According to a new psychology paper, our political passions can even undermine our very basic reasoning skills. More specifically, the study finds that people who are otherwise very good at math may totally flunk a problem that they would otherwise probably be able to solve, simply because giving the right answer goes against their political beliefs.

I was reminded of it while reading the article “Does Diversity Trump Ability? An Example of the Misuse of Mathematics in the Social Sciences” in the Notices of the AMS. The author, Abigail Thompson, takes on a well known and widely cited paper:

“Diversity” has become an important concept in the modern university, affecting admissions, faculty hiring, and administrative appointments. In the paper “Groups of diverse problem solvers can outperform groups of high-ability problem solvers” [1], L. Hong and S. Page claim to prove that “To put it succinctly, diversity trumps ability.” We show that their arguments are fundamentally flawed.

Why should mathematicians care? Mathematicians have a responsibility to ensure that mathematics is not misused. The highly specialized language of mathematics can be used to obscure rather than reveal truth. It is easy to cross the line between analysis and advocacy when strongly held beliefs are in play. Attempts to find a mathematical justification for “diversity” as practiced in universities provide an instructive example of where that line has been crossed.

Thompson proceeds to shred both the “mathematical theorem” and the numerical examples from the Hong-Page paper. The actual paper is available here, and I have satisfied myself that Thompson is not unfair in her mathematical analysis. Her article, however, does not exist in a vacuum. It will be read in mathematics departments, organizations and committees where “diversity” is viewed as a bureaucratic imposition made on them by distant administrators who don’t understand research, even as their few women faculty often find themselves alienated and sidelined. That’s why I would like to add a few things.

First, there are many sound reasons for diversity that have nothing to do the article in question. (I will restrict this post to the benefits of diversity *per se*, independently of how that diversity was achieved. Affirmative action has its own reasons and will get its own post soon.) It should be common sense, not a mathematical theorem, that there are advantages in having a wider perspective and more than one problem-solving approach. Continue reading