You and I read the article very differently. Based on your comment, it sounds like you interpreted the article as implicit advocation for the idea that mathematics should be represented in a programmatic (i.e. computable) way.

I didn't pick up any ideology in my reading. My interpretation of the article is that the author wanted to provide tips on how to implement mathematics, for two reasons:

1. People have to implement nontrivial mathematics from time to time, and

2. Most mathematics doesn't concern itself with obstacles to implementation, because it doesn't have to.