Existential Quotes (2 quotes)
Mathematical reasoning is deductive in the sense that it is based upon definitions which, as far as the validity of the reasoning is concerned (apart from any existential import), needs only the test of self-consistency. Thus no external verification of definitions is required in mathematics, as long as it is considered merely as mathematics.
When I was growing up, I always knew Id be in the top of my class in math, and that gave me a lot of self-confidence. [But now that students can see beyond their own school, they see that] there are always going to be a million people better than you at times, or someone will always be far better than you. I feel theres an existential angst among young people. I didnt have that. They see enormous mountains, where I only saw one little hill to climb.