[nilaykumar]

Quick comment: I think people are emphasizing too much the 'logic' of mathematics, over its content. Mathematics is NOT about rigorous thinking and logical patterns (unless of course you study logic). It is much freer, pattern-based, and intuitionistic than that. It just so happens that rigorous/logical argumentation is the best way to communicate mathematics.

In this sense, programming is much more algorithmic, and hence I would argue, not particularly like math (the content) at all.