Quotes of All Topics . Occasions . Authors
Most economists, when modeling market behavior, tend to sweep major fluctuations under the rug and assume they are anomalies. What I have found is that major rises and falls in prices are actually inevitable.
A science or an art may be said to be "useful" if its development increases, even indirectly, the material well-being and comfort of men, it promotes happiness, using that word in a crude and commonplace way.
A formal and consistent theory of inductive processes cannot represent the operation of every human mind in detail; it will represent an ideal mind, but it will help the actual mind to approximate that ideal.
Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way.
In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug.
In its evolution from a more primitive nervous system, the brain, as an organ with ten or more billion neurons and many more connections between them must have changed and grown as a result of many accidents.
Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.
The dot was introduced as a symbol for multiplication by Leibniz. On July 29, 1698, he wrote in a letter to Johann Bernoulli: "I do not like X as a symbol for multiplication, as it is easily confounded with x.
It can have its effect only through the intervention of God, inasmuch as in the ideas of God a monad rightly demands that God, in regulating the rest from the beginning of things, should have regard to itself.
It is unnecessary to understand electromagnetic theory before wiring a lamp or to study physics in order to repair a pump. We count on our fingers and give no heed to the proliferating implications of the act.
How can you construct a morality if there's no morality inherent in the way things are? You might be able to delude yourself into thinking you had 'created' a morality, but that's all it would be, an illusion.
Science, as well as technology, will in the near and in the farther future increasingly turn from problems of intensity, substance, and energy, to problems of structure, organization, information, and control.
I like to think of mathematicians as forming a nation of our own without distinctions of geographical origin, race, creed, sex, age or even time... all dedicated to the most beautiful of the arts and sciences.
No matter how much we enjoy following the lives of the rich and famous, we know the world is affected more deeply by quiet, even invisible acts of integrity, kindness, and generosity, than by fame and fortune.
When I got to Princeton I made a point of attending the Philosophy Club and listening to the lectures, but I didn't get involved in any discussions in those clubs. I guess after the first year, I dropped that.
I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world.
Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false.
In symbols one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed the labor of thought is wonderfully diminished.
If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing.
Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.
Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that by their very nature refer to the infinite. This is his glory.
It is indubitable that a 50-year-old mathematician knows the mathematics he learned at 20 or 30, but has only notions, often rather vague, of the mathematics of his epoch, i.e. the period of time when he is 50.
I know that if I could really understand mental illness, then it would be appropriate to make a big career shift. I would become a therapist and a leader in terms of mental illness. But I'm not in the position.
Moreover, broad plans commensurate with our national purpose and resources would bring conviction of our power to every soldier in the front line, to the nations associated with us in the war, and to the enemy.
If you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But ten years later somehow, you dont quite know what problems are worth working on.
Math education has changed over the years. In the 19th century, they taught spherical trigonometry because one of the biggest applications of mathematics was navigating the ocean. This is no longer so relevant.
These disturbing phenomena [Extra Sensory Perception] seem to deny all our scientific ideas. How we should like to discredit them! Unfortunately the statistical evidence, at least for telepathy, is overwhelming.
I shall risk nothing on an attempt to prove the transcendence of p. If others undertake this enterprise, no one will be happier than I in their success. But believe me, it will not fail to cost them some effort.
No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.
For my part, it is difficult for me to say what I owe to Ramanujan - his originality has been a constant source of suggestion to me ever since I knew him, and his death is one of the worst blows I have ever had.
The topdog may win the game of force. But not the moral issue - and when that dawns upon him and his allies, change of consciousness sets in, and demoralization starts thawing the frozen heart. The game is over.
If you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But ten years later somehow, you don't quite know what problems are worth working on.
It wouild be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.' John Horgan.
I'm an agnostic. Sometimes I muse deeply on the forces that are for me invisible. When I am almost close to the idea of God, I feel immediately estranged by the horrors of this world, which he seems to tolerate.
Into this, for good or ill, is woven every belief of every man who has speech of his fellows. A awful privilege, and an awful responsibility, that we should help to create the world in which posterity will live.
A powerful attraction exists, therefore, to the promotion of a study and of duties of all others engrossing the time most completely, and which is less benefited than most others by any acquaintance with science.
We never have a full demonstration, although there is always an underlying reason for the truth, even if it is only perfectly understood by God, who alone penetrated the infinite series in one stroke of the mind.
Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.
If children really want to learn something, and have the opportunity to learn it in use, they do so even if the teaching is poor. For example many learn difficult video games with no professional teaching at all!
In like manner, if I let myself believe anything on insufficient evidence, there may be no great harm done by the mere belief; it may be true after all, or I may never have occasion to exhibit it in outward acts.
Routine is the god of every social system; it is the seventh heaven of business, the essential component in the success of every factory, the ideal of every statesman. The social machine should run like clockwork.
The main importance of Francis Bacon's influence does not lie in any peculiar theory of inductive reasoning which he happened to express, but in the revolt against second-hand information of which he was a leader.
I'm sure that some of them will be very hard and I'll have a sense of achievement again, but nothing will mean the same to me - there's no other problem in mathematics that could hold me the way that this one did.
We are so presumptuous that we wish to be known to all the world, even to those who come after us; and we are so vain that the esteem of five or six persons immediately around us is enough to amuse and satisfy us.
I cannot forgive Descartes. In all his philosophy he would have been quite willing to dispense with God. But he had to make Him give a fillip to set the world in motion; beyond this, he has no further need of God.
Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.
Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer.
The richness of human life is that we have many lives, we live the events that do not happen (and some that cannot) as vividly as those that do, and if thereby we die a thousand deaths, that is the price we pay...
The moon... is a mass, akin to the mass of the earth, attracts the waters by a magnetic force, not because they are liquid, but because they possess earthy substance, and so share in the movements of a heavy body.
Either human intelligence ultimately owes its origin to mindless matter; or there is a Creator. It is strange that some people claim that it is their intelligence that leads them to prefer the first to the second.