So I have just one wish for you – the good luck to be somewhere where you are free to maintain the kind of integrity I have described, and where you do not feel forced by a need to maintain your position in the organization, or financial support, or so on, to lose your integrity. May you have that freedom.

I am not interested in what today's mathematicians find interesting.

I think, however, that there isn't any solution to this problem of education other than to realize that the best teaching can be done only when there is a direct individual relationship between a student and a good teacher - a situation in which the student discusses the ideas, thinks about the things, and talks about the things. It's impossible to learn very much by simply sitting in a lecture, or even by simply doing problems that are assigned. But in our modern times we have so many students to teach that we have to try to find some substitute for the ideal.

What is necessary for 'the very existence of science,' and what the characteristics of nature are, are not to be determined by pompous preconditions, they are determined always by the material with which we work, by nature herself. We look, and we see what we find, and we cannot say ahead of time successfully what it is going to look like. ... It is necessary for the very existence of science that minds exist which do not allow that nature must satisfy some preconceived conditions.

My friends and I had taken dancing lessons, although none of us would ever admit it. In those depression days, a friend of my mother was trying to make a living by teaching dancing in the evening, in an upstairs dance studio. There was a back door to the place, and she arranged it so the young men could come up through the back way without being seen.

There is no learning without having to pose a question. And a question requires doubt.

You see, I get such fun out of thinking that I don't want to destroy this most pleasant machine that makes life such a big kick.