I do all the evil I can before I learn to shun it? Is it not enough to know the evil to shun it? If not, we should be sincere enough to admit that we love evil too well to give it up.
What I must do is all that concerns me, not what people think. This rule,equally arduous in actual and intellectual life, may serve for the whole distinction between greatness and meanness. It is the harder, because you will always find those who think they know what is your duty better than you know it. It is easy in the world to live after the world's opinion; it is easy in solitude to live after our own; but the great man is he who in the midst of the crowd keeps with perfect sweetness the independence of solitude.
Some are born with knowledge, some derive it from study, and some acquire it only after a painful realization of their ignorance. But the knowledge being possessed, it comes to the same thing. Some study with a natural ease, some from a desire for advantages, and some by strenuous effort. But the achievement being made, it comes to the same thing.
[Not enough is known about solid geometry] and for two reasons: in the first place, no government places value on it; this leads to a lack of energy in the pursuit of it, and it is difficult. In the second place, students cannot learn it unless they have a teacher. But then a teacher can hardly be found.
Thinking and spoken discourse are the same thing, except that what we call thinking is, precisely, the inward dialogue carried on by the mind with itself without spoken sound.
Science only means knowledge; and for [Greek] ancients it did only mean knowledge. Thus the favorite science of the Greeks was Astronomy, because it was as abstract as Algebra. ... We may say that the great Greek ideal was to have no use for useful things. The Slave was he who learned useful things; the Freeman was he who learned useless things. This still remains the ideal of many noble men of science, in the sense they do desire truth as the great Greeks desired it; and their attitude is an external protest against vulgarity of utilitarianism.
Ignorance of all things is an evil neither terrible nor excessive, nor yet the greatest of all; but great cleverness and much learning, if they be accompanied by a bad training, are a much greater misfortune.