> I'd argue for the converse: Computer Science is Mathematics

The space of programs is arguably larger than the space of mathematical systems, because programs can be logically inconsistent. This suggests that mathematics is a logically consistent subset of computer science, not the other way around.

Let's just say there is a really big overlap between the two. And each one can learn from the point of view of the other.

That question contains so many false or unnecessary assumptions that it would take far longer to unpack them than it took you to type them, so I will limit myself to the observation that we do not even remotely confine ourselves to first order anything in computer science, nor should we.