Well, I would like to point that both mathematics and computer science are human activities which occur on a substrate of determinant computational processes. Mathematics has a culture, history and set of standards which decide which among results of "proof processes" are "mathematically interesting" whereas Computer Science and Software Engineering engineering also have similar standards determining what's significant among determinant processes.

Naturally, the two standards are distinct though actual results may occasionally intersect. Moreover, being "mathematically interesting" may make be a given item useful for computer programmers at times. Comprehensibility is important for our theories about programming despite programs having the usual requirement (unlike mathematical proofs) that they need a concrete manifestation.

And both mathematics-the-human-endeavor and software-engineering-the-human-endeavor are full of metaphors that are false-but-useful. Computer programs don't literally decacy any more than mathematical truths have "inherent beauty" or exist in any ideal realm. But both metaphors are useful nonetheless.

Also, the parent is confusing logical levels - programming is analogous to mathematical calculation whereas mathematics is analogous to computer-science or software engineering. Programs may be incorrect and calculations may be incorrect so many of distinctions are not germane to math/computer-science split (though the different ways programs are incorrect versus the ways calculations can be incorrect are relevant).