Quotes by Mathematicians - Page 6

The Wine of Life keeps oozing drop by drop, The Leaves of Life keep falling one by one.
Omar Khayyám
Were it not Folly, Spider-like to spinThe Thread of present Life away to win-What? for ourselves, who know not if we shallBreathe out the very Breath we now breathe in!
Omar Khayyám
Somehow it seems to fill my head with ideas—only I don’t exactly know what they are!
Lewis Carroll
[About Pierre de Fermat] It cannot be denied that he has had many exceptional ideas, and that he is a highly intelligent man. For my part, however, I have always been taught to take a broad overview of things, in order to be able to deduce from them general rules, which might be applicable elsewhere.
René Descartes
Hadn't another wise man, the Buddha himself, warned about the evils of attachment?
Manil Suri
How long is forever?Sometimes just one second
Lewis Carroll
All great books contain boring portions, and all great lives have contained uninteresting stretches. Imagine a modern American publisher confronted with the Old Testament as a new manuscript submitted to him for the first time. It is not difficult to think what his comments would be, for example, on the genealogies. 'My dear sir,' he would say, 'this chapter lacks pep; you can't expect your reader to be interested in a mere string of proper names of persons about whom you tell so little. You have begun your story, I admit, in fine style, and at first I was very favourably impressed, but you have altogether too much wish to tell it all. Pick out the highlights, take out the superfluous matter, and bring me back your manuscript when you have reduced it to a reasonable length.' So the modern publisher would speak, knowing the modern reader's fear of boredom.
Bertrand Russell
Boredom is therefore a vital problem for the moralist, since at least half the sins of mankind are caused by the fear of it.
Bertrand Russell
I believe that when I die I shall rot, and nothing of my ego will survive. I am not young and I love life. But I should scorn to shiver with terror at the thought of annihilation. Happiness is nonetheless true happiness because it must come to an end, nor do thought and love lose their value because they are not everlasting. Many a man has borne himself proudly on the scaffold; surely the same pride should teach us to think truly about man's place in the world. Even if the open windows of science at first make us shiver after the cosy indoor warmth of traditional humanizing myths, in the end the fresh air brings vigour, and the great spaces have a splendour of their own.
Bertrand Russell
The "silly" question is the first intimation of some totally new development
Alfred North Whitehead
...reading good books is like engaging in conversation with the most cultivated minds of past centuries who had composed them, or rather, taking part in a well-conducted dialogue in which such minds reveal to us only the best of their thoughts
René Descartes
Where envy is unavoidable it must be used as a stimulus to one’s own efforts, not to the thwarting of the efforts of rivals.
Bertrand Russell
This is the twenty-first century - you have to know what you want, then set upon it with everything you've got.
Manil Suri
For any scientist the real challenge is not to stay within the secure garden of the known but to venture out into the wilds of the unknown.
Marcus du Sautoy
Each problem that I solved became a rule, which served afterwards to solve other problems.
René Descartes
...nothing cements a friendship like hating the same person.
Steven Strogatz
Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not "corrected" as a chance process unfolds, they are merely diluted.
Amos Tversky
The instinct is not completely satisfied unless a man's whole being, mental quite as much as physical, enters into the relation. Those who have never known the deep intimacy and the intense companionship of happy mutual love have missed the best thing that life has to give; unconsciously, if not consciously, they feel this and the resulting disappointment inclines them towards envy, oppression, and cruelty.
Bertrand Russell
Running overtime is the one unforgivable error a lecturer can make. After fifty minutes (one microcentury as von Neumann used to say) everybody's attention will turn elsewhere.
Gian-Carlo Rota
Of course it is,’ said the Duchess, who seemed ready to agree to everythingthat Alice said; ‘there’s a large mustard-mine near here. And the moralof that is– “The more there is of mine, the less there is of yours.
Lewis Carroll
Little Alice fell d o w nthe hOle, bumped her head and bruised her soul
Lewis Carroll
Two things are to be remembered: that a man whose opinions and theories are worth studying may be presumed to have had some intelligence, but that no man is likely to have arrived at complete and final truth on any subject whatever. When an intelligent man expresses a view which seems to us obviously absurd, we should not attempt to prove that it is somehow true, but we should try to understand how it ever came toseemtrue. Thisexercise of historical and psychological imagination at once enlarges the scope of our thinking, and helps us to realize how foolish many of our own cherished prejudices will seem to an age which has a different temper of mind.
Bertrand Russell
Thinking must never submit itself, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, if not to facts themselves, because, for it, to submit would be to cease to be.
Jules Henri Poincaré
God knows nothing gets accomplished in the world these days without terrorism.
Manil Suri
From the standpoint of the upper classes, the system had many merits. They felt that what was paid out of the poor rate was charity, and therefore a proof of their benevolence; at the same time, wages were kept at starvation level by a method which just prevented discontent from developing into revolution...It was plainly the certainty, derived from the old Poor Law, that actual death would be averted by the parish authorities, which induced the rural poor of England to endure their misery patiently...it taught them respect for their 'betters'.While leaving all the wealth that they produced, beyond the absolute minimum required for subsistence, in the hands of the landowners and farmers. It was at this period that landowners built the sham Gothic ruins called 'follies', where they indulged in romantic sensibility about the past while they filled the present with misery and degradation.
Bertrand Russell
The extracellular genesis of cells in animals seemed to me, ever since the publication of the cell theory [of Schwann], just as unlikely as the spontaneous generation of organisms. These doubts produced my observations on the multiplication of blood cells by division in bird and mammalian embryos and on the division of muscle bundles in frog larvae. Since then I have continued these observations in frog larvae, where it is possible to follow the history of tissues back to segmentation.
Robert Remak
And how many hours a day did you do lessons?' said Alice, in a hurry to change the subject.Ten hours the first day,' said the Mock Turtle: 'nine the next, and so on.'What a curious plan!' exclaimed Alice.That's the reason they're called lessons,' the Gryphon remarked: 'because they lessen from day to day.
Lewis Carroll
Geometria est archetypus pulchritudinis mundi-Mathematics is the archetype of the beauty of the world-Kepler
Kepler
Sometimes it is the people who no one imagines anything of who do the things that no one can imagine.
Christopher Morcom
I have become so accustomed to think “scientifically” that I am afraid even to imagine that there may be something else beyond the outer covering of life. I feel like a man condemned to death, whose companions have been hanged and who has already become reconciled to the thought that the same fate awaits him.
P.D. Ouspensky
Formal mathematics is nature's way of letting you know how sloppyyour mathematics is.
Leslie Lamport
Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it need only patience to ransack; it is not a mine, whose treasures may take long to reduce to possessions, but which fill only a limited number of veins 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 limitless as the space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer's gaze; it is as incapable of being restricted within assigned boundaries or being reduced to definitions of permanent validity, as the consciousness, the life, which seems to slumber in each monad, in every atom of matter, in each leaf and bud and cell, and is forever ready to burst forth into new forms of vegetable and animal existence.
James Joseph Sylvester
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 Russell
The language of categories is affectionately known as "abstract nonsense," so named by Norman Steenrod. This term is essentially accurate and not necessarily derogatory: categories refer to "nonsense" in the sense that they are all about the "structure," and not about the "meaning," of what they represent.
Paolo Aluffi
It (proof by contradiction) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
G H Hardy
I entered Princeton University as a graduate student in 1959, when the Department of Mathematics was housed in the old Fine Hall. This legendary facility was marvellous in stimulating interaction among the graduate students and between the graduate students and the faculty. The faculty offered few formal courses, and essentially none of them were at the beginning graduate level. Instead the students were expected to learn the necessary background material by reading books and papers and by organising seminars among themselves. It was a stimulating environment but not an easy one for a student like me, who had come with only a spotty background. Fortunately I had an excellent group of classmates, and in retrospect I think the "Princeton method" of that period was quite effective.
Phillip A. Griffiths
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 the world for ugly mathematics.
G H Hardy
Just as all things speak about God to those that know Him, and reveal Him to those that love Him, they also hide Him from all those that neither seek nor know Him.
Blaise Pascal
The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated ... The importance of this invention is more readily appreciated when one considers that it was beyod the two greatest men of antiquity, Archimedes and Apollonius.
Pierre-Simon Laplace
Adaptability to change is itself a hallmark of successful education.
Peter Hilton
To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.
Paul Cohen
[Benjamin Peirce's] lectures were not easy to follow. They were never carefully prepared. The work with which he rapidly covered the blackboard was very illegible, marred with frequent erasures, and not infrequent mistakes (he worked too fast for accuracy). He was always ready to digress from the straight path and explore some sidetrack that had suddenly attracted his attention, but which was likely to have led nowhere when the college bell announced the close of the hour and we filed out, leaving him abstractedly staring at his work, still with chalk and eraser in his hands, entirely oblivious of his departing class.
William Elwood Byerly
The issue, then, is not, What is the best way to teach? but, What is mathematics really all about?... Controversies about…teaching cannot be resolved without confronting problems about the nature of mathematics.
Reuben Hersh
Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.
Andrew John Wiles
I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind.(Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.)
Andrew John Wiles
Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.
Gian-Carlo Rota
And I'll go even further and say that mathematics, this art of abstract pattern-making — even more than storytelling, painting, or music - is our most quintessentially human art form. This is what our brains do, whether we like it or not. We are biochemical pattern-recognition machines and mathematics is nothing less than the distilled essence of who we are.
Paul Lockhart
How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.
Clifford A. Truesdell
Although some of her passages seek to persuade the reader of the meaninglessness and marginalization of the mathematics, Hayles is content to use mathematics as a means for understanding Borges, perhaps in the same way a sponge riddled with holes is useful in sopping up fluid reality.
Bloch William Goldbloom
[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.
G H Hardy
The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon... when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms.
Joseph Fourier
The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.
Felix Klein
Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.
Hermann Weyl
…numerical precision is the very soul of science, and its attainment affords the best, perhaps the only criterion of the truth of theories and the correctness of experiments.
D'Arcy Wentworth Thompson
Where there is no mathematics, there is no freedom.
Edward Frenkel
It was as though applied mathematics was my spouse, and pure mathematics was my secret lover.
Edward Frenkel
This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.
Emil Artin
For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view.
Louis Poinsot
The first successes were such that one might suppose all the difficulties of science overcome in advance, and believe that the mathematician, without being longer occupied in the elaboration of pure mathematics, could turn his thoughts exclusively to the study of natural laws.
Joseph Louis François Bertrand
Mathematics is the science which draws necessary conclusions.
Benjamin Peirce