To speak freely of mathematics, I find it the highest exercise of the spirit; but at the same time I know that it is so useless that I make little distinction between a man who is only a mathematician and a common artisan. Also, I call it the most beautiful profession in the world; but it is only a profession.
Few men speak humbly of humility, chastely of chastity, skeptically of skepticism.
The sole cause of man's unhappiness is that he does not know how to stay quietly in his room.
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.
Nature is an infinite sphere of which the center is everywhere and the circumference nowhere.
There are two types of mind . . . the mathematical, and what might be called the intuitive. The former arrives at its views slowly, but they are firm and rigid; the latter is endowed with greater flexibility and applies itself simultaneously to the diverse lovable parts of that which it loves.
To deny, to believe, and to doubt well, are to a man what the race is to a horse.
As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.
Let no one say that I have said nothing new... the arrangement of the subject is new. When we play tennis, we both play with the same ball, but one of us places it better.
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.
Man is full of desires: he loves only those who can satisfy them all. "This man is a good mathematician," someone will say. But I have no concern for mathematics; he would take me for a proposition. "That one is a good soldier." He would take me for a besieged town. I need, that is to say, a decent man who can accommodate himself to all my desires in a general sort of way.
Those who write against vanity want the glory of having written well, and their readers the glory of reading well, and I who write this have the same desire, as perhaps those who read this have also.
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?
Those who are accustomed to judge by feeling do not understand the process of reasoning, because they want to comprehend at a glance and are not used to seeking for first principles. Those, on the other hand, who are accustomed to reason from first principles do not understand matters of feeling at all, because they look for first principles and are unable to comprehend at a glance.
We are so presumptuous that we should like to be known all over the world, even by people who will only come when we are no more. Such is our vanity that the good opinion of half a dozen of the people around us gives us pleasure and satisfaction.
Perfect clarity would profit the intellect but damage the will.
Religion is so great a thing that it is right that those who will not take the trouble to seek it if it be obscure, should be deprived of it.
Our notion of symmetry is derived form the human face. Hence, we demand symmetry horizontally and in breadth only, not vertically nor in depth.
Reverend Fathers, my letters did not usually follow each other at such close intervals, nor were they so long.... This one would not be so long had I but the leisure to make it shorter.
Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth.
All err the more dangerously because each follows a truth. Their mistake lies not in following a falsehood but in not following another truth.
I cannot judge my work while I am doing it. I have to do as painters do, stand back and view it from a distance, but not too great a distance. How great? Guess.
It is the heart which perceives God and not the reason.
However vast a man's spiritual resources, he is capable of but one great passion.
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