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.

... 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.

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