Quotes of All Topics . Occasions . Authors
The last proceeding of reason is to recognize that there is an infinity of things which are beyond it. There is nothing so conformable to reason as this disavowal of reason.
Those who make antitheses by forcing the sense are like men who make false windows for the sake of symmetry. Their rule is not to speak justly, but to make accurate figures.
Necessity, that great refuge and excuse for human frailty, breaks through all law; and he is not to be accounted in fault whose crime is not the effect of choice, but force.
Our true dignity consists — in thought. Thence we must derive our elevation, not from space or duration. Let us endeavor then to think well; this is the principle of morals.
Galileo was no idiot. Only an idiot could believe that science requires martyrdom - that may be necessary in religion, but in time a scientific result will establish itself.
An observation, strictly, is only a sensation. Nobody means that we should reject everything but sensations. But as soon as we go beyond sensations we are making inferences.
Aside from rabid Islamists, no one who wishes to be taken seriously can publicly say anything bad about the old Jews of Europe without sounding like reactionary troglodytes.
Given the brief - and generally misleading - exposure most people have to mathematics at school, raising the public awareness of mathematics will always be an uphill battle.
People do not consciously and rationally choose the form of their society. Societies develop through processes of social evolution that are not under rational human control.
So far as the mere imparting of information is concerned, no university has had any justification for existence since the popularization of printing in the fifteenth century.
I was so obsessed by this problem that I was thinking about it all the time - when I woke up in the morning, when I went to sleep at night - and that went on for eight years.
All our life passes in this way: we seek rest by struggling against certain obstacles, and once they are overcome, rest proves intolerable because of the boredom it produces.
If he exalts himself, I humble him. If he humbles himself, I exalt him. And I go on contradicting him Until he understands That he is a monster that passes all understanding.
Some kinds of nails, such as those used for defending the soles of coarse shoes, called hobnails, require a particular form of the head, which is made by the stroke of a die.
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 so, because mathematical reality is built that way.
Man is unique not because he does science, and his is unique not because he does art, but because science and art equally are expressions of his marvelous plasticity of mind.
It's a sort of curious phenomenon that God is somehow not quite as nice as the devil; the devil doesn't punish you for behaving well, but God punishes you for behaving badly.
This is what I see, and what troubles me. I look on all sides, and everywhere I see nothing but obscurity. Nature offers me nothing that is not a matter of doubt and disquiet.
We do not worry about being respected in towns through which we pass. But if we are going to remain in one for a certain time, we do worry. How long does this time have to be?
The developing science departs at the same time more and more from its original scope and purpose and threatens to sacrifice its earlier unity and split into diverse branches.
In the hands of Science and indomitable energy, results the most gigantic and absorbing may be wrought out by skilful combinations of acknowledged data and the simplest means.
We have to understand that the world can only be grasped by action, not by contemplation. The hand is more important than the eye ... The hand is the cutting edge of the mind.
Science has nothing to be ashamed of even in the ruins of Nagasaki. The shame is theirs who appeal to other values than the human imaginative values which science has evolved.
Pointing out that countless great mathematicians had tried to solve the problem and failed before you came along is in particularly bad taste and should be avoided completely.
My life is more than just my work. I am a husband and a father and a proud citizen of two countries: my homeland of Australia and my adopted country here in the United States.
A philosopher of imposing stature doesn't think in a vacuum. Even his most abstract ideas are, to some extent, conditioned by what is or is not known in the time when he lives.
The proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself.
A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don't get something smooth, but irregularities at a smaller scale.
The immortality of the soul is a matter which is of so great consequence to us and which touches us so profoundly that we must have lost all feeling to be indifferent about it.
I feel engulfed in the infinite immensity of spaces whereof I know nothing, and which know nothing of me, I am terrified The eternal silence of these infinite spaces alarms me.
Look somewhere else for someone who can follow you in your researches about numbers. For my part, I confess that they are far beyond me, and I am competent only to admire them.
We see neither justice nor injustice which does not change its nature with change in climate. Three degrees of latitude reverse all jurisprudence; a meridian decides the truth.
La chose la plus importante a' toute la vie est le choix du me tier: le hasard en dispose. The most important thing in life is to choose a profession: chance arranges for that.
For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be: "We must know - we will know!"
Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure.
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.
As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.
Humans alone are created as rational beings in the image of God, capable of a relationship with God and given by him the capacity to understand the universe in which they live.
Whereas Nature does not admit of more than three dimensions ... it may justly seem very improper to talk of a solid ... drawn into a fourth, fifth, sixth, or further dimension.
Cardinal arithmetic will be quite important for us, so we spend some time on it. Since, however, it tends to be trivial, we shall not need to spend much of this time on proofs.
All my life I have been intensely repelled by the idea of 'making an effort'. I hate this idea today as much as I did as a child. I don't know why I hate it so much; I just do.
The leftist is anti-individualistic... He is not the sort of person who has an inner sense of confidence in his own ability to solve his own problems and satisfy his own needs.
It is natural to think that an abstract science cannot be of much importance in affairs of human life, because it has omitted from its consideration everything of real interest.
Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.
Well, 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.
The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty.
Nevertheless, the consuming hunger of the uncritical mind for what it imagines to be certainty or finality impels it to feast upon shadows in the prevailing famine of substance.
Dissent is the mark of freedom, as originality is the mark of independence of mind. … No one can be a scientist … if he does not have independence of observation and of thought.
As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be mathematical facts which are true but unknowable.
The Exclusion Principle is laid down purely for the benefit of the electrons themselves, who might be corrupted (and become dragons or demons) if allowed to associate too freely.