People are always selling the idea that people with mental illness are suffering. I think madness can be an escape. If things are not so good, you maybe want to imagine something better.

With suicide, it's a strange thing in Japanese culture. It's acceptable. My parents would have been devastated if my attempt had been successful, but they would have somehow accepted it.

If the NSF had never existed, if the government had never funded American mathematics, we would have half as many mathematicians as we now have, and I don't see anything wrong with that.

In a certain sense, everything is everywhere at all times. For every location involves an aspect of itself in every other location. Thus every spatio-temporal standpoint mirrors the world

Sometimes a line of mathematical research extending through decades can be thought of as one long conversation in which many mathematicians take part. This is fortunately true at present.

. . . we have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed.

Detest it [a certain difficult mathematics problem] just as much as lewd intercourse; it can deprive you of all your leisure, your health, your rest, and the whole happiness of your life.

The knowledge which we have acquired ought not to resemble a great shop without order, and without an inventory; we ought to know what we possess, and be able to make it serve us in need.

Finally there are simple ideas of which no definition can be given; there are also axioms or postulates, or in a word primary principles, which cannot be proved and have no need of proof.

In most sciences one generation tears down what another has built and what one has established another undoes. In mathematics alone each generations adds a new story to the old structure.

It doesn't matter whether you're talking about bombs or the intelligence quotients of one race as against another if a man is a scientist, like me, he'll always say Publish and be damned.

Poor Capablanca! Thou wert a brilliant technician, but no philosopher. Thou wert not capable of believing that in chess, another style could be victorious than the absolutely correct one.

We are but whirlpools in a river of ever-flowing water. We are not stuff that abides, but patterns that perpetuate themselves. A pattern is a message, and may be transmitted as a message.

It becomes the urgent duty of mathematicians, therefore, to meditate about the essence of mathematics, its motivations and goals and the ideas that must bind divergent interests together.

The foundation of reverence is this perception, that the present holds within itself the complete sum of existence, backwards and forwards, that whole amplitude of time, which is eternity.

I always feel that I have two duties to perform with a parting guest: one, to see that he doesn't forget anything that is his; the other, to see that he doesn't take anything that is mine.

My opinion of mankind is founded upon the mournful fact that, so far as I can see, they find within themselves the means of believing in a thousand times as much as there is to believe in.

There are many cases of these algebras which may obviously be combined into natural classes, but the consideration of this portion of the subject will be reserved to subsequent researches.

Put the world's greatest philosopher on a plank that is wider than need be; if there is a precipe below, although his reason may convince him that he is safe, his imagination will prevail.

If magistrates had true justice, and if physicians had the true art of healing, they would have no occasion for square caps; the majesty of these sciences would itself be venerable enough.

Le nez de Cle opa" tre: s'il e u" t e te plus court, toute la face de la terre aurait change . Cleopatra'snose: if it had beenshorter the whole face of the earth would have been different.

Let us weigh the gain and the loss, in wagering that God is. Consider these alternatives: if you win, you win all, if you lose you lose nothing. Do not hesitate, then, to wager that he is.

Sophie Germain proved to the world that even a woman can accomplish something in the most rigorous and abstract of sciences and for that reason would well have deserved an honorary degree.

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.

[In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory.

What the use of P [the significance level] implies, therefore, is that a hypothesis that may be true may be rejected because it has not predicted observable results that have not occurred.

As a stick, when once it is dry and stiff you may break it, but you can never bend it into a straighter posture; so doth the man become incorrigible who is settled and stiffened into vice.

There is a social injunction implied in the positivist and analyst methods. This social axiom is that :;:;:;:;:;:; We OUGHT to act in such a way that what IS true can be verified to be so.

A linguist would be shocked to learn that if a set is not closed this does not mean that it is open, or again that "E is dense in E" does not mean the same thing as "E is dense in itself".

In the midst of all dwells the Sun. For who could set this luminary in another or better place in this most glorious temple, than whence he can at one and the same time brighten the whole.

To address questions of scientific responsibility does not necessarily imply that one needs technical competence in a particular field (e.g. biology) to evaluate certain technical matters.

Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languanges of the world than to master all mathematics at present known.

The justification for a university is that it preserves the connection between knowledge and the zest of life, by uniting the young and the old in the imaginative consideration of learning.

The antithesis between a technical and a liberal education is fallacious. There can be no adequate technical education which is not liberal, and no liberal education which is not technical.

Can anything be stupider than that a man has the right to kill me because he lives on the other side of a river and his ruler has a quarrel with mine, though I have not quarrelled with him?

The heart has its reasons, which Reason does not know. We feel it in a thousand things. It is the heart which feels God, and not Reason. This, then, is perfect faith: God felt in the heart.

There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.

Let us remember that the automatic machine is the precise economic equivalent of slave labor. Any labor which competes with slave labor must accept the economic consequences of slave labor.

Number theorists say that number theory is too complicated, so let's pretend that there is only one prime number, and then let's combine all these results. Surprisingly, sometimes it works.

It is obvious that [leftists] are not cool-headed logicians systematically analyzing the foundations of knowledge. They are deeply involved emotionally in their attack on truth and reality.

An atmosphere of beliefs and conceptions has been formed by the labours and struggles of our forefathers, which enables us to breathe amid the various and complex circumstances of our life.

Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.

Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced. On floating bodies I, prop 5.

If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in existence, they would not be able to discover anything so stupid as astrology.

This is the Unix philosophy. Write programs that do one thing and do it well. Write programs to work together. Write programs that handle text streams, because that is a universal interface.

If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics.

Nothing is accomplished all at once, and it is one of my great maxims, and one of the most completely verified, that Nature makes no leaps: a maxim which I have called the law of continuity.

When things are in order, if the cause of the orderliness cannot be deduced from the motion of the elements or from the composition of matter, it is quite possibly a cause possessing a mind.

Civilization is not a spontaneous generation with any race or nation known to history, but the torch is handed down from race to race and from age to age, and gains in brilliancy as it goes.

For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear.

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