I have to issues with it: The write-up seems very one-sided as can already be noticed in the language (1) and the paper, as others have pointed out, is not much of a good scientific paper (2). It seems like the whole controversy was engineered or, at least, he deliberately tried to provoke/"troll" the academic community with his paper.
1)
Certain parts of the post ring my alarm bells when it comes to the language used:
For example: "Fortunately for me, I am now retired and rather less easily intimidated—one of the benefits of being a Vietnam combat veteran and former U.S. Army Ranger, I guess."
Also, certain parts don't really seem to pass a smell test:
> Half his board, he explained unhappily, had told him that unless he pulled the article, they would all resign and “harass the journal” he had founded 25 years earlier “_until it died._” Faced with the loss of his own scientific legacy, he had capitulated. “A publication in a dead journal,” he offered, “wouldn’t help you.”
I also find it highly suspicious that so many statisticians, fellow mathematicians etc seem to think of the paper as pseudoscientific. When even the NSF and editorial boards, institutions traditionally very conservative, are unhappy, there is probably a reason why
2)
I'm not mathematician but a cursory glance at the text reveals a few very surprising assumptions. The paper's hypothesis is this:
> SELECTIVITY-VARIABILITY PRINCIPLE. In a species with two sexes A and B, both of which are needed for reproduction, suppose that sex A is relatively selective, i.e., will mate only with a top tier (less than half ) of B candidates [1]. Then from one generation to the next, among subpopulations of B with comparable average attributes, those with greater variability will tend to prevail over those with lesser variability. Conversely, if A is relatively non-selective, accepting all but a bottom fraction (less than half ) of the opposite sex, then subpopulations of B with lesser variability will tend to prevail over those with comparable means and greater variability.
[1] As the author points out himself, this presupposes that there is an absolute scale of attractiveness. However, he hides that fact (and its facial controversy) in a bit more convoluted writing: "it will be assumed that to each individual (or phenotype) in each sex is assigned a numerical desirability value which reflects its desirability to the opposite sex". There is only a larger group of people in the top bracket, e.g. 9s, if that is an absolute value on an universal, absolute scale (i.e. if you pick a set, numerical point on this graph https://i.stack.imgur.com/JWWuw.png). If attractiveness is relative and based on the average for example, your contextual situation and "top bracket" corresponds to e.g. top 10%, than the group size doesn't change and the subpopulation with greater variability doesn't have an advantage. And there is evidence for that when we recall that most people date people from a similar social background and that ideas of attractiveness are (partially) based on your background.
Additionally, looking at statistical evidence, we can see that, while there is a difference in childless partners, - which would imply that one groups dates more selectively - that difference is not as large as the authors allude to: https://www.cbs.nl/en-gb/news/2010/27/more-childless-men. And that is only one crude statistic, best would be number of children per partner.
From the way he writes the paper (and especially this write-up), despite disclaimers to the contrary, he clearly tries to apply his theory to humans with women being the selective sex.