Last year, mathematicians Theodore Hill and Sergei Tabachnikov submitted a paper on a mathematical model that attempted to explain why some studies have found greater variability in various traits among males than females of many species, including humans.

The Math Intelligencer accepted the manuscript, but the journal’s editor-in-chief opted not to publish the paper after four months, before it went on the journal’s website. During that time, the editor, Marjorie Senechal, a professor emerita at Smith College, had begun to receive emails from other researchers who had seen a version of the paper, including on arXiv, a preprint database, and who were, according to the editor, outraged about the manuscript’s content.

The researchers who sent her emails were, according to Senechel, worried that the paper would provoke “strong reactions” and would be interpreted as backing a sexist agenda. “The main reason for pulling...

A month after the manuscript was set aside by The Math Intelligencer, Igor Rivin, a mathematician at Temple University and one of the editors of The New York Journal of Mathematics (NYJM), contacted Hill, a professor of mathematics at Georgia Tech. Rivin had seen a version of the paper and invited Hill to submit it to the journal. 

Rivin’s motivation was to help put more of a spotlight on the journal and not because he had any agenda that was tied to the contents of the paper, he tells The Scientist in an interview. “People are assuming that because they see this paper as a political issue, that my wanting to publish this paper in the journal was also for political reasons, but it was for opportunistic reasons rather than political ones,” says Rivin. 

What’s clearly improper is for journals to accept and even publish papers, and then retract them after the editorial process or publication process is complete, unless there are issues of academic fraud.

—Brian Leiter, University of Chicago

Hill submitted a new draft, as the lone author this time, to the NYJM, and after peer review by two mathematicians, Hill’s model was published on the journal’s website in November 2017. But three days later, the paper had disappeared from the online journal, which Rivin says he was unaware of until Hill pointed out the fact in an email to him. 

According to both Hill’s account and The Scientist’s interview with Rivin, Benson Farb, a mathematician at the University of Chicago and NYJM editor, wrote to the editorial board about the paper and board members raised concerns, including on the quality of the paper’s contents and its appropriateness for a theoretical mathematics journal. Some of the board members pressured the editor-in-chief, Mark Steinberger (who passed away on September 15, 2018), and said that they would quit the journal if the paper were not retracted. Steinberger and the editorial board decided to retract the paper permanently in February of this year but have not issued an official retraction notice. 

For the scientific community, the publication flux of these manuscripts has highlighted issues with the editorial process, and how politics and controversy can get in the way. “It is a great pity that the article was not published in The Mathematical Intelligencer together with a rebuttal,” writes Tim Gowers, a mathematician at the University of Cambridge in the UK, in an email to The Scientist. “This would have led to a useful debate that was not mixed up with issues about publication ethics.”

The variability hypothesis

The variability hypothesis generally states that the males of a species vary more widely in physical and physiological traits than the females. This theory is controversial because, since the beginning of the 20th century, it has mostly been used to refer to cognitive abilities—the purported greater frequency of both lower and higher extremes in intelligence among human males compared with females. 

As Penn State University professor of psychology and women’s studies Stephanie Shields covered in her 1982 historical review (and in a follow-up 2016 review), scientists in the early 1900s asserted that there was a difference in the variability of mental traits between the sexes and attributed this difference to genetics, not considering environment and societal factors. 

“In the case of high intelligence, these scientists assumed that the proportion of men was higher because men were more likely to be judges, explorers, successful businessmen, and achieve other high status compared to women. And that this difference was all due to innate differences between females and males,” writes Shields in an email to The Scientist

Another issue with the hypothesis, according to Shields, is that the same genetic mechanisms were believed to account for sex ratios at the high end of the distribution as at the low end of the distribution. Thus, the higher proportion of “men of genius,” as indicated by social and professional achievement, was believed to have the same cause as the higher proportion of men of very low intelligence, she says. 

These are among the issues that those who wanted Hill’s paper removed have cited—that promoting a theory that implies that biology alone can explain a greater cluster of males at the high end of the cognitive scale is not only inaccurate, but detrimental to the advancement of women in science—and in general.

Hill’s mathematical model—now available in several preprints, including the most current version (although none are the exact drafts that were to be published in the two journals)—is relatively simple. The model describes two sexes that mate, although the paper doesn’t explicitly label the two sexes as “male” and “female”. One of the sexes is split into two groups. One group is more variable and has both more individuals that are, for mating, more desirable to the opposite sex, and also more individuals at the opposite end of the spectrum that are highly undesirable to the opposite sex for mating. All of the individuals in the other group are of medium desirability. 

The model suggests that if the opposite sex is relatively nonselective in mate choice, then the less-variable group will reproduce in greater proportion to its overall prevalence among its sex, giving it a reproductive advantage over the more-variable population. If the opposite sex is relatively selective in its mate choice, then the more-variable group will have a reproductive advantage over the less-variable one and will have a greater opportunity to pass its genes on to the subsequent generation. 

The major flaw in the paper, according to Mark Kirkpatrick, a mathematical geneticist at the University of Texas at Austin who has published models of the evolution of mating preferences and selected traits, is that the rules of inheritance are not taken into account. “The paper’s conclusions are simply wrong,” he says. “The genes of the successful individuals in a population are transmitted to the offspring and [Hill’s] model does not have any equation that links up the genes of one generation with the genes of the next generation.”

Reed Cartwright, a computational evolutionary geneticist at Arizona State University, agrees. “My primary issue with Hill’s model is that it lacks any notion of genetics, and you cannot ignore genetics and make evolutionary conclusions,” Cartwright writes in an email to The Scientist. The model also ignores the role of gene-environment interactions, which are particularly important for complex traits, according to Cartwright. “Hill did not appreciate that if the difference between his two populations of males was due to environment and not genes, then his conclusions would be invalid.”

Editorial controversy

According to Hill, he saw his paper as a “toy model” that would serve as a starting point to explain how one sex could evolve to have greater variability of certain traits, and he makes no claim that it applies to real life, and particularly to human intelligence. 

Hill and Tabachnikov’s paper was accepted for The Mathematical Intelligencer’s Viewpoint column that is meant to spark a “robust but rational debate,” Senechal tells The Scientist

The decision to pull the paper and replace it with a round table was difficult and painful but made in the interest of scientific discourse.

—Marjorie Senechal, Smith College

The paper was approved for publication when Senechal received an email from Amie Wilkinson, a mathematician at the University of Chicago, who had seen a preprint version of the paper and was critical of the model’s scientific merits, suggesting that the journal should publish a rebuttal by experts in the evolutionary biology field. (Wilkinson declined an interview.)

Instead, after consulting with “a significant number of stakeholders,” Senechal decided to pull the paper. Wilkinson’s email did not suggest the paper should be retracted. And other mathematicians tell The Scientist they wish it hadn’t been so that the merits of the model could be properly debated. As part of her decision to stop publication of the paper, Senechal told the authors that her intention was to hold a roundtable discussion among the authors and other interested researchers to debate the merits of the model, to record the dialog, and then publish an edited version in The Mathematical Intelligencer, she writes in an email to The Scientist. 

The biggest concern for those advocating against the decisions by the two journals—despite the criticisms of the paper’s contents—is that academic freedom is at stake.

“What’s clearly improper is for journals to accept and even publish papers, and then retract them after the editorial process or publication process is complete, unless there are issues of academic fraud,” says Brian Leiter, director of the Center for Law, Philosophy, and Human Values at the University of Chicago. “If the journal publishes an awful paper, its reputation deserves to suffer. Members of the editorial board can resign or call for reform of the editorial process. But acceptance after normal review and then rejection isn’t an option if a journal aspires to be a professional operation.”

For Harry Crane, a statistician at Rutgers University and cofounder of researchers.one, a recently created online peer-review platform for the scientific research community to post manuscripts and have their colleagues comment and critique them openly, the events that transpired at both journals point to flaws in the current peer-review publication process. “In the interest of transparency, academic freedom, and scholarly discourse, the criticisms of Hill’s work should be made openly so that the authors can respond and the readers can come to an informed decision based on sound arguments and hard facts,” he tells The Scientist. “This clearly did not happen in this case, not because this particular situation is anomalous, but rather because the current academic publication system is not designed to facilitate open, transparent discourse.”

Senechal, for her part, is well aware of the backlash and did not make the decision lightly, she writes to The Scientist. “These criticisms are not unjust. But The Mathematical Intelligencer is not a research journal . . . and online outrage is a destructive hurricane. The decision to pull the paper and replace it with a round table was difficult and painful but made in the interest of scientific discourse.”

Rivin was not part of the editorial decision to have the paper retracted from the NYJM, he says, and doesn’t agree with it. “It’s certainly anyone’s prerogative to think the paper is terrible, but the paper was properly peer-reviewed. If you don’t like the paper, then write a rebuttal or don’t publish in this journal. But the content of the paper is not an excuse for the retraction.”

Cartwright, for one, believes that the manuscript was not of sufficient quality to merit publication and that it was “unfortunate that the journals’ editors only realized the flaws in his paper after they had accepted the paper.” 

Yet the quelling of the paper has backfired, Crane notes. “This paper is getting much more attention than it would have otherwise. I’ve read a version three times now and I would have never known that it existed otherwise.”

Correction (November 21): The headline and several paragraphs have been altered to clarify that only one paper was retracted, not both, given that the first manuscript was accepted but never published. The Scientist regrets the error.

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