"It is an important and popular fact that things are not always as what they seem. For instance, on the planet earth, man has always assumed that he was more intelligent than dolphins because he had achieved so much: the wheel, New York, wars. [. ] But conversely, the dolphins had always believed that they were far more intelligent than men; for precisely the same reasons."
"42. (The answer to life, the universe, and everything.)"
Douglas Adams (The hitchhiker's guide to the galaxy )
"Mathematics is less related to accounting than it is to philosophy."
Leonard Adleman (quoted in an article by Gina Kolata in the New York Times on 13 December 1994)
"What if everything is an illusion and nothing exists? In that case, I definitely overpaid for my carpet."
"If you don't like your analyst, see your local algebraist!"
Gert Almkvist (founder and director of The Institute for Algebraic Meditation)
"logloglog n has been proved to go to infinity, but has never been observed to do so."
"Anyone can count the seeds in an apple, but no one can count the apples in a seed."
"You can only be truly accomplished at something you love. Don't make money the goal. Instead, pursue the things you love doing, and do them so well that people can't take their eyes off you. All the other tangible rewards will come as a result."
"Probable impossibilities are to be preferred to improbable possibilities."
"It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out."
E. Artin (Geometric Algebra. p. 14)
"Combinatorial analysis, in the trivial sense of manipulating binomial and multinomial coefficients, and formally expanding powers of infinite series by applications ad libitum and ad nauseamque of the multinomial theorem, represented the best that academic mathematics could do in the Germany of the late 18th century."
"If things are nice there is probably a good reason why they are nice: and if you do not know at least one reason for this good fortune, then you still have work to do."
Richard Askey (Ramanujan and Important Formulas. p. 32, in Srinivasa Ramanujan (1887-1920), a Tribute. K.R. Nagarajan and T. Soundarajan, eds. Madurai Kamaraj University, 1987)
"In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life."
Michael Atiya (Notices of the AMS. 2010)
"Spending time with math people is a lot of fun. As a result of the play, I've had semi-drunken dinners with mathematicians all over the country. I recommend the experience."
David Auburn (playwright of Proof )
"Quapropter bono christiano, sive mathematici, sive quilibet impie divinantium, maxime dicentes vera, cavendi sunt, ne consortio daemoniorum animam deceptam, pacto quodam societatis irretiant."
("Thus the good christian should beware of mathematicians and all those who make false prophecies, however much they may in fact speak the truth; lest, being in league with the devil, they may deceive errant souls into making common cause.")
Augustinus (De genesis ad literam. Liber 2, Caput XVII, Nr. 37)
"Z is complicated."
Eric Babson (MSRI, 12/18/08)
"If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one."
"It takes a village to count integer points."
"Lattice points are like cockroaches, if you see one, you know there are a lot of others hiding around."
"This algorithm has been proved to work, but has never been observed to do so" (about the Monte Carlo Markov Chain method for approximate counting of contingency tables).
Alexander Barvinok (Joint Summer Research Conference, Snowbird, UT, 7/16/03, Illinois Mathematics Colloquium, 02/05, and Joint Summer Research Conference, Snowbird, UT, 6/15/06)
"One and one and one is three."
The Beatles (Come together )
"Obvious is the most dangerous word in mathematics."
E. T. Bell
"Mathematics is a collection of cheap tricks and dirty jokes."
"The origins of graph theory are humble, even frivolous."
N. Biggs, E. K. Lloyd, and R. J. Wilson (Graph Theory: 1736-1936 )
"No WLAN [wi-fi]. Please just talk to each other and get drunk."
Blackboard outside a bar on Kollwitzstrasse, Berlin
"Life is the twofold internal movement of composition and decomposition at once general and continuous."
Henri de Blainville (American Journal of the Medical Sciences. 1858)
"There are two versions of math in the lives of many Americans: the strange and boring subject that they encountered in classrooms and an interesting set of ideas that is the math of the world, and is curiously different and surprisingly engaging. Our task is to introduce this second version to today's students, get them excited about math, and prepare them for the future."
Jo Boaler (What's Math Got to Do with It?. Penguin 2008)
"5 out of 4 people have trouble with fractions."
Board in Danby, NY
"Suppose that you want to teach the 'cat' concept to a very young child. Do you explain that a cat is a relatively small, primarily carnivorous mammal with retractible claws, a distinctive sonic output, etc. I'll bet not. You probably show the kid a lot of different cats, saying 'kitty' each time, until it gets the idea. To put it more generally, generalizations are best made by abstraction from experience."
R. P. Boas (Can we make mathematics inelligible?. American Mathematical Monthly 88 (1981), pp. 727-731)
"We all agree that your theory is crazy, but is it crazy enough?"
Niels Bohr (1885-1962)
"My special pleasure in mathematics rested particularly on its purely speculative part."
Bernhard Bolzano (1781-1848)
"Mathematics as we know it and as it has come to shape modern science could never have come into being without some disregard for the dangers of the infinite."
David Bressoud (A radical approach to real analysis. MAA, 2007, p. 22)
"There are no problems, just pauses between ideas."
The Brotherhood of the Rose
"There are three kinds of people: those who can count and those who can't."
Bumpersticker on a car in Ithaca, NY
"Abstraction consists essentially in the creation and utilization of ambiguity."
"Logic moves in one direction, the direction of clarity, coherence and structure. Ambiguity moves in the other direction, that of fluidity, openness, and release. Mathematics moves back and forth between these two poles. [. ] It is the interaction between these different aspects that gives mathematics its power."
William Byers (How Mathematicians Think. Princeton University Press, 2007)
"Too many people are thinking of security instead of opportunity. They seem more afraid of life than death."
James F. Byrnes
"The essence of mathematics resides in its freedom."
"To ask the right question is harder than to answer it."
"Alice laughed: 'There's no use trying,' she said; 'one can't believe impossible things.' 'I daresay you haven't had much practice,' said the Queen. 'When I was younger, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast.' "
"Where shall I begin" he asked. "Begin at the beginning", the king said, "and stop when you get to an end."
"And what is the use of a book," thought Alice, "without pictures or conversations?"
Lewis Carroll (Alice in Wonderland )
"The peculiar interest of magic squares and all lusus numerorum in general lies in the fact that they possess the charm of mystery. They appear
to betray some hidden intelligence which by a preconceived plan produces the impression of intentional design, a phenomenon which finds its close analogue in nature."
Paul Carus (in W. S. Andrews, Magic Squares and Cubes. 1960)
"First, it is necessary to study the facts, to multiply the number of observations, and then later to search for formulas that connect them so as thus to discern the particular laws governing a certain class of phenomena. In general, it is not until after these particular laws have been established that one can expect to discover and articulate the more general laws that complete theories by bringing a multitude of apparently very diverse phenomena together under a single governing principle."
Augustin Louis Cauchy (1789-1857)
"To make a great dream come true, the first requirement is a great capacity to dream; the second is persistence."
"I'm a mathematical optimist: I deal only with positive integers."
"The hardest thing being with a mathematician is that they always have problems."
"Everyone engaged in research must have had the experience of working with feverish and prolonged intensity to write a paper which no one else will read or to solve a problem which no one else thinks important and which will bring no conceivable reward -- which may only confirm a general opinion that the researcher is wasting his time on irrelevancies."
Noam Chomsky (A Review of B. F. Skinner's Verbal Behavior. Language, 35, No. 1 (1959), 26-58)
"A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty."
"I saw, as one might see the transit of Venus, a quantity passing through infinity and changing its sign from plus to minus. I saw exactly how it happened. but it was after dinner and I let it go."
Winston Churchill (My early life. 1930)
"11:15 Restate my assumptions:
1. Mathematics is the language of nature.
2. Everything around us can be represented and understood through numbers.
3. If you graph these numbers, patterns emerge. Therefore: There are patterns everywhere in nature."
Max Cohen (played by Sean Gullette, in Pi. a film by Darren Aronofsky)
"To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples. "
John B. Conway ( Subnormal Operators. Pitman Advanced Publishing Program, 1981)
"I hate algebra."
John H. Conway (Invited AMS address, Toronto, 9/23/00)
"I have photographed many people: artists, writers, and scientists, among others. In speaking about their work, mathematicians use the words 'elegance', 'truth', and 'beauty' more than everyone else combined."
Mariana Cook (in the preface of her book Mathematicians: An Outer View of the Inner World with Clifford Gunning, Princeton University Press, 2009).
"The mathematical phenomenon always develops out of simple arithmetic, so useful in everyday life, out of numbers, those weapons of the gods: the gods are there, behind the wall, at play with numbers."
"A mathematician is a blind man in a dark room looking for a black cat which isn't there."
Charles R. Darwin
"Je serais reconnaissant a toute personne ayant compris cette demonstration de me l'expliquer."
Pierre Deligne (Theorie des topos et cohomologie etale des schemas, Tome 3. p. 584)
"Mathematicians care no more for logic than logicians for mathematics."
Augustus De Morgan
"Basically, what we did the last four weeks was speed-dating polytopes."
Jessica De Silva (MSRI-UP, 27 July 2012)
"I certainly do care about measuring educational results. But what is an 'educational result?' The twinkling eyes of my students, together with their heartfelt and beautifully expressed mathematical arguments are all the results I need."
"The grand thing is to be able to reason backwards."
Arthur Conan Doyle (A study in scarlet )
"A lot of mathematicians are a little bit strange in one way or another. It goes with creativity."
"Suppose that we think of the integers lined up like dominoes. The inductive step tells us that they are close enough for each domino to knock over the next one, the base case tells us that the first domino falls over, the conclusion is that they all fall over. The fault in this analogy is that it takes time for each domino to fall and so a domino which is a long way along the line won't fall over for a long time. Mathematical implication is outside time."
Peter J. Eccles (An Introduction to Mathematical Reasoning. p. 41)
"I have not failed. I've just found 10,000 ways that won't work."
Thomas Alva Edison (1847-1931)
"The most beautiful experience is the mysterious. It is the source of true art and science."
"Everything should be made as simple as possible, but not simpler."
"Not everything that can be counted counts, and not everything that counts can be counted."
"Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater."
"I never think of the future--it comes soon enough."
"Imagination is more important than knowledge."
"It's not that I'm so smart. It's just that I spent more time on problems."
"Insofern sich die Sätze der Mathematik auf die Wirklichkeit beziehen, sind sie nicht sicher, und insofern sie sicher sind, beziehen sie sich nicht auf die Wirklichkeit."
"Wenn ein gewisses technisches Können erreicht ist, verschmelzen Wissenschaft und Kunst gern zur Ästhetik. Die grossen Wissenschaftler sind auch immer Künstler."
Albert Einstein (1879-1955)
"The secret to education is respecting the pupil."
Ralph Waldo Emerson
"Analysis is the art of taming infinity."
Neil Falkner (Amer. Math. Monthly 116 (2009), p. 658)
"One cannot understand. the universality of laws of nature, the relationship of things, without an understanding of mathematics. There is no other way to do it."
Richard P. Feynman
"Education's purpose is to replace an empty mind with an open one."
"Spoon feeding, in the long run teaches us nothing but the shape of the spoon."
E. M. Forster
"Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them."
Jean Baptiste Joseph Fourier (1768-1830)
"In 1906, it was estimated that one in eight Americans bought a postcard every day."
John Freeman ( The Tyranny of E-mail. p. 46; the book is quite good otherwise)
"When I am working on a problem I never think about beauty. I only think about how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong."
"Everything you've learned in school as 'obvious' becomes less and less obvious as you begin to study the universe. For example, there are no solids in the universe. There's not even a suggestion of a solid. There are no absolute continuums. There are no surfaces. There are no straight lines."
Buckminster Fuller (1895-1983)
"Philosophy is written in this grand book--I mean the universe--which stands continually open to our glaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it."
Galileo Galilei (Il Saggiatore. 1623)
"Bart: Hey, Houdini! Why don't you saw Martin in half?
Magician: Oh, I'm not the kind of magician who does tricks. I'm a mathemagician!
Magician: Now, prepare to marvel at the mysteries of the universe, as I make this remainder disappear. [writes 7 goes into 28 three times]
Lisa: But 7 goes into 28 four times.
Magician: Uh, this is a magic 7."