I don't think any of the research mathematicians I know exhibit a degree of ignorance like the one depicted in the article towards the philosophical underpinnin

I don't think any of the research mathematicians I know exhibit a degree of ignorance like the one depicted in the article towards the philosophical underpinnings of their field - the implied attitude towards rigorous proof in particular seems to be an egregious strawman. It is generally accepted that any research mathematician, given an arbitrarily chosen section of a high-level proof, should be able to convert it to a structured step-by-step proof (though possibly at the expense of a prohibitive amount of time), and the same generally holds for any half-decent graduate student by the time they've spent a year or two in their field. The choice of title makes it even more questionable - imagine a similarly uncharitable piece titled "The ideal [racial category]". (That being said, the insinuation that mathematicians tend to play the motte-and-bailey game with formalism and platonism does ring true.)