Evidence for this hypothesis is fairly robust and has been reported in species ranging from adders and sockeye salmon to wasps and orangutans, as well as humans. Multiple studies have found that boys and men are over-represented at both the high and low ends of the distributions in categories ranging from birth weight and brain structures and 60-meter dash times to reading and mathematics test scores. There are significantly more men than women, for example, among Nobel laureates, music composers, and chess champions—and also among homeless people, suicide victims, and federal prison inmates.
Darwin had also raised the question of why males in many species might have evolved to be more variable than females, and when I learned that the answer to his question remained elusive, I set out to look for a scientific explanation. My aim was not to prove or disprove that the hypothesis applies to human intelligence or to any other specific traits or species, but simply to discover a logical reason that could help explain how gender differences in variability might naturally arise in the same species.
I came up with a simple intuitive mathematical argument based on biological and evolutionary principles and enlisted Sergei Tabachnikov, a Professor of Mathematics at Pennsylvania State University, to help me flesh out the model. When I posted a preprint on the open-access mathematics archives in May of last year, a variability researcher at Durham University in the UK got in touch by email. He described our joint paper as “an excellent summary of the research to date in this field,” adding that “it certainly underpins my earlier work on impulsivity, aggression and general evolutionary theory and it is nice to see an actual theoretical model that can be drawn upon in discussion (which I think the literature, particularly in education, has lacked to date). I think this is a welcome addition to the field.”
So far, so good.
Once we had written up our findings, Sergei and I decided to try for publication in the Mathematical Intelligencer, the ‘Viewpoint’ section of which specifically welcomes articles on contentious topics. The Intelligencer’s editor-in-chief is Marjorie Wikler Senechal, Professor Emerita of Mathematics and the History of Science at Smith College. She liked our draft, and declared herself to be untroubled by the prospect of controversy. “In principle,” she told Sergei in an email, “I am happy to stir up controversy and few topics generate more than this one. After the Middlebury fracas, in which none of the protestors had read the book they were protesting, we could make a real contribution here by insisting that all views be heard, and providing links to them.”
Professor Senechal suggested that we might enliven our paper by mentioning Harvard President Larry Summers, who was swiftly defenestrated in 2005 for saying that the GMVH might be a contributing factor to the dearth of women in physics and mathematics departments at top universities. With her editorial guidance, our paper underwent several further revisions until, on April 3, 2017, our manuscript was officially accepted for publication. The paper was typeset in India, and proofread by an assistant editor who is also a mathematics professor in Kansas. It was scheduled to appear in the international journal’s first issue of 2018, with an acknowledgement of funding support to my co-author from the National Science Foundation. All normal academic procedure.
* * *
Coincidentally, at about the same time, anxiety about gender-parity
erupted in Silicon Valley. The same anti-variability argument used to
justify the sacking of President Summers resurfaced when Google engineer
James Damore suggested that several innate biological factors,
including gender differences in variability, might help explain gender
disparities in Silicon Valley hi-tech jobs. For sending out an internal
memo to that effect, he too was summarily fired.No sooner had Sergei posted a preprint of our accepted article on his website than we began to encounter problems. On August 16, a representative of the Women In Mathematics (WIM) chapter in his department at Penn State contacted him to warn that the paper might be damaging to the aspirations of impressionable young women. “As a matter of principle,” she wrote, “I support people discussing controversial matters openly … At the same time, I think it’s good to be aware of the effects.” While she was obviously able to debate the merits of our paper, she worried that other, presumably less sophisticated, readers “will just see someone wielding the authority of mathematics to support a very controversial, and potentially sexist, set of ideas…”
A few days later, she again contacted Sergei on behalf of WIM and invited him to attend a lunch that had been organized for a “frank and open discussion” about our paper. He would be allowed 15 minutes to describe and explain our results, and this short presentation would be followed by readings of prepared statements by WIM members and then an open discussion. “We promise to be friendly,” she announced, “but you should know in advance that many (most?) of us have strong disagreements with what you did.”
On September 4, Sergei sent me a weary email. “The scandal at our department,” he wrote, “shows no signs of receding.” At a faculty meeting the week before, the Department Head had explained that sometimes values such as academic freedom and free speech come into conflict with other values to which Penn State was committed. A female colleague had then instructed Sergei that he needed to admit and fight bias, adding that the belief that “women have a lesser chance to succeed in mathematics at the very top end is bias.” Sergei said he had spent “endless hours” talking to people who explained that the paper was “bad and harmful” and tried to convince him to “withdraw my name to restore peace at the department and to avoid losing whatever political capital I may still have.” Ominously, “analogies with scientific racism were made by some; I am afraid, we are likely to hear more of it in the future.”
The following day, I wrote to the three organisers of the WIM lunch and offered to address any concrete concerns they might have with our logic or conclusions or any other content. I explained that, since I was the paper’s lead author, it was not fair that my colleague should be expected to take all the heat for our findings. I added that it would still be possible to revise our article before publication. I never received a response.
Instead, on September 8, Sergei and I were ambushed by two unexpected developments.
First, the National Science Foundation wrote to Sergei requesting that acknowledgment of NSF funding be removed from our paper with immediate effect. I was astonished. I had never before heard of the NSF requesting removal of acknowledgement of funding for any reason. On the contrary, they are usually delighted to have public recognition of their support for science.
The ostensible reason for this request was that our paper was unrelated to Sergei’s funded proposal. However, a Freedom of Information request subsequently revealed that Penn State WIM administrator Diane Henderson (“Professor and Chair of the Climate and Diversity Committee”) and Nate Brown (“Professor and Associate Head for Diversity and Equity”) had secretly co-signed a letter to the NSF that same morning. “Our concern,” they explained, “is that [this] paper appears to promote pseudoscientific ideas that are detrimental to the advancement of women in science, and at odds with the values of the NSF.” Unaware of this at the time, and eager to err on the side of compromise, Sergei and I agreed to remove the acknowledgement as requested. At least, we thought, the paper was still on track to be published.
But, that same day, the Mathematical Intelligencer’s editor-in-chief Marjorie Senechal notified us that, with “deep regret,” she was rescinding her previous acceptance of our paper. “Several colleagues,” she wrote, had warned her that publication would provoke “extremely strong reactions” and there existed a “very real possibility that the right-wing media may pick this up and hype it internationally.” For the second time in a single day I was left flabbergasted. Working mathematicians are usually thrilled if even five people in the world read our latest article. Now some progressive faction was worried that a fairly straightforward logical argument about male variability might encourage the conservative press to actually read and cite a science paper?
In my 40 years of publishing research papers I had never heard of the rejection of an already-accepted paper. And so I emailed Professor Senechal. She replied that she had received no criticisms on scientific grounds and that her decision to rescind was entirely about the reaction she feared our paper would elicit. By way of further explanation, Senechal even compared our paper to the Confederate statues that had recently been removed from the courthouse lawn in Lexington, Kentucky. In the interests of setting our arguments in a more responsible context, she proposed instead that Sergei and I participate in a ‘Round Table’ discussion of our hypothesis argument, the proceedings of which the Intelligencer would publish in lieu of our paper. Her decision, we learned, enjoyed the approval of Springer, one of the world’s leading publishers of scientific books and journals. An editorial director of Springer Mathematics later apologized to me twice, in person, but did nothing to reverse the decision or to support us at the time.
So what in the world had happened at the Intelligencer? Unbeknownst to us, Amie Wilkinson, a senior professor of mathematics at the University of Chicago, had become aware of our paper and written to the journal to complain. A back-and-forth had ensued. Wilkinson then enlisted the support of her father—a psychometrician and statistician—who wrote to the Intelligencer at his daughter’s request to express his own misgivings, including his belief that “[t]his article oversimplifies the issues to the point of embarrassment.” Invited by Professor Senechal to participate in the proposed Round Table discussion, he declined, admitting to Senechal that “others are more expert on this than he is.” We discovered all this after he gave Senechal permission to forward his letter, inadvertently revealing Wilkinson’s involvement in the process (an indiscretion his daughter would later—incorrectly—blame on the Intelligencer).
I wrote polite emails directly to both Wilkinson and her father, explaining that I planned to revise the paper for resubmission elsewhere and asking for their criticisms or suggestions. (I also sent a more strongly worded, point-by-point rebuttal to her father.) Neither replied. Instead, even long after the Intelligencer rescinded acceptance of the paper, Wilkinson continued to trash both the journal and its editor-in-chief on social media, inciting her Facebook friends with the erroneous allegation that an entirely different (and more contentious) article had been accepted.
At this point, faced with career-threatening reprisals from their own departmental colleagues and the diversity committee at Penn State, as well as displeasure from the NSF, Sergei and his colleague who had done computer simulations for us withdrew their names from the research. 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. So, I continued to revise the paper, and finally posted it on the online mathematics archives.
* * *
On October 13, a lifeline appeared. Igor Rivin, an editor at the widely respected online research journal, the New York Journal of Mathematics,
got in touch with me. He had learned about the article from my
erstwhile co-author, read the archived version, and asked me if I’d like
to submit a newly revised draft for publication. Rivin said that Mark
Steinberger, the NYJM’s editor-in-chief, was also very positive
and that they were confident the paper could be refereed fairly
quickly. I duly submitted a new draft (this time as the sole author)
and, after a very positive referee’s report and a handful of supervised
revisions, Steinberger wrote to confirm publication on November 6, 2017.
Relieved that the ordeal was finally over, I forwarded the link to
interested colleagues.Three days later, however, the paper had vanished. And a few days after that, a completely different paper by different authors appeared at exactly the same page of the same volume (NYJM Volume 23, p 1641+) where mine had once been. As it turned out, Amie Wilkinson is married to Benson Farb, a member of the NYJM editorial board. Upon discovering that the journal had published my paper, Professor Farb had written a furious email to Steinberger demanding that it be deleted at once. “Rivin,” he complained, “is well-known as a person with extremist views who likes to pick fights with people via inflammatory statements.” Farb’s “father-in law…a famous statistician,” he went on, had “already poked many holes in the ridiculous paper.” My paper was “politically charged” and “pseudoscience” and “a piece of crap” and, by encouraging the NYJM to accept it, Rivin had “violat[ed] a scientific duty for purely political ends.”
Unaware of any of this, I wrote to Steinberger on November 14, to find out what had happened. I pointed out that if the deletion were permanent, it would leave me in an impossible position. I would not be able to republish anywhere else because I would be unable to sign a copyright form declaring that it had not already been published elsewhere. Steinberger replied later that day. 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.”
* * *
Colleagues I spoke to were appalled. None of them had ever heard of a
paper in any field being disappeared after formal publication. Rejected
prior to publication? Of course. Retracted? Yes, but only after an
investigation, the results of which would then be made public by way of
explanation. But simply disappeared? Never. If a formally
refereed and published paper can later be erased from the scientific
record and replaced by a completely different article, without any
discussion with the author or any announcement in the journal, what will
this mean for the future of electronic journals?Meanwhile, Professor Wilkinson had now widened her existing social media campaign against the Intelligencer to include attacks on the NYJM and its editorial staff. As recently as April of this year, she was threatening Facebook friends with ‘unfriending’ unless they severed social media ties with Rivin.
In early February, a friend and colleague suggested that I write directly to University of Chicago President Robert Zimmer to complain about the conduct of Farb and Wilkinson, both of whom are University of Chicago professors. The previous October, the conservative New York Times columnist Bret Stephens had called Zimmer “America’s Best University President.” The week after I wrote to Zimmer, the Wall Street Journal would describe Chicago as “The Free-Speech University” based upon its president’s professed commitment to the principles of free inquiry and expression. Furthermore, Professor Zimmer is a mathematician from the same department and even the same subfield as Farb and Wilkinson, the husband-wife team who had successfully suppressed my variability hypothesis research and trampled on the principles of academic liberty. Surely I would receive a sympathetic hearing there?
And so I wrote directly to Professor Zimmer, mathematician to mathematician, detailing five concrete allegations against his two colleagues. When I eventually received a formal response in late April, it was a somewhat terse official letter from the vice-provost informing me that an inquiry had found no evidence of “academic fraud” and that, consequently, “the charges have been dismissed.” But I had made no allegation of academic fraud. I had alleged “unprofessional, uncollegial, and unethical conduct damaging to my professional reputation and to the reputation of the University of Chicago.”
When I appealed the decision to the president, I received a second official letter from the vice-provost, in which he argued that Farb and Wilkinson had “exercised their academic freedom in advocating against the publication of the papers” and that their behavior had not been either “unethical or unprofessional.” A reasonable inference is that I was the one interfering in their academic freedom and not vice versa. My quarrel, the vice-provost concluded, was with the editors-in-chief who had spiked my papers, decisions for which the University of Chicago bore no responsibility. At the Free Speech University, it turns out, talk is cheap.
* * *
Over the years there has undoubtedly been significant bias and
discrimination against women in mathematics and technical fields.
Unfortunately, some of that still persists, even though many of us have
tried hard to help turn the tide. My own efforts have included tutoring
and mentoring female undergraduates, graduating female PhD students, and
supporting hiring directives from deans and departmental chairs to seek
out and give special consideration to female candidates. I have been
invited to serve on two National Science Foundation gender and race
diversity panels in Washington.Which is to say that I understand the importance of the causes that equal opportunity activists and progressive academics are ostensibly championing. But pursuit of greater fairness and equality cannot be allowed to interfere with dispassionate academic study. No matter how unwelcome the implications of a logical argument may be, it must be allowed to stand or fall on its merits not its desirability or political utility. First Harvard, then Google, and now the editors-in-chief of two esteemed scientific journals, the National Science Foundation, and the international publisher Springer have all surrendered to demands from the radical academic Left to suppress a controversial idea. Who will be the next, and for what perceived transgression? If bullying and censorship are now to be re-described as ‘advocacy’ and ‘academic freedom,’ as the Chicago administrators would have it, they will simply replace empiricism and rational discourse as the academic instruments of choice.
Educators must practice what we preach and lead by example. In this way, we can help to foster intellectual curiosity and the discovery of fresh reasoning so compelling that it causes even the most sceptical to change their minds. But this necessarily requires us to reject censorship and open ourselves to the civil discussion of sensitive topics such as gender differences, and the variability hypothesis in particular. In 2015, the University of Chicago’s Committee on Freedom of Expression summarized the importance of this principle beautifully in a report commissioned by none other than Professor Robert Zimmer:
In a word, the University’s fundamental commitment is to the principle that debate or deliberation may not be suppressed because the ideas put forth are thought by some or even by most members of the University community to be offensive, unwise, immoral, or wrong-headed.Supporting documentation for this account can be found here.
Ted Hill is Professor Emeritus of Mathematics at Georgia Tech, and currently a research scholar in residence at the California Polytechnic State University in San Luis Obispo. His memoir PUSHING LIMITS: From West Point to Berkeley and Beyond was recently published jointly by the American Mathematical Society and the Mathematical Association of America.
