The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.
It is almost inevitable that our faith will be challenged. We may at times find ourselves surrounded by others and yet standing in the minority or even standing alone concerning what is acceptable and what is not. Do we have the moral courage to stand firm for our beliefs, even if by so doing we must stand alone?
It often happens that we blurt out things that may in some kind of way be harmful to us, but we are silent about things that may make us look ridiculous; because in this case effect follows very quickly on cause.
In things which we know, everyone will trust us ... and we may do as we please, and no one will like to interfere with us; and we are free, and masters of others; and these things will be really ours, for we shall turn them to our good.
Better it is toward the right conduct of life to consider what will be the end of a thing, than what is the beginning of it: for what promises fair at first may prove ill, and what seems at first a disadvantage, may prove very advantageous.
The fun of talk is to explore, but much of it and all that is irresponsible should not be written. Once written you have to stand by it. You may have said it to see whether you believed it or not.
We may divide thinkers into those who think for themselves and those who think through others. The latter are the rule and the former the exception. The first are original thinkers in a double sense, and egotists in the noblest meaning of the word.
No matter how we may single out a complex from nature...its theoretical treatment will never prove to be ultimately conclusive... I believe that this process of deepening of theory has no limits.