I agree with you generally, but how much mathematical thinking will help you still depends extremely on the kind of job you are doing. In my experience the sin

I agree with you generally, but how much mathematical thinking will help you still depends extremely on the kind of job you are doing. In my experience the single thing in which mathematical thinking can help you best is going meta. When you reason about the program as the program were data. It is not a coincidence that smart people with mathematical talent wants to go meta: they love to write frameworks, new programing languages, compilers, (graphical, database) engines. But most of the programmers have to write good old application logic (so called business logic) using languages, frameworks, engines, technologies made by other people. I go further: most people have to use bad programming languages, programming languages which are not their choice. Most people have to maintain bad quality code created by other people. For these tasks mathematical thinking is really secondary. You have to have other skills: very good memory, finding your way in a complex mess, etc... If you are mathematically 'smart', you will find patterns, you will be bored, you will go meta, and they need to find another guy for the mundane task.