We come now to the question: what is a priori certain or necessary, respectively in geometry (doctrine of space) or its foundations? Formerly we thought everything; nowadays we think nothing. Already the distance-concept is logically arbitrary; there need be no things that correspond to it, even approximately.
Measured objectively, what a man can wrest from Truth by passionate striving is utterly infinitesimal. But the striving frees us from the bonds of the self and makes us comrades of those who are the best and the greatest.
A theory is the more impressive the greater is the simplicity of its premises, the more different are the kinds of things it relates and the more extended the range of its applicability.
I cannot conceive of a personal God who would directly influence the actions of individuals, or would directly sit in judgment on creatures of his own creation. I cannot do this in spite of the fact that mechanistic causality has, to a certain extent, been placed in doubt by modern science. My religiosity consists in a humble admiration of the infinitely superior spirit that reveals itself in the little that we, with our weak and transitory understanding, can comprehend of reality. Morality is of the highest importance - but for us, not for God.
This subject brings me to that vilest offspring of the herd mind -- the odious militia. The man who enjoys marching in line and file to the strains of music falls below my contempt; he received his great brain by mistake -- the spinal cord would have been amply sufficient. This heroism at command, this senseless violence, this accursed bombast of patriotism -- how intensely I despise them! War is low and despicable, and I had rather be smitten to shreds than participate in such doings.
But the creative principle resides in mathematics. In a certain sense, therefore, I hold true that pure thought can grasp reality, as the ancients dreamed.
We must begin to inculcate our children against militarism by educating them in the spirit of pacifism. Our schoolbooks glorify war and conceal it's horror. I would teach peace rather than war.