"The natural language which has been effectively used for thinking about computation, for thousands of years, is mathematics."

I'm not sure if this is true. Harold Abelson creates the distinction[1] between Mathematics being the study of truth and Computing being the study of process. It seems to me that these really are different things and Mathematics isn't the "natural language" to discuss computations, but rather truth and patterns. But of course process (computing) can only happen within the boundaries of mathematical truths and patterns.

[1] https://www.youtube.com/watch?v=2Op3QLzMgSY the first few minutes