... if one were to refuse to have direct, geometric, intuitive insights, if one were reduced to pure logic, which does not permit a choice among every thing that is exact, one would hardly think of many questions, and certain notions ... would escape us completely.

... if one were to refuse to have direct, geometric, intuitive insights, if one were reduced to pure logic, which does not permit a choice among every thing that is exact, one would hardly think of many questions, and certain notions ... would escape us completely.

In my opinion a mathematician, in so far as he is a mathematician, need not preoccupy himself with philosophy-an opinion, moreover, which has been expressed by many philosophers.

Mathematicians have never been in full agreement on their science, though it is said to be the science of self-evident verities -- absolute, indisputable and definitive. They have always been in controversy over developing aspects of mathematics, and they have always considered their own age to be in a period of crisis.

The only teaching that a professor can give, in my opinion, is that of thinking in front of his students.