Quotations on Mathematics

(and not only...)

In no particular order....
"L'inteletto umano ne intende alcune [proposizioni] cosi' perfettamente, e ne ha cosi' assoluta certezza, quanto se n'abbia l'istessa natura; e tali sono le scienze matematiche pure, cioe' la geometria e l'aritmetica, delle quali l'intelletto divino ne sa bene infinite proposizioni di piu', perche' le sa tutte, ma di quelle poche intese dell'intelletto umano credo che la cognizione agguagli la divina nella certezza obiettiva". -- G. Galilei
La matematica pura e' costituita interamente da asserzioni del tipo: se una proposizione cosi' e cosi' e' vera per qualunque cosa, allora un'altra proposizione cosi' e cosi' e' vera per quella cosa. E' essenziale non discutere se la prima proposizione sia effettivamente vera e non precisare che cosa sia la qualunque cosa per cui si presume sia vera.... Se la nostra ipotesi riguarda qualunque cosa e non una o piu' cose particolari, allora le nostre deduzioni fanno parte della matematica. Cosi' la matematica puo' essere definita come la disciplina in cui non si sa mai di che cosa si sta parlando, ne' se cio' che si sta dicendo sia vero." -- B. Russel
"It would be better for the true physics if there were no mathematicians on Earth." -- D. Bernoulli
"Nature laughs at the difficulties of integration." -- P.S. de Laplace
"We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover up all the tracks, to not worry about the blind alleys or describe how you had the wrong idea first, and so on. Si there isn't any place to publish, in a dignified manner, what you actually did in order to get to do the work." -- R.P. Feynman
"We are not very pleased when we are forced to accept a mathematical truth by virtute of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context". -- H. Weyl
"As for everything else, so for a mathematical theory: beauty can be perceived but not explained." -- A. Cayley
"Mathematics is often erroneously reffered to as the science of common sense. Actually, it may trascend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense." -- E. Kasner and J. Newman
"God exists since mathematics is consistent, and the Devil exists since we cannot prove it." -- A. Weil
"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." -- Alice in Wonderland.
"The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics." -- G.H. Hardy
"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
"In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy. " -- G.H. Hardy
"Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. `Immortality' may be a silly word, but probably a mathematician has the best chance of whatever it may mean." -- G.H. Hardy
"Rigour is the affair of philosophy, not of mathematics" -- B. Cavalieri
"The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell." -- Saint Augustine
"I never came across one of Laplace's 'Thus it plainly appears' without feeling sure that I have hours of hard work before me to fill up the chasm and find out and show how in plainly appears." -- N. Bowditch
"A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies." -- Stefan Banach
"Forse questo bisogno di giocare si nasconde anhe nella Matematica pura. Non vi e' molta differenza tra il piacere provato da un dilettante nel risolvere un abile rompicapo ed il piacere che un matematico prova nel dominare un problema piu' difficile. Entrambi guardano alla bellezza pura, quell'ordine limpido, nettamente definito, misterioso, estasiante che permea tutte le strutture." -- M. Gardner
"Suppose a contradiction were to be found in the axioms of set theory. Do you seriously believe that a bridge would fall down?" -- F. Ramsey
"The only real valuable thing is inituition" -- A. Einstein
"God does not care about our mathmatical difficulties. He integrates empirically" -- A. Einstein
"Science is like sex: sometimes something useful comes out, but that is not the reason we are doing it" -- Richard Feynman
"Not everything that counts can be counted, not everything that can be counted counts" -- A. Einstein
"Ogni insieme puo' essere dotato di una metrica che non serve assolutamente a niente, ma esiste"
"Se ogni aperto fosse compatto, saremmo disoccupati" -- R. M. Colombo
"Mathematic is the art of giving things misleading names" -- I. Podlubny
"He who has imagination without learning has wings but no feet."
"Geometry is the rules of all mental investigation" -- M. V. Lomonosov
"A mathematician is a device for turning coffee into theorems." -- P. Erdos
"If I have seen farther than others, it is because I was standing on the shoulders of giants." -- Isaac Newton
"If I have not seen as far as others, it is because giants were standing on my shoulders." -- Hal Abelson
"Il libro della natura e' scritto coi caratteri della Geometria." -- Galileo
"Esplorare l'esplorabile, contemplare silenziosamente l'inesplorabile." -- Max Planck
"Nulla e' troppo meraviglioso per essere vero" -- Michael Faraday
"Mathematics is the only science where one never knows what one is talking about nor whether what is said is true" -- Russell
"Mathematicians practice absolute freedom." -- Henry Adams
"The moving power of mathematics is not reasoning but imagination." -- Augustus De Morgan
"The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver." -- I.N. Herstein
"Logic is the anatomy of thought." -- John Locke
"The art of doing mathematics consists in finding that special case which contains all the germs of generality." -- D. Hilbert
"Dio ha creato i numeri interi; tutto il resto e' lavoro dell'Uomo." -- Kronecker
"Non c'e' niente da fare, la matematica deve avere la sua estetica: x=2.... Bello. La semplicita'..." -- G. Gaber
"Any good idea can be stated in fifty words or less." -- S. Ulam
"Geometry is the science of correct reasoning on incorrect figures" -- George Polya
"Mathematics is the art of giving the same name to different things." -- H. Poincar�
"An expert is a man who has made all the mistakes, which can be made, in a very narrow field." -- N. Bohr
"It is true that a mathematician who is not also something of a poet will never be a perfect mathematician." -- K. Weierstrass
"The mathematician's best work is art, a high perfect art [...]. Mathematical genius and artistic genius touch one another." -- G. Mittag-Leffler
"It can be of no practical use to know that π is irrational, but if we can know, it surely would be intolerable not to know." -- Edward Titchmarsh
"Life is good for only two things, discovering mathematics and teaching mathematics." -- S. Poisson
"A good mathematical joke is better, and better mathematics, than a dozen mediocre papers." -- J. E. Littlewood
"Try a hard problem. You may not solve it, but you will prove something else." -- J. E. Littlewood
"Mathematics is a dangerous profession; an appreciable proportion of us goes mad." -- J. E. Littlewood
"Never think that God's delays are God's denials. Hold on; hold fast; hold out. Patience is genius." -- G. Buffon
"If there is a problem you can't solve, then there is an easier problem you can't solve: find it." -- G. P�ya
"Mathematics consists of proving the most obvious thing in the least obvious way." -- G. P�ya
"Mathematics is the cheapest science. [...] All one needs for mathematics is a pencil and paper." -- G. P�ya
"There are many questions which fools can ask that wise men cannot answer." -- G. P�ya
"The science of pure mathematics ... may claim to be the most original creation of the human spirit." -- A. Whitehead
"Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions." -- F. Klein
"...Unix, MS-DOS, and Windows NT (also known as the Good, the Bad, and the Ugly)." -- Matt Welsh
"Errare e' umano, ma per fare veramente casino ci vuole la password di root"
"Benedetta gente, farebbero qualsiasi cosa per far finta che la magia non esiste, anche quando ce l'hanno sotto il naso..." -- Hagrid
"Un amico e' uno che sa tutto di te e nonostante questo gli piaci." -- Elbert Hubbard
"La vita e i sogni sono fogli di uno stesso libro. Leggerli in ordine e' vivere, sfogliarli a caso e' sognare." -- Arthur Schopenauer
"Tomorrow, this will be part of the unchangeable past but fortunately, it can still be changed today."
"Siamo un esercito di sognatori: per questo siamo invincibili"
"Col viso ritornai per tutte quante
le sette sfere, e vidi questo globo
tal, ch'io sorrisi del suo vil sembiante" -- Dante Alighieri
"E' meglio essere ottimisti ed avere torto piuttosto che essere pessimisti ed avere ragione." -- Albert Einstein
"Tutto cio' che accade tu lo scrivi", disse. "Tutto cio' che io scrivo accade", fu la risposta.
"Che importa l'esser nati nel cortile delle anitre, quando si esce da un ovo di cigno?" -- H. Christian Andersen
"The mind is not a vessel to be filled. It is a fire to be kindled." -- Plutarch
"Se riesci a mantenere la calma quando tutti intorno a te hanno perso la testa, forse non hai afferrato bene la situazione." -- J. Kerr
"La distanza piu' breve tra due persone e' un sorriso." -- Eberhard Zeidler
"To see the world in a grain of sand
and heaven in a wild flower;
hold infinity in your hand
and eternity in an hour" -- W. Blake
"Ci fu un terribile, mortale silenzio.
Ci fu un terribile, mortale silenzio.
Ci fu un terribile, mortale silenzio." -- Douglas Adams
"Ogni sublime umorismo comincia con la rinuncia dell'uomo a prendere sul serio la propria persona." -- Hermann Hesse