I'm of two minds about this. Everything you mention is great background to have. (Though non-trivial programs can't be reasoned about mathematically much more than biological systems can).
I think this deep background is a great goal. But in another way programming is a craft. You can learn as you go. There are millions of bright people who could do useful, quality work without an MIT-level CS education. They just need some guidance, structure, and encouragement.
> (Though non-trivial programs can't be reasoned about mathematically much more than biological systems can).
I wouldn't be so sure. I once applied for a company that was about proving various safety properties of control and signalling applications (for trains). Sizeable applications. They have problems with the halting problem and combinatorial explosions, but they get around those and do it anyway.
I think this deep background is a great goal. But in another way programming is a craft. You can learn as you go. There are millions of bright people who could do useful, quality work without an MIT-level CS education. They just need some guidance, structure, and encouragement.