> I'm majoring in Pure Maths and this is annoying to see yet another poor scientific article on Math.
I dislike personal qualifications-based arguments, so I'm loathe to contribute to them. However, for people who are persuaded by mentions of qualifications: I have a PhD in mathematics and I think Quanta magazine is more-or-less the best popular-level writing available on the subject.
Still, I will attempt to contribute on issues of substance. I thought that everything in this article was fine. It's an old idea, as mentioned in this comment: https://en.wikipedia.org/wiki/Hilbert%E2%80%93P%C3%B3lya_con...
As such, perhaps the article would benefit from some history. As mentioned on the Wikipedia page https://en.wikipedia.org/wiki/Hilbert%E2%80%93P%C3%B3lya_con... observations regarding the distribution of zeros on the critical line led directly to early results in random matrix theory. This 2009 interview with Freeman Dyson discusses this connection, as well as this approach to the Riemann Hypothesis (Dyson refers to it as "a fourth joke of nature"): http://www.ams.org/notices/200902/rtx090200212p.pdf
I recommend reading that interview in its entirety, or at least the section on "jokes of nature", for Dyson's thoughts on a lot of subjects.