Arithmetic is where the answer is right and everything is nice and you can look out of the window and see the blue sky—or the answer is wrong and you have to start over and try again and see how it comes out this time.

—Carl Sandburg *(1878–1967) American Biographer, Novelist, Socialist*

So-called professional mathematicians have, in their reliance on the relative incapacity of the rest of mankind, acquired for themselves a reputation for profundity very similar to the reputation for sanctity possessed by theologians.

—Georg Christoph Lichtenberg *(1742–99) German Philosopher, Physicist*

I have often admired the mystical way of Pythagoras, and the secret magic of numbers.

—Thomas Browne *(1605–82) English Author, Physician*

All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.

—Roger Bacon *(1214–94) English Philosopher, Scientist*

Mathematics, rightly viewed, posses not only truth, but supreme beauty a beauty cold and austere, like that of sculpture.

—Bertrand A. Russell *(1872–1970) British Philosopher, Mathematician, Social Critic*

In the one branch he most needed

—Henry Adams *(1838–1918) American Historian, Man of Letters*

If we are truly prudent we shall cherish those noblest and happiest of our tendencies—to love and to confide.

—Edward Bulwer-Lytton, 1st Baron Lytton *(1803–73) British Novelist, Poet, Politician*

The teacher pretended that algebra was a perfectly natural affair, to be taken for granted, whereas I didn’t even know what numbers were. Mathematics classes became sheer terror and torture to me. I was so intimidated by my incomprehension that I did not dare to ask any questions.

—Carl Gustav Jung *(1875–1961) Swiss Psychologist, Psychiatrist, Philosopher*

Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.

—Friedrich Nietzsche *(1844–1900) German Philosopher, Scholar, Writer*

Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.

—Simone Weil *(1909–1943) French Philosopher, Political Activist*

Yet what are all such gaieties to me whose thoughts are full of indices and surds?

—Charles Lutwidge Dodgson (Lewis Carroll) *(1832–98) British Anglican Author, Mathematician, Clergyman, Photographer, Logician*

It is amusing to discover, in the twentieth century, that the quarrels between two lovers, two mathematicians, two nations, two economic systems, usually assumed insoluble in a finite period should exhibit one mechanism, the semantic mechanism of identification—the discovery of which makes universal agreement possible, in mathematics and in life.

—Alfred Korzybski *(1879–1950) Polish-American Scientist, Philosopher of Language*

What would life be without arithmetic, but a scene of horrors?

—Sydney Smith *(1771–1845) English Clergyman, Essayist, Wit*

If a man’s wit be wandering, let him study the mathematics.

—Francis Bacon *(1561–1626) English Philosopher*

Nobody before the Pythagorean had thought that mathematical relations held the secret of the universe. Twenty-five centuries later, Europe is still blessed and cursed with their heritage. To non-European civilizations, the idea that numbers are the key to both wisdom and power, seems never to have occurred.

—Arthur Koestler *(1905–83) British Writer, Journalist, Political Refugee*

There are no creeds in mathematics.

—Peter Drucker *(1909–2005) Austrian-born Management Consultant*

The study of mathematics cultivates the reason; that of the languages, at the same time, the reason and the taste. The former gives grasp and power to the mind; the latter both power and flexibility. The former, by itself, would prepare us for a state of certainties, which nowhere exists; the latter, for a state of probabilities, which is that of common life. Each, by itself, does but an imperfect work: in the union of both, is the best discipline for the mind, and the best mental training for the world as it is.

—Tryon Edwards *American Theologian*

The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

—Bertrand A. Russell *(1872–1970) British Philosopher, Mathematician, Social Critic*

The laws of Nature are written in the language of mathematics…the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.

—Galileo Galilei *(1564–1642) Italian Astronomer, Physicist, Mathematician*

I … am always glad to touch the living rock again and dip my hand in the high mountain air.

—Isaac Asimov *(1920–92) Russian-born American Writer, Scientist*

Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.

—Bertrand A. Russell *(1872–1970) British Philosopher, Mathematician, Social Critic*

In studying mathematics or simply using a mathematical principle, if we get the wrong answer in sort of algebraic equation, we do not suddenly feel that there is an anti-mathematical principle that is luring us into the wrong answers.

—Eric Butterworth *(1916–2003) American Spirituality Writer*

Avoid witicisms at the expense of others.

—Horace Mann *(1796–1859) American Educator, Politician, Educationalist*

How happy the lot of the mathematician! He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve. No cashier writes a letter to the press complaining about the incomprehensibility of Modern Mathematics and comparing it unfavorably with the good old days when mathematicians were content to paper irregularly shaped rooms and fill bathtubs without closing the waste pipe.

—W. H. Auden *(1907–73) British-born American Poet, Dramatist*

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 Byron (George Gordon Byron) *(1788–1824) English Romantic Poet*

To the pure geometer the radius of curvature is an incidental characteristic – like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the cat without a grin and the grin without a cat are equally set aside as purely mathematical fantasies.

—Arthur Eddington *(1882–1944) English Astronomer*

Mathematics may be compared to a mill of exquisite workmanship, which grinds your stuff to any degree of fineness; but, nevertheless, what you get out depends on what you put in; and as the grandest mill in the world will not extract wheat flour from peas cods, so pages of formulae will not get a definite result out of loose data.

—Thomas Henry Huxley *(1825–95) English Biologist*

I once asked Richard Feynman whether he thought of mathematics and, by extension, the laws of physics as having an independent existence. He replied: The problem of existence is a very interesting and difficult one. if you do mathematics, which is simply working out the consequences of assumptions, you’ll discover for instance a curious thing if you add the cubes of integers. One cubed is one, two cubed is two times two times two, that’s eight, and three cubed is three times three times three, that’s twenty-seven. If you add the cubes of these, one plus eight plus twenty-seven- let’s stop there – that would be thirty-six. And that’s the square of of another number, six, and that number is the sum of those same integers. one plus two plus three…Now, that fact which I’ve just told you about might not have been known to you before. You might say Where is it, what is it, where is it located, what kind of reality does it have?’ And yet you came upon it. When you discover these things, you get the feeling that they were true before you found them. So you get the idea that somehow they existed somewhere, but there’s nowhere for such things. It’s just a feeling…Well, in the case of physics we have double trouble. We come upon these mathematical interrelationships but they apply to the universe, so the problem of where they are is doubly confusing…Those are philosophical questions that I don’t know how to answer.

—Richard Feynman *(1918–88) American Physicist*

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method

—Nicholas Murray Butler *(1862–1947) American Philosopher, Diplomat, Educator*

One has to be able to count if only so that at fifty one doesn’t marry a girl of twenty.

—Maxim Gorky *(1868–1936) Russian Writer, Dramatist, Political Activist, Novelist*

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 A. Russell *(1872–1970) British Philosopher, Mathematician, Social Critic*

Now I feel as if I should succeed in doing something in mathematics, although I cannot see why it is so very important… The knowledge doesn’t make life any sweeter or happier, does it?

—Helen Keller *(1880–1968) American Author*

But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.

—Antonin Artaud *(1896–1948) French Actor, Drama Theorist*

It is from this absolute indifference and tranquillity of the mind, that mathematical speculations derive some of the most considerable advantages; because there is nothing to interest the imagination; because the judgment sits free and unbiased to examine the point. All proportions, every arrangement of quantity, is alike to the understanding, because the same truths result to it from all; from greater from lesser, from equality and inequality.

—Edmund Burke *(1729–97) British Philosopher, Statesman*

Pure mathematics do remedy and cure many defects in the wit and faculties of individuals; for if the wit be dull, they sharpen it; _ if too wandering they fix it; if too inherent in the sense, they abstract it.

—Francis Bacon *(1561–1626) English Philosopher*

In the midst of this chopping sea of civilized life, such are the clouds and storms and quicksands and thousand-and-one items to be allowed for, that a man has to live, if he would not founder and go to the bottom and not make his port at all, by dead reckoning, and he must be a great calculator indeed who succeeds.

—Henry David Thoreau *(1817–62) American Philosopher*

It is a mathematical fact that the casting of this pebble from my hand alters the centre of gravity of the universe.

—Thomas Carlyle *(1795–1881) Scottish Historian, Essayist*

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 *(1879–1955) German-born Physicist*

Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight.

—Johann Wolfgang von Goethe *(1749–1832) German Poet*

Mathematicians are like Frenchman: whatever you say to them they translate Into their own language, and forthwith it is something entirely different.

—Johann Wolfgang von Goethe *(1749–1832) German Poet*

I would advise you Sir, to study algebra, if you are not already an adept in it: your head would be less muddy, and you will leave off tormenting your neighbors about paper and packthread, while we all live together in a world that is bursting with sin and sorrow.

—Samuel Johnson *(1709–84) British Essayist*