Actually, he didn't "produce" those terms (let alone "describe" anything with them - at best, he used them as inept labels, not descriptions). They already exist and are in common usage in the area of politics. I'm surprised you didn't know that ;-)
Seriously, the point is that to borrow the terms "right-wing" and "left-wing" for the notions he is describing is misleading unless the analogy is clear (which it is not). Misleading readers is the opposite of good explanation.
On the contrary: it's the things that he LIKES, and that all mathematicians like (certainty) that he labels "right-wing."
Would that include the part where he says, "Like right wing policies, for all that it appeals to individuals who crave certitude in life, the right wing definition of mathematical proof is an unrealistic ideal that does not survive the first contact with the real world."?
I see your point about how (what he calls) "right-wing" is meant to stand for, The traditional way mathematics is done. However, I don't think it's a correct interpretation of this article to say that it's "right-wing" mathematics which he "likes". It seems like what he's really saying is, Things are changing (becoming "left-wing") in mathematics and you ought to get used to it, because I have.
He's just using words he chose because he couldn't think of any more descriptive words.
I'll have to take your word for it that you know what was in the author's mind when he wrote this, I guess. As far as the supposed inability to think of more descriptive words, he was doing fine with the "right-or-wrong" vs. "fuzzy" dichotomy. What exactly did the terms "right-wing"/"left-wing" add? To fail to understand that these terms are loaded is a failure of the author.
Sheesh, don't take it so personally.
Who's taking it "personally"? What I said was that it was an eye-roll-inducing and misleading use of terminology that distracted me from the (valid) point of the article and (almost) prevented me from reading it.
No skin off my nose. *His* loss, not mine, if his inept and gratuitous terminology reduces his readership.
There's no political agenda here.
I am not as convinced as you are of that.
It's mathematics he's talking about, for God's sake.
Well, except for the gratuitous and unsupported crack about "right wing policies", of course.
I'd have liked this essay much more if it had actually focused on the mathematics as much as you seem to think it did.
OK, I'll grant there's a definite "lean" to that part of the article.
It still doesn't amount to anything near a super-gaggo mega-upchuck barf alert.