Software engineering is an optimisation problem in the same sense that other engineering fields are optimisation problems. There are tradeoffs to be made on many dimensions, just like in any engineering discipline.

Again, mathematical tools can be used to prove the correctness of programs.

I think you are missing the science and math aspect of this. This isn't a contest. Physicians make lots of money by following tradition and practicing medicine as an art. There is huge debate that Physicians could lose their monopoly powers if medical is a science.

This is vague. Please clarify your point. What aspect are you talking about?