I am trying to develop a short course on financial theory, covering the fundamentals of forward and options pricing, and 'efficient market' theory. I want to reduce the amount of mathematics to a minimum. This is not because the audience does not include mathematicians (it does) but rather because in my view mathematics generally detracts from the simplicity and beauty of a subject. Mathematics also focuses on the process of derivation from assumptions, rather than the assumptions themselves.
My question is whether this would be possible for financial theory. In particular (a) are there any basic principles of financial theory that cannot be grasped without complex mathematics and (2) are there any important results (i.e. derived results) which cannot be explained except by complex mathematics?
For a sense of where I am coming from, this page http://mathworld.wolfram.com/PythagoreanTheorem.html on beautiful versus complicated proofs of Pythagoras.