I think, that despite this be a good rebutal, it show exactly why the first article. When try to justify why programing is math then it focus in the kind of task that benefit a lot for it, then dismiss "the kind of applications that we haven’t yet automate".
In real life, even in math-heavy task, the dominate factor is doing that kind of stuff.
The problem that people that say "please, programming is not math!" is get rid of the elitistic mindset where if not good at math, then worse at programming, and dismiss the importance of other kind of knwoledge (art, writing, other domains, etc). Math is a part, but is not the whole. This is the message.
> wouldn't software also be able to create and analyze mathematical theory ("conjecture, proof, and building theories")?
Already happening.
e.g. Douglas Lenat's Automated Mathematician [1]... there are probably newer, better examples.
Please forgive me if I'm making the most heretical question possible, but once we reach the level of software sophistication the author hints at ("how to automate the translation of drawn sketches to good HTML and CSS") wouldn't software also be able to create and analyze mathematical theory ("conjecture, proof, and building theories")?