The archive

“It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils.”

“Give me a place to stand on, and I can move the earth.”

“For the things we have to learn before we can do them, we learn by doing them.”

“Mathematics is the part of physics where experiments are cheap.”

“Reading maketh a full man; conference a ready man; and writing an exact man.”

“We begin with the hypothesis that any subject can be taught effectively in some intellectually honest form to any child at any stage of development.”

“In mathematics the art of proposing a question must be held of higher value than solving it.”

“Let the main object of this, our Didactic, be as follows: To seek and to find a method of instruction, by which teachers may teach less, but learners may learn more; by which schools may be the scene of less noise, aversion, and useless labour, but of more leisure, enjoyment, and solid progress.”

“In science nothing capable of proof ought to be accepted without proof.”

“It is not enough to have a good mind; the main thing is to apply it well.”

“It is more important to have beauty in one’s equations than to have them fit experiment.”

“Above all, don’t lie to yourself. The man who lies to himself and listens to his own lie comes to such a pass that he cannot distinguish the truth within him, or around him, and so loses all respect for himself and for others. And having no respect he ceases to love.”

“Talk nonsense, but talk your own nonsense, and I’ll kiss you for it. To go wrong in one’s own way is better than to go right in someone else’s.”

“For the secret of man’s being is not only to live but to have something to live for.”

“There is no royal road to geometry.”

“Nothing is too wonderful to be true, if it be consistent with the laws of nature; and in such things as these, experiment is the best test of such consistency.”

“The first principle is that you must not fool yourself—and you are the easiest person to fool.”

“Everything can be taken from a man but one thing: the last of the human freedoms—to choose one’s attitude in any given set of circumstances, to choose one’s own way.”

“Ultimately, man should not ask what the meaning of his life is, but rather must recognize that it is he who is asked. In a word, each man is questioned by life; and he can only answer to life by answering for his own life.”

“When we are no longer able to change a situation … we are challenged to change ourselves.”

“Philosophy is written in this grand book, the universe, which stands continually open to our gaze. … 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; without these, one wanders about in a dark labyrinth.”

“Truly, it is not knowledge but learning, not possessing but acquiring, not being there but getting there, that grants the greatest enjoyment.”

“Pauca sed matura: few, but ripe.”

“The best way to learn is to do; the worst way to teach is to talk.”

“Beauty is the first test: there is no permanent place in the world for ugly mathematics.”

“They must be true because, if they were not true, no one would have had the imagination to invent them.”

“A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”

“A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts.”

“We must know. We shall know.”

“It is true that Fourier had the opinion that the principal aim of mathematics was public utility and explanation of natural phenomena; but a philosopher like him should have known that the sole end of science is the honor of the human mind, and that under this title a question about numbers is worth as much as a question about the system of the world.”

“No reception without reaction, no impression without correlative expression—this is the great maxim which the teacher ought never to forget.”

“Your vision will become clear only when you can look into your own heart. Without, everything seems discordant; only within does it coalesce into unity. Who looks outside dreams; who looks inside awakes.”

“One does not become enlightened by imagining figures of light, but by making the darkness conscious. The latter procedure, however, is disagreeable and therefore not popular.”

“The creation of something new is not accomplished by the intellect but by the play instinct acting from inner necessity. The creative mind plays with the objects it loves.”

“Many who have never had an opportunity of knowing any more about mathematics confound it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination, and one of the leading mathematicians of our century states the case quite correctly when he says that it is impossible to be a mathematician without being a poet in soul.”

“God made the integers; all else is the work of man.”

“Read Euler, read Euler, he is the master of us all.”

“Music is a hidden arithmetic exercise of the soul, which does not know that it is counting.”

“A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.”

“We may say most aptly, that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.”

“The true Logic for this world is the Calculus of Probabilities.”

“If politics is the art of the possible, research is surely the art of the soluble.”

“The beauty of mathematics only shows itself to more patient followers.”

“If I have seen further it is by standing on ye sholders of Giants.”

“My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously.”

“People are generally better persuaded by the reasons which they have themselves discovered than by those which have come into the mind of others.”

“In the fields of observation chance favours only the prepared mind.”

“The principal goal of education is to create men who are capable of doing new things, not simply of repeating what other generations have done—men who are creative, inventive, and discoverers.”

“Let no one ignorant of geometry enter.”

“For the mind does not require filling like a bottle, but rather, like wood, it only requires kindling to create in it an impulse to think independently and an ardent desire for the truth.”

“It is by logic that we prove, but by intuition that we discover.”

“Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.”

“Mathematics is the art of giving the same name to different things.”

“We can know more than we can tell.”

“A great discovery solves a great problem but there is a grain of discovery in the solution of any problem.”

“Science must begin with myths, and with the criticism of myths.”

“Consider the possibility that any man could, if he were so inclined, be the sculptor of his own brain, and that even the least gifted may, like the poorest land that has been well cultivated and fertilized, produce an abundant harvest.”

“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.”

“The process is mutual; for men learn while they teach.”

“The measure of our success is whether what we do enables people to understand and think more clearly and effectively about mathematics.”

“What the child can do in cooperation today he can do alone tomorrow.”

“My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful.”

“Civilization advances by extending the number of important operations which we can perform without thinking about them.”

“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.”