The diversity statement controversy, III


Chad Topaz was scheduled to speak at 9:30 this morning at the Joint Mathematics Meeting in Denver, at the AMS Special Session on the Mathematics of Social Justice.    His title was Diversity through a Data Science Lens, and you can read his abstract here.  His talk was cancelled, however, so I won’t be able to tell you whether or not he touched on the topic of the article excerpted above.   Since his name is out of alphabetical order I assume he was the lead author.  The article sheds a not entirely unexpected light on the controversy over diversity hiring statements to which I have already devoted three blog posts.  Here is the summary:

We report on a study of the signatories’ demographics, which we infer using a crowdsourcing approach. Letter A highlights diversity and social justice. The pool of signatories contains relatively more individuals inferred to be women and/or members of underrepresented ethnic groups. Moreover, this pool is diverse with respect to the levels of professional security and types of academic institutions represented. Letter B does not comment on diversity, but rather, asks for discussion and debate. This letter was signed by a strong majority of individuals inferred to be white men in professionally secure positions at highly research intensive universities. Letter C speaks out specifically against diversity statements, calling them “a mistake,” and claiming that their usage during early stages of faculty hiring “diminishes mathematical achievement.” Individuals who signed both Letters B and C, that is, signatories who both privilege debate and oppose diversity statements, are overwhelmingly inferred to be tenured white men at highly research intensive universities.

There is a very interesting rhetorical move here.  It can be presumed that many of those who signed Letters B and C take their “professionally secure positions at highly research intensive universities” as license to speak out with authority on matters affecting the discipline.  Although the report by Topaz et al. does not say so explicitly, it seems to imply that it is precisely the “professionally secure position” that disqualifies its holder as an objective observer.   In other words, the article questions the legitimacy of the charismatic hierarchy that is the subject of chapter 2 of MWA:  to the hierarchy’s claim to be based on professional merit, the article replies with a reading that sees it as a self-sustaining system designed to maintain undeserved (disproportionately white male) privilege.

This is not a new perspective; it was commonplace during the period of the science wars, from the late 1980s to the early 1990s, when it became less noticeable in the aftermath of the Sokal affair.  Thirty years ago, however, this point of view was not widely shared among mathematicians.  Please correct me if I’m wrong, but I don’t think there were regular sessions on Mathematics of Social Justice at Joint Mathematical Meetings in the 1980s and 1990s.

The starting point of the diversity statement controversy, I believe, is the undeniable fact that the community of professional mathematicians in the US is demographically extremely skewed relative to the country’s population.  “Underrepresented minorities,” in particular, are really underrepresented.  All the mathematicians I know see this as a real problem.   Some of the positions mentioned at the Mathematics of Social Justice session suggest that mathematics as currently constituted — in its pedagogy, its recruitment, and its charismatic hierarchy— is designed in such a way as (not necessarily intentionally) to exclude the underrepresented populations.  The solution would then be to replace the existing structures of mathematics by something new.

How might we imagine that something new?  Over the past few days in Denver I learned a great deal about a variety of inspiring initiatives at universities and schools around the country.  Some of them can be found at this list on the AMS inclusion/exclusion blog (which certainly did not exist thirty years ago).   I will be studying them over the coming weeks — I encourage readers to do the same — and it’s likely I’ll be writing about some of them.

I am pretty sure, though, that none of the new initiatives has anything to do with diversity statements.  I strongly believe that in the controversy that (as Topaz et al indicates) has not yet died down, the diversity statement itself is serving as a proxy for some more substantial objective.  This is confirmed by a message I received from one of the signatories of Letter A:

At this point the fight seems to be about whether understanding and working with students’ different backgrounds should be treated as part of the professorial job description, with Thompson representing what is probably the majority default of something like “colorblind racism”. So I think there’s value in saying loudly that the colorblind position is no longer an acceptable starting point for a worthwhile contribution to diversity/equity/justice, with the emphasis being on using diversity frameworks as a stepping stone to what we really want, which is a justice-based framework.

Where I come from, “colorblind racism” counts as fighting words.  The most obvious defect of Letter A is its inclusion of the expression “reverse racism” in quotes, when it appeared nowhere in Abigail Thompson’s letter.  For all I know, many people who signed Letter A sincerely believed that Thompson had accused the supporters of diversity statements of “reverse racism.”  But leaving misrepresentation aside, I have tried to argue that diversity frameworks are a particularly slippery stepping stone, since they were explicitly designed as an alternative to a “justice-based framework.”  The author of this comment believed as well that “[i]f you belong to the ‘fundamentally not fair’ camp, then you’re stuck with the unfortunate ‘diversity’ formulation, but at least from there the door can be wedged open.”  As far as I’m concerned this is magical thinking, as is the claim in the same comment that support for diversity statements is “an affirmative sign of where the institutional leadership stands” — as if the very institution targeted by the Bakke decision would make any effort to use the decision’s framework to undermine the decision.

Here, on the other hand, is a comment from a colleague who signed Letter B:

I thought the letters in support of Abigail were not about the diversity per se, but rather about the bullying that she became the subject of. Typical exclusion in the name of inclusion …
I objected to the use of the word “bullying.”
Has she been attacked by powerful people, or only by noisy but mainly powerless people?  I would reserve the term “bullying” for the former.
And my colleague replied:
Not sure who is powerful anymore, your allegedly powerless people can easily destroy people’s lives and, certainly, careers.
It seems to me that the threat to Abigail Thompson’s career — presumably from Chad Topaz’s initial reaction to her article — was no less exaggerated than her comparison of diversity statements to loyalty oaths, but it also seems to me likely that most of the people who signed Letters B and C were responding to this imagined threat — I didn’t sign any of the letters but I am no more inclined than they to trust “institutional leadership”  — and not to defend their privileged status of overrepresentation.  This is one reason the Topaz et al. article is so interesting; because it aims to undermine the presumption that privileged positions are awarded solely (better to say almost solely) on the basis of merit.
I would like to hear from the authors of that article how they imagine mathematics would look if the charismatic hierarchy were undermined.  But that’s a complicated issue, and I would like to end on an observation that Topaz et al. may have missed.  The article calculates that women made up 27.8% of the signatories of Letter C — making them underrepresented by some measure and within the representative range by others.  I went through the list and discovered that, of the 45 women who signed, exactly 4 were from the US (though a few may have acquired US citizenship).  I can attest that students in France are not taught to look to the US for good ideas about managing race relations, and I suspect something similar is true in the countries where most of these women grew up.

23 thoughts on “The diversity statement controversy, III

  1. Scott

    Dear Prof. Harris,

    You write “The starting point of the diversity statement controversy, I believe, is the undeniable fact that the community of professional mathematicians in the US is demographically extremely skewed relative to the country’s population. “Underrepresented minorities,” in particular, are really underrepresented. All the mathematicians I know see this as a real problem.”

    I am a mathematician, and I wonder how much of your experience is due to the fact that your colleagues fear social (and possibly career) costs if they tell you that they do not see this underrepresentation as a real problem.

    Speaking for myself, I believe that discrimination (to the extent that it exists) is a real problem. However, the available evidence, which is certainly incomplete (see last link below) nonetheless strongly suggests to me that there are underlying differences between certain groups that explain *part of * the underrepresentation and I *do not* see that as a real problem. I would be unlikely to say this publicly though, not because I think there is anything shameful about my beliefs, but because as a relatively junior mathematician, I fear professional sanctions if I did so.

    Perhaps it would be useful to have an anonymous survey of mathematicians to get a better idea of what percentage of them *actually* believe what you claim they do?

    In an earlier article ( ) on the Ted Hill affair you wrote “That means in particular that we should not be compelled to waste our time engaging with such ideas. Claims that differences in group social achievements can be explained “scientifically” by genetic differences, although they are encountered much more frequently than holocaust denial, belong in the same category. ” Is it surprising then that others would be unlikely to tell you if they think that underrepresentation is not a real problem, given your status as a eminent senior mathematician?

    Also are you actually aware of the science of sex differences, e.g., the sources given here:

    I ask you these questions not to troll but because I genuinely want to know.


    1. mathematicswithoutapologies Post author

      Thank you for sending this in on Martin Luther King Day! I had a long conversation with a colleague in Denver on the diversity statement controversy, and he was convinced that none of his colleagues thinks this way. Now I can tell him that he was mistaken.

      I suppose I should be flattered to be told that I can impose social as well as career costs upon those who disagree with me. And the Scientific American post seems to have some good news. The traits the author claims are “exaggerated among females” look overall more promising for success in mathematics than the stereotypically male traits of “emotional stability, assertiveness/dominance, dutifulness, conservatism, and conformity to social hierarchy and traditional structure”; so maybe the underrepresentation of women will resolve itself once the effects of male “assertiveness” are neutralized.

      In my Politics/Letters article I wrote “As a general rule, it is advisable to question the motivations behind an experiment or theoretical model that rationalizes an injustice embedded in the status quo.” This applies as well to the results reported in the Scientific American blog piece. I have been reading this literature since I was a graduate student, when one of my roommates was working in Richard Herrnstein’s lab (long before the Herrnstein-Murray book). He reported that Herrnstein sincerely believed that black people were not genetically adapted to intellectual work, but that it was OK because they were so good at basketball and jazz. That is practically a verbatim quote. Dare I say that it’s a good thing that my colleagues would feel uncomfortable expressing such opinions these days?


      1. Scott James

        Thank you for your reply.

        Regarding this: “The traits the author claims are “exaggerated among females” look overall more promising for success in mathematics than the stereotypically male traits of “emotional stability, assertiveness/dominance, dutifulness, conservatism, and conformity to social hierarchy and traditional structure”; so maybe the underrepresentation of women will resolve itself once the effects of male “assertiveness” are neutralized…”

        the article also had the following footnotes which are probably more relevant to the underrepresentation of women than the traits you highlighted.

        “Footnote [2]: However, it should be noted that men are typically found to show more variance in general cognitive ability scores than women (see here and here).”

        “Footnote [3]: One notable exception is an interest in people vs. an interest in things. The sex differences on this dimension are actually quite large, with some large studies finding greater than 1 standard deviation of a difference between males and females on average on this dimension”

        I dare say that these two factors may be relevant.

        Also what do you feel about the position of the article’s author when he writes that

        “First and foremost, I think this requires a recognition that none of the findings I presented in this article, nor any findings that will ever come out– justifies individual discrimination. We should treat all people as unique individuals first and foremost. No matter what the science says, if an individual shows the interest and ability to enter a field in which their sex is extremely underrepresented (e.g., women in math and science, men in nursing and education), we should absolutely be encouraging that individual to enter the field and do everything we can to help them feel a sense of belonging. I may be weird, but I don’t see any contradiction whatsoever between being an advocate for equitable opportunity for all people and being an equally strong advocate for respecting scientific findings and attempting to get as close as possible to the truth about average sex differences.”?

        Do you not consider this to be an acceptable position (from an ethical point of view) for someone to hold?


      2. mathematicswithoutapologies Post author

        I’d just say that “conservatism” and “conformity to social hierarchy” are poor predictors of success in mathematics; and that I doubt that “the truth about average sex differences” means anything, as far as cognitive ability is concerned, when cognitive ability is so poorly understood.


      3. Scott James

        Prof Harris, regarding your statement
        “I doubt that “the truth about average sex differences” means anything, as far as cognitive ability is concerned, when cognitive ability is so poorly understood. ”

        I see this kind of statements from mathematicians (who by-and-large are unaware of recent developments in cognitive, social and evolutionary psychology) a lot. It was common to see this after the Ted Hill controversy (e.g. on Gowers’ blog). I find it incredibly frustrating. It is simply not true! Yes, we do not understand cognitive ability perfectly yet. But there is a lot that we do understand. And the science is progressing rapidly. As in any area where there is a lot of work left to do (e.g., the Langlands program), it is easy to find things where do not understand things clearly. That does not preclude the fact that we also do understand a great deaI already, and are likely to understand more and more every year, given the work that is going on.

        If you would like to read about the stare-of-the-art, there is no better place to start than Dr. Kaufman’s book “Wired to Create: Unraveling the Mysteries of the Creative Mind”.

        Finally, even if (for the sake of argument) it were true that cognitive ability is poorly understood currently, it does not in any way contradict the hypothesis that the variance in (relevant facets of) mental ability might be different between males and females, implying very large difference at the high end of the spectrum, which might explain a significant part of the sex-difference in mathematics. If something is poorly understood, the default position should be “We do not really know at present” not “We will assume that all differences are due to social structures”.

        (As an aside, the greater-male-variability is something that is seen across numerous species, across a wide range of traits. Are they all due to to social conditioning of the species concerned?)


  2. Katherine Bryant

    Scott, there are many researchers “attempting to get as close as possible to the truth about average sex differences.” But that is a separate issue from the topic of Dr. Harris’ post, which is the use of diversity statements.

    If you agree with Dr. Kaufman that “if an individual shows the interest and ability to enter a field in which their sex is extremely underrepresented (e.g., women in math and science, men in nursing and education), we should absolutely be encouraging that individual to enter the field and do everything we can to help them feel a sense of belonging”, then you should support diversity statements, because that is exactly what they are designed to do.

    Liked by 1 person

    1. Scott James

      Dear Katherine,

      Sorry I disagree.

      Please take a look at how diversity statements were used in a recent job hire at Berkeley.

      Do you endorse this? Do you really agree that this kind of thing is the right way to ensure under-represented groups feel a sense of belonging?

      I also would be interested to know what Prof Harris feels about this and how this gels with his insistence that universities are bound by the Bakke decision. How is this kind of viewpoint discrimination in hiring consistent with Bakke in any way?


      1. mathematicswithoutapologies Post author

        I’ve written something here to the effect that the Bakke decision barred affirmative action for the purpose of reparative justice but allowed affirmative action for the sake of diversity. I’m in favor of reparative justice so it doesn’t bother me if Berkeley is not respecting the Bakke decision. It undoubtedly would bother Berkeley’s lawyers, however, and I assume they believe they are allowed to use diversity statements as in the example you cite.

        It had occurred to me that the UC diversity statements were a means of sneaking justice in under the court’s nose, but it seemed too risky to me. But I’m not qualified to second-guess Berkeley’s lawyers.

        I do hope that someone who signed Letter A will reply to your first question.


  3. Rachel

    First of all, I just found your blog and I’m really enjoying it! Although I left the world of pure math after my earning undergraduate degree, I find it really encouraging to see these conversations take place.
    Scott, regarding your point, I feel there are two very important bits of context that should be acknowledged whenever scientific differences between groups are being discussed. First of all, science is not as beautiful, pure, and objective as we’ve all been led to believe. There is a very long history of science being used to defend and support discriminatory beliefs. (Wikipedia has a gentle introduction to the topic here: And while all of the forms of science in the article have been discredited, they were accepted and validated in their time. I especially want to draw attention to the use of IQ tests to support racist beliefs ( I think it’s important to keep this history in mind whenever you’re discussing biological differences that may lead to demographic representational differences.
    Secondly, please consider that bias against racial minorities and women are very well documented in job applications and educational success overall. (See or These aspects have a much clearer connection to the representation of women and racial minorities in STEM. There are studies showing that girls tend to perform better with female teachers as opposed to male (, suggesting that male-dominated fields will self-reinforce the sex difference in performance. It also begs the question of what differences we may observe if academia as a whole had not been founded by and dominated by men, historically. There’s also ‘stereotype threat’, a well-documented phenomenon where simply asking people their sex or race before a test has a negative impact on their scores as they are reminded of stereotypes they are afraid of reinforcing (

    This got *way* longer than I meant it to. What I am trying to say is that it is impossible to measure differences in women’s and men’s abilities or skills or personalities impartially, because it is impossible to find test subjects free of the impact of culture. If we say that it is fair to hire less women if they perform worse, and they consistently perform worse because they are taught in an environment dominated by men, where is the fairness or justice?


    1. STEM Caveman


      A lot of studies on these topics, including some of the ones you cite, either:

      – have been hit hard by the replication crisis (stereotype threat is the poster child for this)

      – are mischaracterized in articles and Internet discussions, with the findings of the study often being 100% reversed in the retelling. It’s not uncommon for the *authors* of the study to mis-state or misunderstand their own findings. Relying on abstract, introduction and conclusions is not enough, one has to look at the quantitative sections and judge what they do and do not say.

      I read through the study on whether female teachers help girls (or hurt boys) and as far as I can tell the results are in the opposite direction of what you wrote. They had large sample sizes, on the order of 10000, tried many different specifications, but could not find any significant negative effect of female teachers on girls’ performance in math. They did find, consistently across specifications,

      – negative effects of female teachers on boys in math;
      – negative effects of female teachers on both boys *and girls* in math;
      – all these negative effects were statistically significant and larger than the non-significant (i.e., not distinguishable from zero despite large sample) positive effect of female teachers on girls’ math performance.

      This is interesting and counterintuitive. They used data from the 1980’s, and in those days, even more than today, one would have mathematically capable women to disproportionately end up as school math teacher (increasing the average ability of female math teachers relative to men), to be quite a bit less likely than men to discourage their female students from studying math, and better at the teacher-stuff that needs “oxytocin” as our host puts it (nurturing, empathizing, bonding, connecting). Yet the study found effects in the opposite direction, on a large sample.


      1. STEM Caveman

        >they could not find any significant negative effect of female teachers on girls’ performance in math.

        That should say they could not find a POSITIVE effect of same-sex teacher on girls.

        Independent of that study there does seem to be some benefit of single-sex classrooms, no matter the sex of the instructor. Though I have not read those studies carefully and maybe I am just another guy on the Internet repeating the conclusions because they fit my prior suspicions.


      2. mathematicswithoutapologies Post author

        To avoid confusion, I should explain that the “oxytocin” comment is the sort of thing I imagine people writing in the near future when they are looking for biological explanations for why women are (statistically) so much better than men at mathematics. I expect this will be an issue 20-30 years from now but if I am around to see it I will still be pointing out the misconceptions inherent in biological explanations.


      3. STEM Caveman

        Theoretically, the low representation of women (and other groups) in mathematics could already be a manifestation of higher ability. In this model, women with the relevant interests and abilities would tend to also have more of some mental capacity than men, such as intelligence or social understanding or maturity; or lack some negative capacities that afflict men, such as overconfidence or status-seeking). Because of these cognitive advantages the women (or blacks, etc) are likely to engage in a rational cost-benefit calculation whose conclusion is “don’t specialize in mathematics”.

        This would make not one bit of difference to the Bell Curve statistical phenomenon that would result. Women or other groups would be underrepresented in math, especially at the higher levels, not because they are not smart enough to succeed but because they are too smart to take the bait. As long as there is a systematic and hard to change difference, whether biological or not, then no amount of Diversity Statement filtering is going to alter the demographics of math PhD’s by very much nationally. It would temporarily diversitize the hiring at places like Berkeley, until other places start imposing the same requirement, at which point an extra layer of work would be added to the entire US academic hiring process, without changing the composition of the pool of candidates who apply, and with little effect on the hiring except to make it a lot more unpredictable.

        Many years ago I saw an old book (I wish I could remember the title), published in the first half of the 20th century, about all the different forms of black superiority that supposedly existed. It was written by an American Jewish couple, husband and wife, probably card-carrying Communists, and compiled a large amount of trivia and anecdotes resembling the later writings of Afrocentrists, only without the malice. The material was fun to read because of the shamelessly propagandistic and over-eager tabloid presentation, like Pravda presented as a comic book. The authors were, understandably and for good reasons, promoting the idea of a grand future with unlimited potential for African Americans, to counter the racist narratives of the day. I guess we can imagine a similar triumphal future for women in mathematics 30 years from now. But which way would you bet things will play out? It looks to me like there are a host of robust and interlocking indicators that at least in the case of women there is no reason to expect equal representation in mathematics except by forcing it on everyone, including the women.


      4. Another Michael

        Stemcave, the point about equity and participation in the mathematics profession continues to be that bias and discrimination are not hypothetical, but are actually experienced by real people. One or another cognitive hypothesis about the innate capabilities or predispositions of a group of people does not change the fact that actual people face identifiable barriers, from social expectation to mentoring bias to harassment or assault, based on their identities. You would do well to pay more attention to these kinds of real experiences instead of chasing the hypothetical characteristics of populations.
        Understanding and responding to these is a real skill that benefits the mathematics community and university departments. Don’t make diversity statements out to be something they’re not. The main purpose is right on the label: to identify skills and experience related to this aspect of professional work in mathematics.


  4. Scott James

    Dear Rachel,

    Thanks for the comment. I am familiar with the various biases you cite. I agree that they exist. In fact there are many other biases that exist that you haven’t mentioned. All of these might contribute in subtle ways to under-representation of women (as well as certain ethnic groups, nationalities etc.). I won’t mention these additional factors as I assume you are familiar with many of them.

    On the flipside, there is a lot of literature that suggests that much of social science is skewed because papers that support the dominant political ideology (in the social sciences and humanities) get much more likely to be published than opposing papers of similar rigour. So it is likely that the biases play less of a role than what many people think.

    However, I disagree with you here: “What I am trying to say is that it is impossible to measure differences in women’s and men’s abilities or skills or personalities impartially, because it is impossible to find test subjects free of the impact of culture.”

    What you are claiming would apply equally well to differences between individuals. That is, one might say “It is impossible to measure what part of the differences between individuals’ abilities or skills or personalities is genetic and what part is due to environmental factors, because it is impossible to find test subjects free of the impact of culture.” Right? Yet mankind, in its infinite ingenuity, has figured out a way to tease out the difference. This is via the separated identical twin studies. Identical twins share 100% of the genome. When raised separately (and often never having met each other), it is found that they are nonetheless incredibly similar in various traits, cognitive scores, life-choices, even political beliefs; far more similar than siblings raised together are. Using this, researchers have estimated that for most traits, over 50% of the difference is genetic. Isn’t this amazing? A great book for this is “Blueprint” by Robert Plomin.

    That’s what mankind does via science and mathematics. We make progress on difficult problems that might appear hopeless on first sight. One of Prof Harris’ works is his proof of Local Langlands for GL_n with Richard Taylor. Local Langlands is an incredibly amazing connection between two very different sets of objects. Yet we progress, we tease out the differences, we succeed in expanding our understanding.

    Currently, our knowledge of the cause of group differences (as opposed to individual differences) are limited because we do not have powerful tools like the separated twin studies. Yet I have no doubt that our knowledge will continue to progress. The available evidence *currently* suggests fairly strongly (but is by no means overwhelming yet!) that the sex-difference in STEM is partly to due to social factors and partly due to genetics, with both components playing a prominent role. As we learn more, the evidence towards what I just wrote might become overwhelming, or (unlikely, but it can happen!) it might flip and we might realize that genetics play little or no part (or for that matter, social factors play little or no part).

    My moral system is robust: I believe that we should treat individuals as individuals regardless of what the science says about group differences. On the other hand, if someone advocates for their particular version of fairness, justice and non-discrimination based on an unproven hypothesis that differences are largely or exclusively due to social factors, then their moral system will collapse like a house of cards if this hypothesis is shown to be false.

    Finally, I would like to make a proposal to you. Since none of this has probably changed your mind, I would like to suggest a book for you to read. (Books tend to go into these matters in more depth than a comment on a blog can.) In return I promise to read fully any book that you choose for me to read with an open mind, within the next 6 months.

    If you take up my offer, please let me know what you want me to read. The book I would suggest you to read is “The ape that understood the universe” by Steve Stewart-Williams. We could all learn more from each other!


  5. Another Michael

    Since this thread seems to have lost steam of its own accord, I will just offer two missing pieces for the sake of anyone who happens to encounter it later on.

    First, to MWA’s invitation for someone who signed letter A to comment on Scott’s question about the Berkeley Life Sciences searches, I can say (as such a signatory) that the use of diversity statements in that context seems to have been entirely proper and appropriate. If you read past the “viewpoint discrimination” bluster to the report Leiter & co cite, you will see that diversity statements were put at the center of a collection of searches specifically intended to hire faculty with skills and experience relevant to diversity, equity, and inclusion—areas identified by the hiring institution as priorities for faculty skills and experience, undoubtedly influenced by research and experience across American universities and in the UC system that these are valuable capabilities for faculty to have.

    Conducting a search that emphasizes evidence of the capacities prioritized for that search is not just acceptable, it’s the ordinary and responsible way to approach hiring. If the identified priority were calculus teaching or theoretical cosmology, one would hope and expect to see a comparable emphasis on evidence of those respective skills in teaching and research statements and other available materials, and it would not be “viewpoint discrimination” to ask for such evidence and evaluate it accordingly. These searches were moreover identified as part of a “pilot project” in recognition that the institution was still exploring the best way to achieve these goals, reflecting a laudable openness to try and evaluate efforts to reach institutional goals.

    Second, the other missing element in Scott’s call for open-minded exploration of the causes of existing disparities is the overwhelming body of evidence and research identifying and explaining the effects of bias, discrimination, harassment, inequality of opportunity, differential access to resources, and other barriers to full and equitable participation that arise both within universities and in wider societies. One does not need any hypotheses about cognitive difference to explain what we see in universities today, or to understand how explicit attention to these well-studied conditions may help improve matters. Moreover, what we know about these conditions also explains (a) why group-level cognitive difference is unlikely to be a major source of insight into existing disparaties and (b) how research that prioritizes cognitive difference hypotheses tends to reinforce some of the known harmful conditions.

    Scott, if you are sincere in wanting to read more about this, I suggest you start with the excellent recent wider-audience books by Angela Saini, *Inferior* (2017) and *Superior* (2019). These will introduce you to some of the research and perspectives that your posts here seem to be missing.


    1. Another Michael

      (Rachel, of course, has already pointed to some of the evidence and research from my second point here, though apparently Scott has not taken these to heart in their reply.)


    2. Scott

      To Another Michael,

      The first sentence of your penultimate paragraph does not contradict anything I wrote. (In fact, I explicitly wrote that biases exist). And the second sentence of that paragraph does not follow from the first. The fact that biases and barriers exist does not imply that other factors do not play a role. I am also puzzled by your phrase “One does not need..” You seem to believe that differences in personality, interests, and variability, (all of which are well-documented) should play a strictly second tier role, akin to some strange hypothesis that should not be called upon unless absolutely needed, while biases and social barriers should always be called upon first as a source of explanation. But you give no reason for this strange assymetry so I can only surmise that you prefer to only consider explanations that are ideologically palatable. Unfortunately, this is not the best way to pursue truth.

      I have read “Inferior”. It makes many good points but it certainly does not show that the causes you mention explain all or most differences in outcomes. It also does a strange dance of acknowledging certain innate differences but then spends much of the book pretending they don’t matter.

      I have not read “Superior”. But I recently read a review of it which (together with my experience with “Inferior”) did not really suggest to me that I would find anything new there.


      1. mathematicswithoutapologies Post author

        My opinion of Quillette, and of the people who publish there, should be clear from what I wrote in as well as in this post. Those texts also attempt to explain the persistence of attempts to ascribe existing power imbalances to biological factors. I will not rehash these arguments here, but I will just say once again that anyone who claims to know what “cognitive abilities” are relevant to success in mathematics should not be trusted.

        The good news is that a high level of oxytocin does seem to favor mathematical creativity. The mechanism is unclear, but how else to explain that the current international leaders in two central branches of mathematics are women with 5 and 6 children, respectively?


      2. mathematicswithoutapologies Post author

        STEM Caveman has replied with a comment that begins as follows:

        > MH: “oxytocin does seem to favor mathematical creativity. …. how else to explain that the current international leaders in two central branches of mathematics are women with 5 and 6 children, respectively?”

        The women you refer to have explained things in interviews. Both had the French childcare system. Both held positions with zero teaching requirements at CNRS, which allowed work at home. A…. So it may not be oxytocin so much as optimal living and working conditions for producing mathematics, well-chosen parents and good genetics. Do we only get to observe the effect of such benefits on women, or also men?

        The remainder of STEM Caveman’s comment consists of information that identifies the two women, including their names. This information is hardly secret but if I had wanted to name the women I would have done so.

        I certainly agree with STEM Caveman that the two women in question benefited enormously from the generosity of the French welfare state, as well as the priority given to support of basic research and the elitist public education system. The current French government is determined to temper this generosity, and if it succeeds I don’t expect French mathematics to retain its influence much longer.

        STEM Caveman’s allusion to “genetics” is code for the belief that mathematical talent inheres in the individual. The belief is admirably materialist but the causal chain leading from DNA to prestigious positions (and offers of prestigious positions that have been refused) is broken at so many points that it wouldn’t deserve mention even if its investigation served another function than to ratify the status quo.

        My oxytocin theory, on the other hand, though proposed with tongue in cheek, has the merit of being testable with a minimum of intervention. Give some men (or male mice or macaques) a dose of oxytocin, wheel them into the MRI, and watch their brains light up. Google finds the expression “nursing a hypothesis” on 18300 pages. This can’t be a coincidence.

        My apologies again to Caveman for censoring (his? her? their?) comment.


      3. Another Michael

        Hi Scott. I am fascinated by how you use “strange” in this comment, and I think it says a lot about what you take for granted. This is not the place to unpick the mistakes in your interpretation of my comment or in your inferences therefrom, and it is certainly not the place to offer a remedial education (in the best and most optimistic sense of the phrase) in the relevant areas of sociology, education, history, biology, statistics, and other fields related to the interests you have expressed here. However, if you let me know where you are based I would be happy to suggest some courses at a local educational institution to get you started.


  6. STEM Caveman

    The comment named several other relevant factors that your exemplars had in addition to childcare and non-teaching positions. Some were in their stars and some were in their selves.

    It is not particularly controversial that achievement in mathematics as in any other competitive area depends on a mixture of nature, nurture, opportunities, networking, fortune (in both senses), etc. Admitting that nature is part of the list, and a major part, does not make one a “materialist” any more than admitting that wealth, another very material thing, is part of the formula. The higher the level of achievement, the more factors are likely to have worked in favor of any particular individual and that is exactly what we see for apex achievements like “winner of top math prizes with an unusually high number of children”. DNA and well-chosen parents are among those factors. Check out the biographies of, say, Fields medalists to see how often the parents are mathematicians, STEM professors, professors, or have PhD’s.

    Finally, for a variety of reasons, it is not a good idea to disclose the exact details of even the most blatantly fake emails of your users on WordPress. It allows, among other security problems, spoofing of the user in various settings, or making the user (the real life person, not the online pseudonym) more identifiable to third parties if the same login was used elsewhere. It is not such a big deal in my case, I rotate the usernames and fake addresses over time and am not hiding in a cabin in Montana. But since you are so protective as to prevent published online information about famous people that you mentioned from entering the discussion, then it would be nice to not jump on your commenters in this way.



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