Index-learning turns no student pale,
Yet holds the eel of Science by the tail.
Index-learning is a term used to mock pretenders who acquire superficial knowledge merely by consulting indexes.
Men grind and grind in the mill of a truism, and nothing comes out but what was put in. But the moment they desert the tradition for a spontaneous thought, then poetry, wit, hope, virtue, learning, anecdote, and all flock to their aid.
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.
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.
The faculty for remembering is not diminished in proportion to what one has learnt, just as little as the number of moulds in which you cast sand lessens its capacity for being cast in new moulds.
[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.