I disagree entirely. Systems that have proved amenable to mathematical analysis remain relatively few. Pick any one book that aims to describe some aspect of the world; chances are it won't contain a single formula.
This is a pretty weird argument. You can replace math with physics, chemistry, or whatever other science you can think of and the argument still goes through. If his argument is invariant with respect to subject change it means he's not really addressing anything specific to math but just pointing out that hard things tend to be exclusive things.
So in essence the people that say "math is everywhere" are trying to democratize it. Whereas the argument in the SciAm article seems to point to a more stifled mathematical landscape. I've never seen someone make an argument "X is elitist" in order to democratize something. If anything people usually get their pitchforks out and all the folks with an agenda come out of the woodworks and start using the mob to advance their own goals. In this case I suspect there are a few folks that would like to kill funding for basic mathematical research and this guy has started selling them the pitchforks.
Michael J. Barany, the OP of the scientificamerican article, wrote a response to this response: http://mbarany.com/ReplyToThonyC.html (not very convincing, IMHO, mainly because all the "math is elitist"-arguments Barany makes are not specific to math, but to any intellectual endeavour. One could /s/math/writing/g in the whole article and it would continue to make sense.)
That's an interesting thought. But I don't generally share the resentment (although I didn't even read the link).
Writing still has to be logical, most of the time. Math papers are verbalized a lot. You can't draw a fine line between writing (literature) and maths. That's why the argument still holds. They are both the same thing from a different perspective, what you called intellect.
Mathematics is the most reduced form, though, and it is maybe more exclusive by nature, since it is all about learning and abstraction, whereas literature and language is most basically developed from calls to action, like, literally developed from calls.
Does this strike anyone else as a bit of a circle jerk?
"Hey, this guy in a popular science magazine wrote about how math is so important, so I'm going to write a blog post about how math is slightly less important than he said it was."
The way I interpret it, is that if you study how anything works in enough detail, there is almost always a way to understand it mathematically.