Quotes by Mathematicians - Page 13

Remember that [scientific thought] is the guide of action; that the truth which it arrives at is not that which we can ideally contemplate without error, but that which we may act upon without fear; and you cannot fail to see that scientific thought is not an accompaniment or condition of human progress, but human progress itself.
William Kingdon Clifford
For me, the best thing about Cyberpunk is that it taught me how to enjoy shopping malls, which used to terrify me. Now I just imagine the whole thing is two miles below the moon’s surface, and that half the people’s right-brains have been eaten by roboticized steel rats. And suddenly it’s interesting again.
Rudy Rucker
Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don't look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.
Gian-Carlo Rota
Making mathematics accessible to the educated layman, while keeping high scientific standards, has always been considered a treacherous navigation between the Scylla of professional contempt and the Charybdis of public misunderstanding.
Gian-Carlo Rota
Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.
George Pólya
I have tried to read philosophers of all ages and have found many illuminating ideas but no steady progress toward deeper knowledge and understanding. Science, however, gives me the feeling of steady progress: I am convinced that theoretical physics is actual philosophy. It has revolutionized fundamental concepts, e.g., about space and time (relativity), about causality (quantum theory), and about substance and matter (atomistics), and it has taught us new methods of thinking (complementarity) which are applicable far beyond physics.
Max Born
Fifty years from now if an understanding of man's origins, his evolution, his history, his progress is not in the common place of the school books we shall not exist.
Jacob Bronowski
How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
Henri Poincaré
I've found out so much about electricity that I've reached the point where I understand nothing and can explain no
Pieter van Musschenbroek
Whence then come my errors? They come from the sole fact that since the will is much wider in its range and compass than the understanding, I do not restrain it within the same bounds, but extend it also to things which I do not understand: and as the will is of itself indifferent to these, it easily falls into error and sin, and chooses the evil for the good, or the false for the true.
René Descartes
We cannot tell that we are constantly splitting into duplicate selves because our consciousness rides smoothly along only one path in the endlessly forking chains
Martin Gardner
If you could blow the brain up to the size of a mill and walk about inside, you would not find consciousness.
Gottfried Wilhelm Leibniz
Richard Dawkins regards faith as an evil to be eliminated; he takes all religious faith to be blind faith. (Dawkins says) ‘Scientific belief is based on publicly checkable evidence, religious faith not only lacks evidence, its independence from evidence is its joy, shouted from the rooftops.’ However, taking Dawkins own advice we ask: where is the evidence that religious faith is not based on evidence? Mainstream Christianity will insist that faith and evidence are inseparable. Indeed, faith is a response to evidence, not a rejoicing in the absence of evidence. The apostle Paul says what many pioneers of modern science believed, that nature itself is part of the evidence for the existence of God ,‘ Since the creation of the world, God’s invisible qualities- his eternal power and divine nature – have been clearly seen, being understood from what has been made. So that men are without an excuse.’ Dawkins’ definition of faith turns out to be the direct opposite of the biblical one. Curious that he does not seem to be aware of the discrepancy.
John C. Lennox
Men never do evil so completely and cheerfully as when they do it from religious conviction.
Blaise Pascal
The essence of dramatic tragedy is not unhappiness. It resides in the solemnity of the remorseless working of things.
Alfred North Whitehead
My coming brought no profit to the sky,Nor does my going swell its glory;My two ears have never heard anyone that could say,Why I came here and why I will go away.
Omar Khayyám
It is a shame for anyoneto be well-known for righteousness.It is a great disgrace to feeldistress at the injustice of the turning of the wheels of fate.
Omar Khayyám
The Divine Light is always in man, presenting itself to the senses and to the comprehension, but man rejects it.
Giordano Bruno
Would you tell me, please, which way I ought to go from here?""That depends a good deal on where you want to get to.""I don't much care where –""Then it doesn't matter which way you go.
Lewis Carroll
No, no! The adventures first, explanations take such a dreadful time.
Lewis Carroll
Even those who write against fame wish for the fame of having written well, and those who read their works desire the fame of having read them.
Blaise Pascal
Madam, I have just come from a country where people are hanged if they talk.
Leonhard Euler
To all the talented young men who wander about feeling that there is nothing in the world for them to do, I should say: 'Give up trying to write, and, instead, try not to write. Go out into the world; become a pirate, a king in Borneo, a labourer in Soviet Russia; give yourself an existence in which the satisfaction of elementary physical needs will occupy almost all your energies.' I do not recommend this course of action to everyone, but only to those who suffer from the disease which Mr Krutch diagnoses. I believe that, after some years of such an existence, the ex-intellectual will fin that in spite of is efforts he can no longer refrain from writing, and when this time comes his writing will not seem to him futile.
Bertrand Russell
Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, 'How did he do it? He must be a genius!
Gian-Carlo Rota
She generally gave herself very good advice (though she very seldom followed it), and sometimes she scolded herself so severely as to bring tears into her eyes; and once she remembered trying to box her own ears for having cheated herself in a came of croquet she was playing against herself, for this curious child was very fond of pretending to be two people.
Lewis Carroll
...we ought not meanwhile to make use of doubt in the conduct of life.
René Descartes
It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.
Mark Kac
There are considerable mysteries surrounding the strange values that Nature's actual particles have for their mass and charge. For example, there is the unexplained 'fine structure constant' ... governing the strength of electromagnetic interactions, ....
Roger Penrose
Desire urges me on, while fear bridals me.
Giordano Bruno
All who are not lunatics are agreed about certain things. That it is better to be alive than dead, better to be adequately fed than starved, better to be free than a slave. Many people desire those things only for themselves and their friends; they are quite content that their enemies should suffer. These people can be refuted by science: mankind has become so much one family that we cannot insure our own prosperity except by insuring that of everyone else. If you wish to be happy yourself, you must resign yourself to seeing others also happy.
Bertrand Russell
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.
Richard Courant
...love must feel the ego of the beloved person as important as one's own ego, and must realize the other's feelings and wishes as though they were one's own.
Bertrand Russell
Life is complex in its expression, involving more than percipience, namely desire, emotion, will, and feeling.
Alfred North Whitehead
There was a footpath leading across fields to New Southgate, and I used to go there alone to watch the sunset and contemplate suicide. I did not, however, commit suicide, because I wished to know more of mathematics.
Bertrand Russell
Scholarship that is indifferent to human suffering is immoral.
Richard Levins
It is a curious and painful fact that almost all the completely futile treatments that have been believed in during the long history of medical folly have been such as caused acute suffering to the patient. When anesthetics were discovered, pious people considered them an attempt to evade the will of God. It was pointed out, however, that when God extracted Adam's rib He put him into a deep sleep. This proved that anesthetics are all right for men; women, however, ought to suffer, because of the curse of Eve.
Bertrand Russell
The aim of scientific thought, then, is to apply past experience to new circumstances; the instrument is an observed uniformity in the course of events. By the use of this instrument it gives us information transcending our experience, it enables us to infer things that we have not seen from things that we have seen; and the evidence for the truth of that information depends on our supposing that the uniformity holds good beyond our experience.
William Kingdon Clifford
We think in generalities, but we live in detail. To make the past live, we must perceive it in detail in addition to thinking of it in generalities.
Alfred North Whitehead
When I use a word,’ Humpty Dumpty said, in rather a scornful tone, ‘it means just what I choose it to mean—neither more nor less.
Lewis Carroll
[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.
Paul R. Halmos
Most information doesn’t constitute a story. Think of a telephone directory: lots of information, strong cast, but a bit weak on narrative. What counts in a story is its meaning. And that’s a very different concept from information.
Ian Stewart
If there is no meaning in it," said the King, "that saves a world of trouble, you know, as we needn't try to find any. And yet I don't know.
Lewis Carroll
Tut, tut, child!" said the Duchess. "Everything's got a moral, if only you can find it.
Lewis Carroll
When I turn my mind's eye upon myself, I understand that I am a thing which is incomplete and dependent on another and which aspires without limit to ever greater and better things...
René Descartes
We may take it that the world is undoubtedly itself [i.e., is indistinct from itself], but, in any attempt to see itself, as an object, it must, equally, undoubtedly act so as to make itself distinct from and therefore false to itself.In this sense, in respect to its own information, the universe must expand to escape the telescopes through which we, who are it, are trying to capture it, which is us.
G. Spencer Brown
The belief that personality is mysterious and irreducible has no scientific warrant, and is accepted chiefly because it is flattering to our human self esteem.
Bertrand Russell
Thus the perception of the infinite is somehow prior in me to the perception of the finite, that is, my perception of God is prior to my perception of myself. For how would I understand that I doubt and that I desire, that is, that I lack something and that I am not wholly perfect, unless there were some idea in me of a more perfect being, by comparison with which I might recognize my defects?
René Descartes
There is a widespread philosophical tendency towards the view which tells us that Man is the measure of all things, that truth is man-made, that space and time and the world of universals are properties of the mind, and that, if there be anything not created by the mind, it is unknowable and of no account for us. This view, if our previous discussions were correct, is untrue; but in addition to being untrue, it has the effect of robbing philosophic contemplation of all that gives it value, since it fetters contemplation to Self. What it calls knowledge is not a union with the not-Self, but a set of prejudices, habits, and desires, making an impenetrable veil between us and the world beyond. The man who finds pleasure in such a theory of knowledge is like a man who never leaves the domestic circle for fear his word might not be law.
Bertrand Russell
Some care is needed in using Descartes' argument. "I think, therefore I am" says rather more than is strictly certain. It might seem as though we are quite sure of being the same person to-day as we were yesterday, and this is no doubt true in some sense. But the real Self is as hard to arrive at as the real table, and does not seem to have that absolute, convincing certainty that belongs to particular experiences.
Bertrand Russell
If one does not develop, one goes down. In life, in ordinary conditions everything goes down, or one capacity may develop at the expense of another.
P.D. Ouspensky
For all bodies are in perpetual flux like rivers, and parts are passing in and out of them continually.
Gottfried Wilhelm Leibniz
Humans are actually spirit beings who each possess a mind and a body and what we do with them is entirely up to us.
Vaughan Jones
Religion is what an individual does with his solitariness.
Alfred North Whitehead
We see, surrounding the narrow raft illuminated by the flickering light of human comradeship, the dark ocean on whose rolling waves we toss for a brief hour; all the loneliness of humanity amid hostile forces is concentrated on the individual soul, which must struggle alone, with what of courage it can command, against the whole weight of a universe that cares nothing for its hopes and fears. Victory, in this struggle with the powers of darkness, is the true baptism into the glorious company of heroes, the true initiation into the overmastering beauty of human existence.
Bertrand Russell
It'll be no use their putting their heads down and saying "Come up again, dear!"I shall only look up and say "Who am I then? Tell me that first, and then,if I like being that person, I'll come up: if not, I'll stay down heretill I'm somebody else"--but, oh dear!' cried Alice, with a sudden burstof tears, 'I do wish they WOULD put their heads down! I am so VERY tiredof being all alone here!
Lewis Carroll
...what is the use of making everybody rich if the rich themselves are miserable?
Bertrand Russell
Men fear thought as they fear nothing else on earth -- more than ruin, more even than death.
Bertrand Russell
What matter it how far we go?" his scaly friend replied."There is another shore, you know, upon the other side.
Lewis Carroll
You cannot simply read the Quran,not if you take it seriously.You either have surrendered to it already or you fight it.It attacks tenaciously,directly,personally; it debates,criticizes,shames and challenges.From the outset it draws the line of battle, and I was on other side.
Jeffrey Lang
As I read the Qur’an and prayed the Islamic prayers, a door to my heart was unsealed and I was immersed in an overwhelming tenderness.
Jeffrey Lang