Mathematical quotes

"If you do not rest on the good foundation of nature, you will labour with little honor and less profit." - Leonardo Da Vinci

 "The man who discredits the supreme certainty of mathematics is feeding on confusion, and can never silence the contradictions of sophistical sciences, which lead to eternal quackery" - Leonardo Da Vinci"

The known is finite, the unknown infinit; Intellectually we stand on an islet in the midst of an illimitable ocean of inexplicability. Our business in every generation is to reclaim a little more land." - T. H. Huxley"

If a faithfull account was rendered of man's ideas of divinity, he would be obliged to acknowledge, that for the most part the word "gods" has been used to express the concealed, remote, unknown causes of the effects he witnesses; that he applies this term when the spring of the natural, the source of known causes, ceases to be visible: as soon as he loses the thread of these causes, or as soon as his mind can no longer follow the chain, he solves the difficulty, terminates his research, by ascribing it to his gods . . . When, therefore, he ascribes to his gods the production of some phenomenon . . . does he, in fact, do anything more than substitute for the darkness of his own mind, a sound to which he has been accustomed to listen with reverential awe?" - Paul Heinrich Dietrich, Baron von Holbach, Systeme de la Nature, London, 1770

 "The ancients who wished to illustrate illustrious virtue throughout the Kingdom first ordered well their own states. Wishing to order well their states, they first regulated their families. Wishing to regulate their families, they first cultivated their persons. Wishing to cultivate their persons, they first rectified their hearts. Wishing to rectify their hearts, they first sought to be sincere in their thoughts. Wishing to be sincere in their thoughts, they first extended to the utmost their knowledge. Such extension of knowledge lay in the investigation of things." - Confusious

 "Let me not seem to have lived in vain . . . let me not seem to have lived in vain." - Tycho Brahe

 "and still it moves" - Galileo

 "Philosophy(nature) is written in that great book which ever lies before our eyes - I mean the universe - but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language, and the symbols are triangles, circles, and other geometric figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth." - Galileo


 "All men are mortal
Socrates is Mortal; therefore,
Socrates must die" - Plato

 "there is no royal road to geometry" - Euclid

"This, therefore, is mathematics: she reminds you of the invisible form of the soul; she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she obolishes oblivion and ignorance which are ours by birth."  Proclus

"- . . . someone who had begun to learn geometry from Euclid, when he had learned the first theorem, asked Euclid "What shall I get out of what he learns?" Euclid called his slave and said "Give him threepence since he must make gain out of what he learns." Strabasus, about Euclid

"I do not know what I appear to the world; but to myself, i seem to have been only like a boy playing on the seashore ,and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me." - Isaac Newton

"If i have seen a little farther than others, it is because i have stood on the shoulders of giants." - Isaac Newton

"The time will come when diligent research over long periods will bring to light things which now lie hidden. A single lifetime, even though entirely devoted to the sky, would not be enough for the investigation of so vast a subject . . . And so this knowledge will be unfolded only through long successive ages. There will come a time when our descendents will be amazed that we did not know things that are so plain to them . . . many discoveries are reserved for ages still to come, when memory of us will have been effaced. Our universe is a sorry little affair unless it has in it something for every age to investigate . . . Nature does not reveal her mysteries once and for all." - Seneca, Natural Questions, Book 7, first century A.D.

Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patients to ransack; it is not a mine, whose treasures may take long to reduce into possession, but which fill on a limited number of reeins(not to sure about this word in my quote) and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined; it is as limitless as that space which it finds too narrow for its aspirations; its possibilities are as infinit as the worlds which are forever crowding in and multiplying upon the astronomical gaze; it is as incapable of being restricted within assigned boundaries or being reduced to definitions of permanent validity, as the consciousness of life," - James Sylvester

"Logic can be patient, for it is eternal." - Oliver Heaviside

"Logic is invincible because in order to combat logic it is necessary to use logic." - Pierre Boutroux.

"The science of pure mathematics in its modern development, may claim to be the most original creation of the human spirit," - A. N. Whitehead

"I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting hamlet from the play which is named after him. That would be claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming, and a little mad. Let us grant that the pursuit of mathematics is a devine madness of the human spirit, a refuge from the goading urgency of contingent happenings." - A.N. Whitehead

"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 Russel

"Proof is the idol which the mathematician tortures himself." - Sir Arthur Eddington

"We have found that where science has progressed the farthest, the mind has but regained from nature that which the mind has put into nature. We have found a strange footprint on the shores of the unknown. We have devised profound theories, one after another, to account for its origin. At last we have succeeded in reconstructing the creature that made the footprint. and Lo! it is our own!" - Sir Arthur Eddington

"the question of the foundations and the ultimate meaning of mathematics remains open; we do not know in what direction it will find its final solution or even whether a final objective answer can be expected at all. "Mathematizing" may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalization." - Herman Weyl

"These people are all anxious that we shall behave well, and yet that we shall not question how we behave." - Jacob Bronowski

"If you want to think of the goal of the human race, there it is. To learn about the universe and ourselves." - I.I. Rabi

"Our job in physics . . . is to understand a great many complicated phenomenon in a unified way." - Steven Weinberg

"Whatever may be one's opinion as to the simplicity of either the laws or the material structures of Nature, there can be no question that the possessors of such conviction have a real advantage in the race for physical discovery. Doubtless, there are many simple connections still to be discovered, and he who has a strong conviction of the existence of these simple connections is much more likely to find them than he who is not at all sure that they are there." - Percy Bridgeman

"the knowledge at which geometry aims is knowledge of the eternal, and not of aught perishing and transient" - Plato

"Since the earliest times, all critical revisions of the principles of mathematics as a whole, or any branch of it, have almost invariably followed periods of uncertainty, where contradictions did appear and had to be resolved . . . . there are now twenty-five centuries during which the mathematians have had the practice of correcting their errors and thereby seeing their science enriched, not impoverished; this gives them the right to view the future with serenity." - Bourbaki

space exploration is the moral equivalent of war - William James

"there is probably no other science which presents such different appearances to one who cultivates it and one who does not, as mathematics. To[the later] it is ancient, venerable, and complete; a body of dry, irrafutable, unambiguous reasoning. To the mathematician, on the other hand, his science is yet in the purple bloom of vigorous youth." - C.H. Chapman

"Knowing others is intelligence;
knowing yourself is true wisdom.
Mastering others is strength;
mastering yourself is true power."
— Lao Tzu

"We are all agreed," said Bohr, "that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance to be correct. My own feeling is that it is not crazy enough." - Neils Bohr

"You have written this hugh book on the system of the world without once mentioning the author of the universe. Sire, Laplace retorted, I had no need of that hypothesis." - exchange between Napoleon Bonaparte and Laplace

"Newton was a most fortunate man because there is just one universe and Newton had discovered its laws." - Laplace

"What is laid down, ordered, factual, is never enough to embrace the whole truth: life always spills over the rim of every cup." - Boris Pasternak

"What is now proved was once only imagin'd." - William Blake

"The Earch is the cradle of mankind, but one cannot stay in the cradle forever." - Konstantin Tsiolkovsky

"Any sufficiently advanced technology is indistinguishable from magic." - Arthur C. Clarke

"Man is the Measure of all things." - Protagoras

"That's one small step for a man, one giant leap for mankind" - Neil Armstrong

"Failure Is Not an Option" - Gene Kranz

"the contemplation of this world beckoned like a liberation" - Albert Einstein

"In most sciences one generation tears down what another has built, and what one has established another undoes. In mathematics alone each generation adds a new story to the old structure." - Hermann Hankel

"there is no truth, if there were it could not be comprehended-and if comprehended, it could not be communicated" - character in a Plato dialog

"to create a healthy philosophy you should renounce metaphysics but be a good mathematician" - Bertrand Russel

"We shall not cease from exploration, and the end of all our exploring will be to arrive where we started and know the place for the first time." - T.S. Eliot

"if you understand something today, it must already be obsolete'.". - anonymus

"If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet." - Niels Bohr

"Mathematicians must keep their heads in the clouds and their feet on the ground." - Morris Kline

"Should anyone find it singular that we have been able to found a Course of Mathematics on the sole concept of a system of coordinates, he may be reminded that it is preciselly these systems which characterize the phases and stages of science. Without the invention of rectangular coordinates, algebra might still be where Diophantus and his commentators left it, and we should lack both the infinitesimal calculus and analytic mechanics. Without the introduction of spherical coordinates, celestial mechanics would be absolutely impossible; and without elliptic coordinates, illustrious mathematicians would have been unable to solve several important problems of this theory . . . . Subsequently the reign of general curvilinear coordinates supervened, and these alone are capable of attacking the new problems[of mathematical physics] in all their generality. Yes, this definitive epoch will arrive, but tardily: those who first recognized these new implements will have ceased to exist and will be completely forgotten-unless some archaeological mathematician revives their names. Well, what of it, provided science has advanced?" - G. Lame(french)

"1:9 The thing that hath been, it is that which shall be; and that which is done is that which shall be done: and there is no new thing under the sun." - Bible's Ecclesiastes(not that I support this view!)

"cosmologists are often wrong but never in dought" - common saying

"in mathematics you don't understand things, you just get used to them" - John Von Neuman

"A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." - Max Planck

"It is essential that such a treatise should be rid of everything superfluous(for this is an obstacle to the aquisition of knowledge); it should select everything that embraces the subject and bring it to a point(for this is of supreme service to science); it must have great regard at once to clearness and conciseness(for their opposites trouble our understanding); it must aim at the embracing of theorems in general terms(for the piecemeal division of instruction into the more partial makes knowledge difficult to grasp)." - Geminus through Proclus

"The taste for the abstract sciences in general and, above all, for the mysteries of numbers, is very rare; this is not surprising, since the charms of this sublime science in all their beauty reveal themselves only to those who have the courage to fathom them." - Carl Frederich Gauss

"Euclid alone . . . has looked on Beauty bare." - Ena St Vincent Millay

"Socrates. Very good; let us begin then, Protarchus, by asking a question . . . Protarchus. What question? . . . Socrates. Whether all this which they call the universe is left to the guidance of unreason and chance medley, or, on the contrary, as our fathers have declared, ordered and governed by a marvellous intelligence and wisdom . . . Protarchus. Wide asunder are the two assertions, illustrious Socrates, for that which you are just now saying to me appears blasphemy, but the other assertion, that mind orders all things, is worthy of the aspect of the world . . . " - Plato: Philebus