If any philosopher had been asked for a definition of infinity, he might have produced some unintelligible rigmarole, but he would certainly not have been able to give a definition that had any meaning at all.

Americans need rest, but do not know it.

Conventional people are roused to fury by departure from convention, largely because they regard such departure as a criticism of themselves.

The wise man thinks about his troubles only when there is some purpose in doing so; at other times he thinks about other things, or, if it is night, about nothing at all.

From India to Spain, the brilliant civilization of Islam flourished. What was lost to christendom at this time was not lost to civilization, but quite the contrary.

Belief in a Divine mission is one of the many forms of certainty that have afflicted the human race.

But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was not more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.