(1) What makes math universal? Its results seem independent of time and place. No one doubts Euclid's or Pythagoras' theorems of thousands of years ago, even if we think some of the proofs aren't correct. No one since Hitler and Stalin thinks its correctness depends on race, religion or nationality. But will the same math be found wherever there's life in the universe?
(2) Why is math so useful? Try spending a day without thinking about numbers.
(3) Its results seem absolutely true. But are they? If they are, how can we prove it? And if we can prove it, how do we know our proof is correct?
Readings:
Essays in Humanistic Mathematics: Mathematical Association of America
What is Mathematics Really? R. Hersh, Oxford University Press
Where Mathematics Comes from: G. Lakoff & R Nunez, Basic Books
The Math Gene: K. Devlin, Basic Books