[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.
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.
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.
We all learn by experience, and your lesson this time is that you should never lose sight of the alternative. Sherlock Holmes speaking with Dr. Watson.
The Creative knows the great beginnings. The Receptive completes the finished things. The Creative is decided and therefore shows to men the easy. The Receptive is yielding and therefore shows to men the simple. Learning is movement from moment to moment.
When he is pushed, tormented, defeated, he has a chance to learn something; he has been put on his wits, on his manhood; he has gained facts; learns his ignorance; is cured of the insanity of conceit; has got moderation and real skill.
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.
Recognizing and confronting our history is important. Transcending our history is essential. We are not limited by what we have done, or what we have left undone. We are limited only by what we are willing to do.