Mathematics has long been a source of wonder and inspiration, shaping the way we understand the world around us. From brilliant minds who have unlocked its mysteries to thinkers who use numbers to explore complex ideas, math continues to fuel creativity and innovation. In this collection, we bring you 116 inspiring mathematics quotes that celebrate the beauty, power, and elegance of this timeless discipline. Whether you’re a student, educator, or simply a lover of numbers, these quotes are sure to motivate and enlighten.
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. “Since the mathematicians have invaded the theory of relativity I do not understand it myself any more.” - Albert Einstein
9. “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
10. “What comes, is called.” - Ki Longfellow
11. “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
12. “Its a mathematical fact that two negatives make a positive so even under adverse circumstances think positively.” - Dr. Amit Abraham
13. “Your Excellency, I have no need of this hypothesis.” - Pierre Laplace
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. “The Ludolphian number is fixed in eternity— not a digit out of place, all characters in their proper order, an endless sentence written to the end of the world by the division of the circle’s diameter into its circumference.” - Richard Preston
16. “The oldest problem in economic education is how to exclude the incompetent. A certain glib mastery of verbiage-the ability to speak portentously and sententiously about the relation of money supply to the price level-is easy for the unlearned and may even be aided by a mildly enfeebled intellect. The requirement that there be ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device.” - John Kenneth Galbraith
17. “My beautiful proof lies all in ruins.” - Georg Cantor
18. “Nothing takes place in the world whose meaning is not that of some maximum or minimum.” - Leonhard Euler
19. “I am no friend of probability theory, I have hated it from the first moment when our dear friend Max Born gave it birth. For it could be seen how easy and simple it made everything, in principle, everything ironed and the true problems concealed. Everybody must jump on the bandwagon [Ausweg]. And actually not a year passed before it became an official credo, and it still is.” - Erwin Schrödinger
20. “Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.” - Lord Kelvin
21. “Infinite is a meaningless word: except – it states / The mind is capable of performing / an endless process of addition.” - Louis Zukofsky
22. “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
23. “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
24. “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
25. “All mathematicians live in two different worlds. They live in a crystalline world of perfect platonic forms. An ice palace. But they also live in the common world where things are transient, ambiguous, subject to vicissitudes. Mathematicians go backward and forward from one world to another. They’re adults in the crystalline world, infants in the real one.” - Sylvain Cappell
26. “I guess I think of lotteries as a tax on the mathematically challenged.” - Roger Jones
27. “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
28. “I had a polynomial once. My doctor removed it.” - Michael Grant
29. “But in my opinion, all things in nature occur mathematically.” - Rene Decartes
30. “With me, everything turns into mathematics.” - René Descartes
31. “I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.” - Malcolm X
32. “There is no great religion without a great schism. All of them have it. And that's because you're dealing with something called faith. And faith is not something you can prove; faith is personal opinion. Uh, when you're dealing with something with certainty, like, y'know, science or logic, you don't have the--there's no wiggle room; that's why history is not filled with warring math cults, y'know, because you can settle the issue; you can prove something to be right or wrong, and that's the end of the argument: next case. Whereas, when you're dealing with faith, you can forever argue your point, or another point, because you're dealing with intangibles. Personally, I think, faith is what you ask of somebody when you don't have the goods to prove your point.” - Tom Quinn
33. “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
34. “A relativist is an individual who doesn't know the difference between an adjective and an adverb.” - Bill Gaede
35. “A mathematician is a magician who converts adjectives into nouns: continuous into continuum, infinite into infinity, infinitesimal into location, 0D into point, 1D into line, curved into geodesic...” - Bill Gaede
36. “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
37. “Increasingly, the mathematics will demand the courage to face its implications.” - Michael Crichton
38. “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
39. “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
40. “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
41. “I should attempt to treat human vice and folly geometrically... the passions of hatred, anger, envy, and so on, considered in themselves, follow from the necessity and efficacy of nature... I shall, therefore, treat the nature and strength of the emotion in exactly the same manner, as though I were concerned with lines, planes, and solids.” - Baruch Spinoza
42. “Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.” - Deepak Chopra
43. “Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world.” - Robert Langlands
44. “Real mathematics must be justified as art if it can be justified at all.” - G.H. Hardy
45. “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
46. “Some people believe in imaginary friends. I believe in imaginary numbers.” - R.M. ArceJaeger
47. “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
48. “If you plug in a number and the math starts getting creepy (anything involving fractions or negative numbers is creepy)...” - Doug Pierce
49. “This is the team. We're trying to go to the moon. If you can't put someone up, please don't put them down.” - NASA
50. “Atheism is the opium of the mathematicians. Atheism is the religion of Mathematics.” - Bill Gaede
51. “A mathematician believes that describing the speed of Mercury with equations amounts to science.” - Bill Gaede
52. “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
53. “A mathematician says that an electromagnetic wave travels from Andromeda to your eye and that it also extends from Andromeda to your eye.” - Bill Gaede
54. “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
55. “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
56. “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
57. “[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on.” - Paul Lockhart
58. “No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a "mixed number " while 5/2 is an "improper fraction." They're EQUAL for crying out loud. They are the exact same numbers and have the exact same properties. Who uses such words outside of fourth grade?” - Paul Lockhart
59. “In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide -- a relief from daily life, an anodyne to the practical workaday world.” - Paul Lockhart
60. “It is the story that matters not just the ending.” - Paul Lockhart
61. “Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being made over something so simple is to make people doubt their own intuition. Calling into question the obvious by insisting that it be 'rigorously proved' ... is to say to a student 'Your feelings and ideas are suspect. You need to think and speak our way.” - Paul Lockhart
62. “It's a simple matter of mathematics.” - Jean Lee Latham
63. “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
64. “The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there" all along I just couldn't see it. And now I can! This is really what keeps me in the math game-- the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods.” - Paul Lockhart
65. “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
66. “When Republicans recently charged the President with promoting 'class warfare,' he answered it was 'just math.' But it's more than math. It's a matter of morality.Republicans have posed the deepest moral question of any society: whether we're all in it together. Their answer is we're not.President Obama should proclaim, loudly and clearly, we are.” - Robert B. Reich
67. “College is the grinding machine of the Mathematical Establishment, a conveyor belt that takes individuals from one cookie cutter to another so that the product comes within tight control limits out of the assembly line.” - Bill Gaede
68. “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
69. “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
70. “I had been to school most all the time, and could spell, and read, and write just a little, and could say the multiplication table up to six times seven is thirty-five, and I don't reckon I could ever get any further than that if I was to live forever. I don't take no stock in mathematics, anyway.” - Mark Twain
71. “Solving a problem for which you know there’s an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. And it’s not always at the top of the mountain. It might be in a crack on the smoothest cliff or somewhere deep in the valley.” - Yoko Ogawa
72. “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
73. “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
74. “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
75. “Ideas that require people to reorganize their picture of the world provoke hostility.” - James Gleick
76. “She would not have cared to confess how infinitely she preferred the exactitude, the star-like impersonality, of figures to the confusion, agitation, and vagueness of the finest prose.” - Virginia Woolf
77. “Do you know what the mathematical expression is for longing? ... The negative numbers. The formalization of the feeling that you are missing something.” - Peter Høeg
78. “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
79. “Physicists have come to realize that mathematics, when used with sufficient care, is a proven pathway to truth.” - Brian Greene
80. “The language of categories is affectionately known as "abstract nonsense," so named by Norman Steenrod. This term is essentially accurate and not necessarily derogatory: categories refer to "nonsense" in the sense that they are all about the "structure," and not about the "meaning," of what they represent.” - Paolo Aluffi
81. “Mathematics is the art of explanation.” - Paul Lockhart
82. “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
83. “Mathematics effectively began when a few Greek friends got together to talk about numbers and lines and angles.” - C.S. Lewis
84. “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
85. “A brick can be used to represent the zero probability of this book being any good.” - Amy Riekhof
86. “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
87. “Formal mathematics is nature's way of letting you know how sloppyyour mathematics is.” - Leslie Lamport
88. “Seni sama pentingnya dengan matematika. Seni memanusiakan manusia. Seni menciptakan rasa empati” - Wahyu Aditya
89. “Life is about solving for x” - Jane Lescarbeau
90. “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
91. “The land of easy mathematics where he who works adds up and he who retires subtracts.” - Núria Añó
92. “My mathematics is simple: one plus one = one.” - Dejan Stojanovic
93. “I lose faith in mathematics, logical and rigid. What with those that even zero doesn’t accept?” - Dejan Stojanovic
94. “Mathematics doesn’t care about those beyond the numbers.” - Dejan Stojanovic
95. “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
96. “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
97. “Mathematicians deal with large numbers sometimes, but never in their income.” - Isaac Asimov
98. “They shouldn't be allowed to teach math so early in the morning.” - Kendare Blake
99. “. . . we come astonishingly close to the mystical beliefs of Pythagoras and his followers who attempted to submit all of life to the sovereignty of numbers. Many of our psychologists, sociologists, economists and other latter-day cabalists will have numbers to tell them the truth or they will have nothing. . . . We must remember that Galileo merely said that the language of nature is written in mathematics. He did not say that everything is. And even the truth about nature need not be expressed in mathematics. For most of human history, the language of nature has been the language of myth and ritual. These forms, one might add, had the virtues of leaving nature unthreatened and of encouraging the belief that human beings are part of it. It hardly befits a people who stand ready to blow up the planet to praise themselves too vigorously for having found the true way to talk about nature.” - Neil Postman
100. “Just as all things speak about God to those that know Him, and reveal Him to those that love Him, they also hide Him from all those that neither seek nor know Him.” - Blaise Pascal
101. “Teaching Ramanujan was like writing on a blackboard covered with excerpts from a more interesting lecture.” - Lawrence Young
102. “And, most important of all," added the Mathemagician, "here is your own magic staff. Use it well and there is nothing it cannot do for you."He placed in Milo's breast pocket a small gleaming pencil which, except for the size, was much like his own.” - Norton Juster
103. “Is everyone with one face called a Milo?""Oh no," Milo replied; "some are called Henry or George or Robert or John or lots of other things.""How terribly confusing," he cried. "Everything here is called exactly what it is. The triangles are called triangles, the circles are called circles, and even the same numbers have the same name. Why, can you imagine what would happen if we named all the twos Henry or George or Robert or John or lots of other things? You'd have to say Robert plus John equals four, and if the four's name were Albert, things would be hopeless.""I never thought of it that way," Milo admitted."Then I suggest you begin at once," admonished the Dodecahedron from his admonishing face, "for here in Digitopolis everything is quite precise.” - Norton Juster
104. “Luck is the grand equalizer.” - Nassim Nicholas Taleb
105. “. . . the world in which we live has an increasing number of feedback loops, causing events to be the cause of more events (say, people buy a book because other people bought it), thus generating snowballs and arbitrary and unpredictable planet-wide winner-take-all effects.” - Nassim Nicholas Taleb
106. “Music is the pleasure the human mind experiences from counting without being aware that it is counting.” - Martin Nowak
107. “Physics depends on a universe infinitely centred on an equals sign.” - Mark Z. Danielewski
108. “The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated ... The importance of this invention is more readily appreciated when one considers that it was beyod the two greatest men of antiquity, Archimedes and Apollonius.” - Pierre Simon de Laplace
109. “Turing attended Wittgenstein's lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems. Wittgenstein argues that he can see why people don't like contradictions outside of mathematics but cannot see what harm they do inside mathematics. Turing is exasperated and points out that such contradictions inside mathematics will lead to disasters outside mathematics: bridges will fall down. Only if there are no applications will the consequences of contradictions be innocuous. Turing eventually gave up attending these lectures. His despair is understandable. The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russel pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russel replied immediately that 'if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1'! A contradictory statement is the ultimate Trojan horse.” - John D. Barrow
110. “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
111. “PHI is one H of a lot cooler than PI!” - Dan Brown
112. “People enjoy inventing slogans which violate basic arithmetic but which illustrate “deeper” truths, such as “1 and 1 make 1” (for lovers), or “1 plus 1 plus 1 equals 1” (the Trinity). You can easily pick holes in those slogans, showing why, for instance, using the plus-sign is inappropriate in both cases. But such cases proliferate. Two raindrops running down a window-pane merge; does one plus one make one? A cloud breaks up into two clouds -more evidence of the same? It is not at all easy to draw a sharp line between cases where what is happening could be called “addition”, and where some other word is wanted. If you think about the question, you will probably come up with some criterion involving separation of the objects in space, and making sure each one is clearly distinguishable from all the others. But then how could one count ideas? Or the number of gases comprising the atmosphere? Somewhere, if you try to look it up, you can probably fin a statement such as, “There are 17 languages in India, and 462 dialects.” There is something strange about the precise statements like that, when the concepts “language” and “dialect” are themselves fuzzy.” - Douglas R. Hofstadter
113. “[...] provability is a weaker notion than truth” - Douglas R. Hofstadter
114. “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
115. “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
116. “A term meant to convey a person's inability to make sense of the numbers that run their lives.” - Douglas R. Hofstadter
