Quotes by Mathematicians - Page 7

Mathematics is the art of giving the same name to different things.
Henri Poincaré
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations’, are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards.
G H Hardy
That's because, if correct, a mathematical formula expresses an eternal truth about the universe. Hence no one can claim ownership of it; it is ours to share. Rich or poor, black or white, young or old - no one can take these formulas away from us. Nothing in this world is so profound and elegant, and yet so available to all.
Edward Frenkel
Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence.
Keith J. Devlin
In adolescence, I hated life and was continually on the verge of suicide, from which, however, I was restrained by the desire to know more mathematics.
Bertrand Russell
More often than not, at the end of the day (or a month, or a year), you realize that your initial idea was wrong, and you have to try something else. These are the moments of frustration and despair. You feel that you have wasted an enormous amount of time, with nothing to show for it. This is hard to stomach. But you can never give up. You go back to the drawing board, you analyze more data, you learn from your previous mistakes, you try to come up with a better idea. And every once in a while, suddenly, your idea starts to work. It's as if you had spent a fruitless day surfing, when you finally catch a wave: you try to hold on to it and ride it for as long as possible. At moments like this, you have to free your imagination and let the wave take you as far as it can. Even if the idea sounds totally crazy at first.
Edward Frenkel
Proofs are to mathematics what spelling (or even calligraphy) is to poetry. Mathematical works do consist of proofs, just as poems do consist of words.
V.I. Arnold
What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?
David Eugene Smith
Only dead mathematics can be taught where competition prevails: living mathematics must always be a communal possession.
Mary Everest Boole
What is it, in fact, that we are supposed to abstract from, in order to get, for example, from the moon to the number 1? By abstraction we do indeed get certain concepts, viz. satellite of the Earth, satellite of a planet, non-self-luminous heavenly body, heavenly body, body, object. But in this series 1 is not to be met with; for it is no concept that the moon could fall under. In the case of 0, we have simply no object at all from which to start our process of abstracting. It is no good objecting that 0 and 1 are not numbers in the same sense as 2 and 3. What answers the question How many? is number, and if we ask, for example, "How many moons has this planet?", we are quite as much prepared for the answer 0 or 1 as for 2 or 3, and that without having to understand the question differently. No doubt there is something unique about 0, and about 1000; but the same is true in principle of every whole number, only the bigger the number the less obvious it is. To make out of this a difference in kind is utterly arbitrary. What will not work with 0 and 1 cannot be essential to the concept of number.
Gottlob Frege
Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can’t be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere – no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what’s also amazing is that we own all of them. No one can patent a mathematical formula, it’s ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It’s too precious to be given away to the “initiated few.” It belongs to all of us.
Edward Frenkel
Mathematics takes us still further from what is human into the region of absolute necessity, to which not only the actual world, but ever possible world, must conform.
Bertrand Russell
One thing the American defense establishment has traditionally understood very well is that countries don't win wars just by being braver than the other side, or freer, or slightly preferred by God. The winners are usually the guys who get 5% fewer of their planes shot down, or use 5% less fuel, or get 5% more nutrition into their infantry at 95% of the cost.
Jordan Ellenberg
The best mathematics is serious as well as beautiful—‘important’ if you like, but the word is very ambiguous, and ‘serious’ expresses what I mean much better
G H Hardy
The ‘seriousness’ of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is ‘significant’ if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas. Thus a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself and even in other sciences.
G H Hardy
How to describe the excitement I felt when I saw this beautiful work and realized its potential? I guess it's like when, after a long journey, suddenly a mountain peak comes in full view. You catch your breath, take in its majestic beauty, and all you can say is "Wow!" It's the moment of revelation. You have not yet reached the summit, you don't even know yet what obstacles lie ahead, but its allure is irresistible, and you already imagine yourself at the top. It's yours to conquer now. But do you have the strength and stamina to do it?
Edward Frenkel
The geometer offers to the physicist a whole set of maps from which to choose. One map, perhaps, will fit the facts better than others, and then the geometry which provides that particular map will be the geometry most important for applied mathematics.
G H Hardy
The play is independent of the pages on which it is printed, and ‘pure geometries’ are independent of lecture rooms, or of any other detail of the physical world.
G H Hardy
It seems that mathematical ideas are arranged somehow in strata, the ideas in each stratum being linked by a complex of relations both among themselves and with those above and below. The lower the stratum, the deeper (and in general more difficult) the idea. Thus the idea of an ‘irrational’ is deeper than that of an integer; and Pythagoras’s theorem is, for that reason, deeper than Euclid’s.
G H Hardy
In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras, and will not end with Einstein, but is the oldest and the youngest of all.
G H Hardy
Two writings of al-Hassār have survived. The first, entitled Kitāb al-bayān wa t-tadhkār [Book of proof and recall] is a handbook of calculation treating numeration, arithmetical operations on whole numbers and on fractions, extraction of the exact or approximate square root of a whole of fractionary number and summation of progressions of whole numbers (natural, even or odd), and of their squares and cubes. Despite its classical content in relation to the Arab mathematical tradition, this book occupies a certain important place in the history of mathematics in North Africa for three reasons: in the first place, and notwithstanding the development of research, this manual remains the most ancient work of calculation representing simultaneously the tradition of the Maghrib and that of Muslim Spain. In the second place, this book is the first wherein one has found a symbolic writing of fractions, which utilises the horizontal bar and the dust ciphers i.e. the ancestors of the digits that we use today (and which are, for certain among them, almost identical to ours) [Woepcke 1858-59: 264-75; Zoubeidi 1996]. It seems as a matter of fact that the utilisation of the fraction bar was very quickly generalised in the mathematical teaching in the Maghrib, which could explain that Fibonacci (d. after 1240) had used in his Liber Abbaci, without making any particular remark about it [Djebbar 1980 : 97-99; Vogel 1970-80]. Thirdly, this handbook is the only Maghribian work of calculation known to have circulated in the scientific foyers of south Europe, as Moses Ibn Tibbon realised, in 1271, a Hebrew translation.[Mathematics in the Medieval Maghrib: General Survey on Mathematical Activities in North Africa]
Ahmed Djebbar
I took especially great pleasure in mathematics because of the certainty and the evidence of its arguments.
René Descartes
See appendix A for a proof that Winston Churchill was a carrot.
Charles Seife
Good general theory does not search for the maximum generality, but for the right generality.
Saunders Mac Lane
When he said someone had "died", Erdős meant that the person had stopped doing mathematics. When he said someone had "left", the person had died.
Paul Erdős
I am not qualified to say whether or not God exists. I kind of doubt He does. Nevertheless I'm always saying that the SF( The SF is the supreme Fascist, the Number-One guy up there) has this transfinite book-transfinite being a concept in mathematics that is larger than infinite-that contains the best proofs of all mathematical theorems, proofs that are elegant and perfect.
Paul Erdős
...317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is, because mathematical reality is built that way.
G H Hardy
Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional.
Charles Proteus Steinmetz
Mathematics is the art of explanation.
Paul Lockhart
My beautiful proof lies all in ruins.
Georg Cantor
All mathematicians live in two different worlds. They live in a crystalline world of perfect platonic forms. An ice palace. But they also live in the common world where things are transient, ambiguous, subject to vicissitudes. Mathematicians go backward and forward from one world to another. They’re adults in the crystalline world, infants in the real one.
Sylvain Cappell
Mathemata mathematicis scribuntur.
Nicolaus Copernicus
Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world.
Robert Langlands
In a way, mathematics is the only infinite human activity. It is conceivable that humanity could eventually learn everything in physics or biology. But humanity certainly won't ever be able to find out everything in mathematics, because the subject is infinite. Numbers themselves are infinite. That's why mathematics is really my only interest.
Paul Erdős
With me, everything turns into mathematics.
René Descartes
I think we need more math majors who don't become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. But we won't get there unless we dump the stereotype that math is only worthwhile for kid geniuses.
Jordan Ellenberg
Nothing takes place in the world whose meaning is not that of some maximum or minimum.
Leonhard Euler
Always speak the truth - think before you speak - and write it down afterwards.
Lewis Carroll
In most gardens", the Tiger-lily said, "they make the beds too soft-so that the flowers are always asleep.
Lewis Carroll
We must keep our thought secret, and judge everything by it, while talking like the people.
Blaise Pascal
Knowing God without knowing our wretchedness leads to pride. Knowing our wretchedness without knowing God leads to despair. Knowing Jesus Christ is the middle course, because in him we find both God and our wretchedness.
Blaise Pascal
A drop of water is not immortal; it can be resolved into oxygen and hydrogen. If, therefore, a drop of water were to maintain that it had a quality of aqueousness which would survive its dissolution we should be inclined to be skeptical. In like manner we know that the brain is not immortal...
Bertrand Russell
And always, in our highly regularised way of life, he is obsessed by thoughts of themorrow. Of all the precepts in the Gospels the one that Christians have most neglected is the commandment to take no thought for the morrow. If a man is prudent, thought for the morrow will lead him to save; if he is imprudent, it will make him apprehensive of being unable to pay his debts. In either case the moment loses its savour. Everything is organised, nothing is spontaneous.
Bertrand Russell
But as men grow more industrialised and regimented, the kind of delight that is common in children becomes impossible to adults because they are always thinking of the next thing and cannot let themselves be absorbed in the moment. This habit of thinking of the ‘next thing’ is more fatal to any kind of aesthetic excellence than any other habit of mind that can be imagined, and if art, in any important sense, is to survive it will not be by the foundation of solemn academies, but by recapturing the capacity for wholehearted joys and sorrows which prudence and foresight have all but destroyed.
Bertrand Russell
All the truths of mathematics are linked to each other, and all means of discovering them are equally admissible.
Adrien-Marie Legendre
The deep study of nature is the most fruitful source of mathematical discoveries. By offering to research a definite end, this study has the advantage of excluding vague questions and useless calculations; besides it is a sure means of forming analysis itself and of discovering the elements which it most concerns us to know, and which natural science ought always to conserve.
Joseph Fourier
No great discovery was ever made without a bold guess.
Isaac Newton
Come back!" the Caterpillar called after her. "I've something important to say."This sounded promising, certainly. Alice turned and came back again."Keep your temper," said the Caterpillar.
Lewis Carroll
For I see not what there is desirable in publick esteeme, were I able to acquire & maintaine it. It would perhaps increase my acquaintance, the thing which I chiefly study to decline.
Isaac Newton
The charm of fame is so great, that we like every object to which it is attached, even death.
Blaise Pascal
In Mathematics the art of proposing a question must be held of higher value than solving it.
Georg Cantor
I am never forget the day I first meet the great Lobachevsky.In one word he told me secret of success in mathematics:Plagiarize!Plagiarize!Let no one else's work evade your eyes!Remember why the good Lord made your eyes!So don't shade your eyes,But plagiarize, plagiarize, plagiarize -Only be sure always to call it please 'resea
Tom Lehrer
Consider anything, only don’t cry!
Lewis Carroll
For my part, while I am as convinced a Socialist as the most ardent Marxian, I do not regard Socialism as a gospel of proletarian revenge, nor even, primarily, as a means of securing economic justice. I regard it primarily as an adjustment to machine production demanded by considerations of common sense, and calculated to increase the happiness, not only of proletarians, but of all except a tiny minority of the human race.
Bertrand Russell
Advocates of capitalism like to appeal to the sacred principles of liberty, which are embodied in one maxim: The fortunate must not be restrained in the exercise of tyranny over the unfortunate.
Bertrand Russell
There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else — but persistent.
Raoul Bott
Mathematics, which most of us see as the most factual of all sciences, constitutes the most colossal metaphor imaginable, and must be judged, aesthetically as well as intellectually in terms of the success of this metaphor.
Norbert Wiener
As long as men massacre animals, they will kill each other. Indeed, he who sows the seeds of murder and pain cannot reap the joy of love.
Pythagoras
No non-poetic account of reality can be complete.
John Myhill
We have sought for firm ground and found none. The deeper we penetrate, the more restless becomes the universe; all is rushing about and vibrating in a wild dance.
Max Born