The majority of people in the world today do not seem especially fond of mathematics. A recent survey of things people greatly disliked rated mathematics near the top of the list! But they should realize mathematics can be an extremely fascinating field packed with beauty and wonder.
No, I am not referring to the long division or tedious multiplication we all suffered through in elementary school. Instead I’m speaking of elegant proofs and conjectures and interesting problems that arise in the higher realms of mathematics, which can be delightful even to the untrained individual.
A nice fact about our modern era is that numerous books are available devoted to describing famous math problems to the average person on the street. Pop math books,” David Foster Wallace calls them. Symmetry and the Monster, Fermat’s Enigma, The Man Who Loved Only Numbers, Music of the Primes, Everything and More: A Compact History of Infinity, Four Colours Suffice, The Man Who Knew Infinity, these are only a few of the great books detailing the stories of famous problems or interesting mathematicians, and you do not need a PhD in number theory to understand them.
All right, but is there another way to take a peek inside the scintillating mathematical labyrinth? I’m sure there are many, but mathematical quotations can also give one access to some of the beauty of math. Below are 39 quotes that I hope will stimulate you to read a popular math book sometime, or maybe even work on a few integral calculus problems for fun!
“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.” – John von Neumann
“The study of the infinite is much more than a dry, academic game. The intellectual pursuit of the Absolute Infinite is a form of the soul’s quest for God. Whether or not the goal is ever reached, an awareness of the process brings enlightenment.” – Rudy Rucker
“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 Churchill
“I believe that scientific knowledge has fractal properties; that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex as the whole was to start with. That, I think, is the secret of the Universe.” – Isaac Asimov
“Go down deep enough into anything and you will find mathematics.” – Dean Schlicter
“Black holes result from God dividing the universe by zero.” – Unknown
“The task is not so much to see what no one has yet seen, but rather to think what no one has yet thought, about that which everyone sees.” – Erwin Schrodinger
“Twice two makes four seems to me simply a piece of insolence. Twice two makes four is a pert coxcomb who stands with arms akimbo barring your path and spitting. I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too.” – Fyodor Dostoevsky
“Poets do not go mad; but chess players do. Mathematicians go mad, and cashiers; but creative artists very seldom. I am not attacking logic: I only say that this danger does lie in logic, not in imagination.” – G. K. Chesterton
“With my full philosophical rucksack I can only climb slowly up the mountain of mathematics.” – Ludwig Wittgenstein
“The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can’t even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions.” – Ronald L. Graham
“Reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.” – G. H. Hardy
“‘Every minute dies a man, Every minute one is born;’ – I need hardly point out to you that this calculation would tend to keep the sum total of the world’s population in a state of perpetual equipoise, whereas it is a well-known fact that the said sum total is constantly on the increase. I would therefore take the liberty of suggesting that in the next edition of your excellent poem the erroneous calculation to which I refer should be corrected as follows: ‘Every moment dies a man, And one and a sixteenth is born.’ I may add that the exact figures are 1.067, but something must, of course, be conceded to the laws of metre.” – From a letter by Charles Babbage to the poet Alfred Lord Tennyson concerning a line in Tennyson’s poem “The Vision of Sin.
I was x years old in the year x2.” (His answer on being asked his age.) – Augustus de Morgan
“I’ve dealt with numbers all my life, of course, and after a while you begin to feel that each number has a personality of its own. A twelve is very different from a thirteen, for example. Twelve is upright, conscientious, intelligent, whereas thirteen is a loner, a shady character who won’t think twice about breaking the law to get what he wants. Eleven is tough, an outdoorsman who likes tramping through woods and scaling mountains; ten is rather simpleminded, a bland figure who always does what he’s told; nine is deep and mystical, a Buddha of contemplation…” – Paul Auster
“For a human, there are gigaplex possible thoughts.” (A gigaplex is a number written as 1 with a billion trailing zeros.) – Rudy Rucker
“An intelligent observer seeing mathematicians at work might conclude that they are devotees of exotic sects, pursuers of esoteric keys to the universe.” – P. Davis and R. Hersh, “The Mathematical Experience”
“In mathematics you don’t understand things, you just get used to them.” – John von Neumann
“Not everything that can be counted counts, and not everything that counts can be counted.” – Albert Einstein
“The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.” – Aristotle
“E = mc2.” (Einstein’s famous equation in which he realized that energy and matter are actually equivalent.)
“As the sun eclipses the stars by its brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more if he solves them.” – Brahmagupta
“2 is not equal to 3 – not even for very large values of 2.” – Grabel’s Law
“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
“How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?” – Albert Einstein
“God exists since mathematics is consistent, and the Devil exists since we cannot prove it.” – Andre Weil
“The infinite we shall do right away. The finite may take a little longer.” – Stanislav Ulam
“Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.” – Henri Poincare
“Structures are the weapons of the mathematician.” – N. Bourbaki
“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.” – Albert Einstein
Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture.” – Bertrand Russell
“Definition of a Statistician: A man who believes figures don’t lie, but admits that under analysis some of them won’t stand up either.” – Evan Esar
“A mathematician is a device for turning coffee into theorems.” – Paul Erdos
“Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.” – John Von Neumann
“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.” – Albert Einstein
“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.” – Bertrand Russell
“I have hardly ever known a mathematician who was capable of reasoning.” – Plato
“Mathematics is the queen of the sciences.” – Carl Friedrich Gauss
