G.H. Hardy and Mrs. Ellis

David, by Michelangelo. Image: Wikimedia
David, by Michelangelo. Image: Wikimedia

If you haven’t yet read this classic essay by Linda Nochlin on the question of why there have been no great women artists, I recommend it very highly. The essay is from 1971, but Nochlin’s points remain very much relevant to today’s arguments about why there have been so few great women philosophers, or mathematicians, or whatever.

Nochlin starts out by questioning the common notion of a “great artist” as a singularity that exists independently of society and history. The truth is, it takes at least a village. Great artists are enabled by the society they live in, draw on its artistic traditions, engage in a dialogue with other practitioners. Indeed, if artistic greatness depended only on innate talent, it would be very difficult to explain what Nochlin calls “conditions generally productive of great art,” such as must have existed, for instance, in the 15th century Florence and Rome, or in France in the second half of the 19th century. (We’ll note here that much of the same can be said of mathematics.)

The society also establishes standards for what qualifies as “great art,” and what does not. In the pre-impressionist Europe, historical painting– understood broadly so as to include biblical scenes, Greek and Roman mythology– was considered the highest and most prestigious form of art. Landscapes, still-lifes, portraits, and other suchlike were deemed less worthy. To wit:

Until the 20th century, Mona Lisa was one among many and not the “most famous painting” in the world as it is termed today. Among works in the Louvre, in 1852 its market value was 90,000 francs compared to works by Raphael valued at up to 600,000 francs.

“Great art,” going back to ancient Greece and Rome and then again starting with Renaissance, more often than not depicted naked and partially naked human bodies. Think Michelangelo, Raphael, Titian, Botticelli, Rubens. Even when the figures are clothed, the paintings still display a thorough knowledge of human anatomy. Such knowledge was usually gained through extensive study of the nude model, a practice that continues to be a mainstay of art programs. And yet, as Nochlin explains in detail, nude models (both male and female) were forbidden to women painters before the end of the 19th century. That right there explains completely why there has been no female Michelangelo or Raphael.

Nochlin cites many other ways in which the society refused to enable women artists: the apprenticeship system, access to academic educational institutions such as the Ecole des Beaux-Arts, opportunities to establish suitable relationships with art patrons, and more.

But the part I want to highlight here is the prevailing attitude to “the lady’s accomplishment”:

In contrast to the single-mindedness and commitment demanded of a chef d’ecole, we might set the image of the “lady painter” established by 19th century etiquette books and reinforced in the literature of the times. It is precisely the insistence upon a modest, proficient, self demeaning level of amateurism as a “suitable accomplishment” for the well brought up young woman, who naturally would want to direct her major attention to the welfare of others–family and husband–that militated, and still militates, against any real accomplishment on the part of women. It is this emphasis which transforms serious commitment to frivolous self-indulgence, busy work, or occupational therapy, and today, more than ever, in suburban bastions of the feminine mystique, tends to distort the whole notion of what art is and what kind of social role it plays.

In Mrs. Ellis’s widely read The Family Monitor and Domestic Guide published before the middle of the 19th century, a book of advice popular both in the United States and in England, women were warned against the snare of trying too hard to excel in any one thing:

“It must not be supposed that the writer is one who would advocate, as essential to woman, any very extraordinary degree of intellectual attainment, especially if confined to one particular branch of study. ‘I should like to excel in something’ is a frequent and, to some extent, laudable expression; but in what does it originate, and to what does it tend? To be able to do a great many things tolerably well, is of infinitely more value to a woman, than to be able to excel in any one. By the former, she may render herself generally useful; by the latter she may dazzle for an hour. By being apt, and tolerably well skilled in everything, she may fall into any situation in life with dignity and ease–by devoting her time to excellence in one, she may remain incapable of every other.”

Which of course brings to mind this famous quote from G.H. Hardy:

… it is undeniable that a gift for mathematics is one of the most specialized talents, and that mathematicians as a class are not particularly distinguished for general ability or versatility. If a man is in any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that he would be silly if he surrendered any decent opportunity of exercising his one talent in order to do undistinguished work in other fields. Such a sacrifice could be justified only by economic necessity or age. […]

It is very hard to find an instance of a first-rate mathematician who has abandoned mathematics and attained first-rate distinction in any other field. There may have been young men who would have been first-rate mathematician if they had stuck in mathematics, but I have never heard of a really plausible example. And all this is fully borne out by my very own limited experience. Every young mathematician of real talent whom I have known has been faithful to mathematics, and not from lack of ambition but from abundance of it; they have all recognized that there, if anywhere, lay the road to a life of any distinction.

And Paul Halmos:

What does it take to be [a mathematician]? I think I know the answer: you have to be born right, you must continually strive to become perfect, you must love mathematics more than anything else, you must work at it hard and without stop, and you must never give up.

I’d like to show these quotes, together, to everyone who professes the theory of “greater male variability”:

It does appear that on many, many different human attributes-height, weight, propensity for criminality, overall IQ, mathematical ability, scientific ability-there is relatively clear evidence that whatever the difference in means-which can be debated-there is a difference in the standard deviation, and variability of a male and a female population. And that is true with respect to attributes that are and are not plausibly, culturally determined. If one supposes, as I think is reasonable, that if one is talking about physicists at a top twenty-five research university, one is not talking about people who are two standard deviations above the mean. And perhaps it’s not even talking about somebody who is three standard deviations above the mean. But it’s talking about people who are three and a half, four standard deviations above the mean in the one in 5,000, one in 10,000 class. Even small differences in the standard deviation will translate into very large differences in the available pool substantially out.

From my professional point of view as a mathematician, here’s how I see this argument. Take a fluid, complex, multidimensional quality such as “math skills.” (Or such as “propensity for criminality,” for that matter.) Assume that this quality can be uniquely quantified, on some scale that covers all types and ranges of “math ability.” Assume further that the resulting distribution is described by a bell curve, because why not. Condition on events of probability practically zero, assume that the same generic, first-approximation model is still accurate on a scale and in a range where it was never meant to be applied, and draw your conclusions about women faculty at R1 universities. It’s not even clear to me that there’s anything here that could be defended. Should you nonetheless feel like reading another rebuttal, this one cites a few studies that refute the hypothesis.

But G.H. Hardy and Mrs. Ellis should also be a part of this discourse, as their writing goes a long way towards explaining why we find the Greater Male Variability theory so intuitive and appealing. The theory “looks right” and “makes sense” to us for the reason that it matches deeply ingrained behaviour standards and stereotypes, the same ones that Hardy and Mrs. Ellis articulate so well. We’ve lived for centuries in a culture that has discouraged women from focused achievement–and by “discouraged” I mean “actively prevented”–directing them towards unassuming mediocrity instead. We’ve lived in a culture that has propagated the stereotype of a woman as an all-round dilettante, while encouraging men possessed of any discernible talent to pursue it to distinction.

These cliches are not even close to dead. Excessive achievement is still often considered “unladylike.” The single-minded focus described by Hardy is still discouraged in women, and rarely available to them in any case.* Our society still disparages the actual existing achievements of women so as to better fit the narrative. More insidiously, we’re confusing nurture for nature. If Mrs. Ellis could have her way with bell curves for women, I assume we’d be talking about very small deviations indeed. The apparent smaller female variability is very easily explained when one considers that those women whose class and financial status might have allowed opportunities for intellectual or artistic achievement, were also the most prone to being brought up according to Mrs. Ellis’s strict standards. Instead, we’re ascribing it to genetics, evolution and essence.

To paraphrase Neil DeGrasse Tyson: if we lived in some other world where G.H. Hardy and Mrs. Ellis have never existed, I’d be very happy to have a conversation about genetic differences and greater male variability. But not here.


*It’s not just family obligations. It’s also that our jobs have extra components that are not required of men, from special feminine negotiating skills, to learning to manage the masculine traits of ambition and competence and compensating for them with “feminine” qualities, to the special attention we must pay to our appearance. Take your pick.

Author: Izabella Laba

Mathematics professor at UBC. My opinions are, obviously, my own.

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