53. “If you can't test it, it's not theorics -- it's metatheorics. A branch of philosophy. So, if you want to think of it this way, our test equipment is what defines the boundary separating theorics from philosophy.” - Neal Stephenson

54. “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.” - Eugene Paul Wigner

55. “Logic, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion - thus:Major Premise: Sixty men can do a piece of work sixty times as quickly as one man.Minor Premise: One man can dig a post-hole in sixty seconds; Therefore-Conclusion: Sixty men can dig a post-hole in one second.This may be called syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.” - Ambrose Bierce

56. “There cannot be a language more universal and more simple, more free from errors and obscurities...more worthy to express the invariable relations of all natural things [than mathematics]. [It interprets] all phenomena by the same language, as if to attest the unity and simplicity of the plan of the universe, and to make still more evident that unchangeable order which presides over all natural causes” - Joseph Fourier

57. “A Puritan twist in our nature makes us think that anything good for us must be twice as good if it's hard to swallow. Learning Greek and Latin used to play the role of character builder, since they were considered to be as exhausting and unrewarding as digging a trench in the morning and filling it up in the afternoon. It was what made a man, or a woman -- or more likely a robot -- of you. Now math serves that purpose in many schools: your task is to try to follow rules that make sense, perhaps, to some higher beings; and in the end to accept your failure with humbled pride. As you limp off with your aching mind and bruised soul, you know that nothing in later life will ever be as difficult.What a perverse fate for one of our kind's greatest triumphs! Think how absurd it would be were music treated this way (for math and music are both excursions into sensuous structure): suffer through playing your scales, and when you're an adult you'll never have to listen to music again. And this is mathematics we're talking about, the language in which, Galileo said, the Book of the World is written. This is mathematics, which reaches down into our deepest intuitions and outward toward the nature of the universe -- mathematics, which explains the atoms as well as the stars in their courses, and lets us see into the ways that rivers and arteries branch. For mathematics itself is the study of connections: how things ideally must and, in fact, do sort together -- beyond, around, and within us. It doesn't just help us to balance our checkbooks; it leads us to see the balances hidden in the tumble of events, and the shapes of those quiet symmetries behind the random clatter of things. At the same time, we come to savor it, like music, wholly for itself. Applied or pure, mathematics gives whoever enjoys it a matchless self-confidence, along with a sense of partaking in truths that follow neither from persuasion nor faith but stand foursquare on their own. This is why it appeals to what we will come back to again and again: our **architectural instinct** -- as deep in us as any of our urges.” - Ellen Kaplan

58. “I abandoned the assigned problems in standard calculus textbooks and followed my curiosity. Wherever I happened to be--a Vegas casino, Disneyland, surfing in Hawaii, or sweating on the elliptical in Boesel's Green Microgym--I asked myself, "Where is the calculus in this experience?” - Jennifer Ouellette

59. “If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos.” - Gary William Flake

60. “Of course, reading novels was just another form of escape. As soon as he closed their pages he had to come back to the real world. But at some point Tengo noticed that returning to reality from the world of a novel was not as devastating a blow as returning from the world of mathematics. Why should that have been? After much deep thought, he reached a conclusion. No matter how clear the relationships of things might become in the forest of story, there was never a clear-cut solution. That was how it differed from math. The role of a story was, in the broadest terms, to transpose a single problem into another form. Depending on the nature and direction of the problem, a solution could be suggested in the narrative. Tengo would return to the real world with that suggestion in hand. It was like a piece of paper bearing the indecipherable text of a magic spell. At times it lacked coherence and served no immediate practical purpose. But it would contain a possibility. Someday he might be able to decipher the spell. That possibility would gently warm his heart from within.” - Haruki Murakami

61. “Ideas that require people to reorganize their picture of the world provoke hostility.” - James Gleick

62. “It is the definition of the word 'object' which destroys all religions.” - Bill Gaede

63. “In the field of Egyptian mathematics Professor Karpinski of the University of Michigan has long insisted that surviving mathematical papyri clearly demonstrate the Egyptians' scientific interest in pure mathematics for its own sake. I have now no doubt that Professor Karpinski is right, for the evidence of interest in pure science, as such, is perfectly conclusive in the Edwin Smith Surgical Papyrus.” - James Henry Breasted

64. “Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity” - G.H. Hardy

65. “Physicists have come to realize that mathematics, when used with sufficient care, is a proven pathway to truth.” - Brian Greene

66. “Mathematics is the art of explanation.” - Paul Lockhart

67. “Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion—not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to; to have a break-through idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it.” - Paul Lockhart

68. “Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. [...] Thus 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. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.” - Bertrand Russell

69. “Mathematics effectively began when a few Greek friends got together to talk about numbers and lines and angles.” - C.S. Lewis

70. “Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.” - Bertrand Russell

71. “A brick can be used to represent the zero probability of this book being any good.” - Amy Riekhof

72. “In his school, Bertrand Russell thought it was better if they had the sex, so they could give their undivided attention to mathematics, which was the main thing.” - Paul Goodman

73. “It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true.” - Herbert S. Gaskill

74. “One can be enlightened about proofs as well as theorems. Without enlightenment, one is merely reduced to memorizing proofs. With enlightenment about a proof, its flow becomes clear and it can become an item of astonishing beauty. In addition, the need to memorize disappears because the proof has become part of your soul.” - Herbert S. Gaskill

75. “The land of easy mathematics where he who works adds up and he who retires subtracts.” - Núria Añó

76. “Mathematics doesn’t care about those beyond the numbers.” - Dejan Stojanovic

77. “One must divide one's time between politics and equations. But our equations are much more important to me, because politics is for the present, while our equations are for eternity.” - Albert Einstein

78. “It appeared that way, Lawrence, but this raised the question of was mathematics really true or was it just a game played with symbols? In other words—are we discovering Truth, or just wanking?” - Neal Stephenson

79. “Mathematicians deal with large numbers sometimes, but never in their income.” - Isaac Asimov

80. “They shouldn't be allowed to teach math so early in the morning.” - Kendare Blake

81. “But that can never be," said Milo, jumping to his feet."Don't be too sure," said the child patiently, "for one of the nicest things about mathematics, or anything else you might care to learn, is that many of the things which can never be, often are. You see," he went on, "it's very much like your trying to reach Infinity. You know that it's there, but you just don't know where — but just because you can never reach it doesn't mean that it's not worth looking for.” - Norton Juster

82. “Music is the pleasure the human mind experiences from counting without being aware that it is counting.” - Martin Nowak

83. “Physics depends on a universe infinitely centred on an equals sign.” - Mark Z. Danielewski

84. “Magic is like a lot of other disciplines that people have recently begun developing, in historic terms. Working with magic is a way of understanding the universe and how it functions. You can approach it from a lot of different angles, applying a lot of different theories and mental models to it. You can get to the same place through a lot of different lines of theory and reasoning, kind of like really advanced mathematics. There's no truly right or wrong way to get there, either--there are just different ways, some more or less useful than others for a given application. And new vistas of thought, theory, and application open up on a pretty regular basis, as the Art develops and expands through the participation of multiple brilliant minds. But that said, once you have a good grounding in it,you get a pretty solid idea of what's possible and what isn't. No matter how much circumlocution you do with your formulae, two plus two doesn't equal five. (Except maybe very, very rarely, sometimes, in extremely specific and highly unlikely circumstances.)” - Jim Butcher

85. “[...] provability is a weaker notion than truth” - Douglas R. Hofstadter

86. “The language of mathematics differs from that of everyday life, because it is essentially a rationally planned language. The languages of size have no place for private sentiment, either of the individual or of the nation. They are international languages like the binomial nomenclature of natural history. In dealing with the immense complexity of his social life man has not yet begun to apply inventiveness to the rational planning of ordinary language when describing different kinds of institutions and human behavior. The language of everyday life is clogged with sentiment, and the science of human nature has not advanced so far that we can describe individual sentiment in a clear way. So constructive thought about human society is hampered by the same conservatism as embarrassed the earlier naturalists. Nowadays people do not differ about what sort of animal is meant by Cimex or Pediculus, because these words are used only by people who use them in one way. They still can and often do mean a lot of different things when they say that a mattress is infested with bugs or lice. The study of a man's social life has not yet brought forth a Linnaeus. So an argument about the 'withering away of the State' may disclose a difference about the use of the dictionary when no real difference about the use of the policeman is involved. Curiously enough, people who are most sensible about the need for planning other social amenities in a reasonable way are often slow to see the need for creating a rational and international language.” - Lancelot Hogben

87. “The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing.[Statement of the second law of thermodynamics, 1862]” - Rudolf Clausius