Following up on Girls=Boys @ Math

The Economic Woman writes up an excellent post bringing up some important points in the recent University of Wisconsin study about the vanishing difference between women and men in math.

I’m not sure, personally, what to make of the difference at the 99th percentile, where the marginal effect in variance between men and women plays a significant role.  What professions need 99th percentile mathematical ability, and what does a “99th percentile mathematical ability” really mean?  As she points out, even economics PhDs rarely require 99th percentile mathematical ability.

I’ll point out, though, that the tests for mathematical ability are as much about mathematical knowledge as they are reasoning, at least the ones that they make you take for graduate school.  There is no definitive test that I’m aware of that tests your ability to reason mathematically without stressing knowledge over reasoning.  To my point, I scored “abysmally” on the math section of the GRE, reaching only the 86th percentile or so, which as far as PhD programs are concerned makes me something on par with a neanderthal.  However, the test asked nothing that happened to touch on my understanding of say, category or group theory or calculus based statistics, which I consider my expertises, and had it, my results would have been through the roof.

There are only a few researchers who practice in these particular fields, and the mathematical ability that even the Math GRE tests for and what is actually required of a practitioner are entirely different. It’s about intuitive grasp of inductive logic, the ability to fact check a proof, and the ability to construct larger proofs out of smaller ones, following a strand of math to a unique logical milestone, and recognizing the milestone when you get there.  No category theorist cares if you can take the square root of 26.4 in your head.  No statistics professor cares if you know before you take the class how to handle a tensor or matrix multiplication.

The professors are interested in how much effort it requires to teach you these skills, your learning curve on them, and what, in the end, is the potential for you doing something interesting and useful with them (with the word useful suitably redefined for application in math).

By way of conclusion, my opinion on the two conclusions of the paper is this.  In “math for life,” “math for professionals,” and “math for nearly all the sciences,” skills, women are entirely equal to men.  In the “mathematica mathematica gratia” (pardon my Latin, or correct it, one or the other) sense, which is useful in theoretical contexts, such as high-energy physics, pure mathematics, theoretical chemistry, and even certain engineering fields is where that variance comes into play.

However, importantly, I suspect that the tests given don’t accurately gauge math ability in the highest percentiles (this is often the case, actually, and usually not a problem), and the conclusions anti-feminists are drawing that men are more likely to be extraordinary in math are as spurious as any other conclusions based on exploring the variance at those high percentiles. To say that the variance is “significant” in statistical speak means only that it is not a discrepancy that can be explained by random chance, not that it is “significant” in any semantic sense.

I suspect, although this is mere hypothesis, that if a test were devised that accurately gauged mathematical ability at the highest levels of human mathematical ability, some kind of mental mathematical Olympian test, that there is no difference between the genders.