The Accidental Mathematician

The 99th percentile


You might have heard of the recent study in Science that compared the performance of boys and girls on school math tests and concluded that there were no noticeable differences. The study generated plenty of headlines along the lines of “girls are as good at math as boys”. Inevitably, the ghost of Lawrence Summers’s notorious remarks on the cause of underrepresentation of women in science was summoned and exorcised. Heather Mac Donald at the City Journal takes issue with this, noticing that the study found twice as many boys as girls above the 99th percentile in 11th grade (hat tip to 3 Quarks Daily):

On the contrary, Science’s analysis of math test scores only confirms the hypothesis that cost Summers his Harvard post: that boys are found more often than girls at the outer reaches of the bell curve of abstract reasoning ability. If you’re hoping to land a job in Harvard’s math department, you’d better not show up with average math scores; in fact, you’d better present scores at the absolute top of the range.

Actually, hiring decisions at Harvard and other math departments are not based on “math scores”, but rather on proven research ability (and other factors that we won’t go into right now). Math professors don’t spend their days solving test problems. We engage in research, a complicated, messy creative activity where you can’t check the answer at the back of the textbook and your work is not graded on a scale from 0 to 100.

A successful career in research depends on many things, not just the raw problem-solving ability. There’s drive, motivation and independence. Creativity. Communication skills. Short-term and long-term strategic planning of a research program where, just like on the stock market, possible benefit is always associated with risk. A good taste – we’re often guided by the beauty and elegance of our theorems as much as by their utility. Entrepreneurial skills: soliciting funds, organizing research activities, managing a group of graduate students and junior personnel. Then there are less obvious but nonetheless important factors, such as Dr. James Austin’s “Chances I- IV” (the quote and further explanation can be found on Marc Andreessen’s blog).

[You] have to look carefully to find Chance IV for three reasons.

The first is that when it operates directly, it unfolds in an elliptical, unorthodox manner.

The second is that it often works indirectly.

The third is that some problems it may help solve are uncommonly difficult to understand because they have gone through a process of selection.

We must bear in mind that, by the time Chance IV finally occurs, the easy, more accessible problems will already have been solved earlier by conventional actions, conventional logic, or by the operations of the other forms of chance. What remains late in the game, then, is a tough core of complex, resistant problems. Such problems yield to none but an unusual approach…

[Chance IV involves] a kind of discrete behavioral performance focused in a highly specific manner. […]

Chance IV favors those with distinctive, if not eccentric hobbies, personal lifestyles, and motor behaviors.

We were talking about, what, exactly? High school standardized tests vs. aptitude for research? Yeah. Right.

Sure, a low SAT score in math suggests that you might not be a professional mathematician in the making. But I don’t see much difference, in terms of research potential, between a student who scored 99% on a high school test and one who scored “only” 95%. The former may have spent more time specifically preparing for the exam, the latter may have had a headache. So what? Both have met high enough standards to merit further consideration. I couldn’t find the full text of the Science article online, but this article reports that girls and boys were almost equally represented in the top 5%.

Which still does not either prove or disprove that girls and boys have the same potential for research in math or science. Or that we should be instituting hiring quota based on the gender breakdown among the top 5% of SAT scores. My point is, the Science study does disprove the popular widesweeping assertions about how girls are generally not as good at math as boys – but the only reliable way to determine your aptitude for research is by doing research (and I suppose that the same is true of other high-end careers in science).

Nor does it say anything about whether women in science departments face gender discrimination. The question there is: if we only consider the small (for whatever reasons) number of women with a proven research capacity who are pursuing an academic career, are those women treated, respected and promoted the same way as their male counterparts? You could bring that up with those undergraduates who insist on calling me “Miss”, as opposed to my male colleagues who are addressed as “Professor” or “Doctor”. You could read my earlier post on the subject. You could read this blog, especially entries like this one here.

It’s not a comfortable subject to talk about. One would have to mention specific people and incidents – people who are often adamant that they do not discriminate against anybody and may well be offended by the suggestion that, in fact, they do. It’s easier to discuss anonymous statistical data, to get into a pointless argument about what SAT scores imply about academic hiring. That, unfortunately, is not going to solve the problem.