After many interruptions I finally finished reading all the comments on Piper Harron’s blog, especially the long exchange (62 comments) entitled “Why I do not talk about math.”  This extended dialogue is deeply educational, and not only for those interested in mathematics.  Repeatedly contributors attempt to demonstrate their good intentions in the name of an abstract universalism, and Harron replies, politely but firmly, pointing out how the form as well as the content of their intervention reflects a position of privilege that is not necessarily conscious.  The entire exchange serves to reinforce the point of Harron’s title, as I understand it, namely that the process of repeatedly pointing out the effect of what (in a different post) Harron calls “oppressive hierarchies” eventually becomes tiresome, if not oppressive.

Harron’s comments overlap with the subject of Chapter 2 of MWA, entitled “How I acquired charisma.”  The chapter is primarily an extended reflection on the hierarchical structure of contemporary mathematics, interspersed (for narrative purposes) with an ideal-typical Bildungsroman whose anti-hero — who for the sake of convenience was chosen to bear a strong resemblance to the author of the book —is conducted, through the apparently natural workings of this hierarchical structure, to a middle-management position (routinized charisma) within the hierarchy.  The original purpose of the chapter was not mainly to engage in social criticism — that’s the focus of (parts of) Chapters 9, 3, and 4 — but rather to formulate a philosophical thesis, a tentative answer to the question formulated by KD on Harron’s blog:

I have always wondered exactly who gets to decide what is “important” or “interesting.”

I take sociology to be the discipline whose role is to answer questions like this, to study how collective decisions by groups of human beings come to be construed as objective and natural, and the chapter has a number of references to the sociology of science, and a handful of references to the much smaller literature in sociology of mathematics.

KD’s question, however, is political rather than sociological, with the implication that those who “get to decide” are exercising power from which those who don’t “get to decide” are excluded.  In the context of Harron’s blog, it is understood that this exclusion is not legitimate — or rather, since legitimacy as such can only be determined within the social order, that the order itself deserves to be called into question; in other words, as Harron writes, “We Need a Revolution. Period.”

In a chapter of The Princeton Companion to Applied Mathematics entitled “Mediated Mathematics:  Representations of Mathematics in Popular Culture and Why These Matter,” Heather Mendick has written about how this exclusion is reflected in popular culture:

…popular culture can include some and exclude others.  For example, while society confers on all a responsibility to become mathematically literate, it suggests that only a special few possess mathematical “ability.”  It overwhelmingly depicts this ability as belonging in white, male, middle-class, heterosexual bodies.

Popular culture is not exactly a mirror of the reality of the profession, but it’s uncomfortably close.  Harron wrote an unconventional thesis in part because she sees this exclusion as rooted in the norms of contemporary mathematical practice; as she wrote

I just think our criteria for “new” “contributions” are seriously flawed and counterproductive and marginalizing. any mathematician who cares about “diversity” needs to be willing to shatter current paradigms.

I have been unhappy with the use of the word “diversity” in this context ever since I learned how it entered American jurisprudence in Christopher Newfield’s book Unmaking the Public University:

…in [Justice Lewis] Powell’s diversity framework, diversity was the expression of an institution’s freedom to choose particularly attractive individuals, and was about ensuring this freedom for powerful institutions like… Harvard College.…Diversity acquired social influence not as a moderate mode in which to pursue racial equality but as an alternative to that pursuit.

But Harron, whose blog is called The Liberated Mathematician, obviously doesn’t have Powell’s framework in mind when she uses the word diversity, so I will leave that discussion for later.  Instead I will engage in utopian speculation, in order to address what I see as the more subversive implications of Harron’s call for “power^people.”  Suppose one could magically do away with all the barriers to participation in mathematics of underrepresented populations, all the forms of exclusion, that are conventionally seen as political.  Would mathematics still be hierarchical?  And if so, would it still be oppressive?

A long tradition sees mathematics, and the sciences more generally, as necessarily hierarchical.  MWA quotes Max Weber on p. 10:

“Democracy should be used only where it is in place,” wrote Max Weber in the  1920s.  “Scientific training …is the affair of an intellectual aristocracy, and we  should not hide this from ourselves.”

And just last year, Alain Badiou wrote

The mathematical aristocracy at the creative level is… the most restrictive of all possible aristocracies.  (Badiou, Éloge des mathématiques, p. 23)

Chapter 2 of MWA exhibits the operations of hierarchy both symbolically (the IBM Men of Modern Mathematics poster, as well as Figures 2.1, 2.2, and 2.3) and materially (the role of the journal system in what Terry Tao called “certifying… significance” and “designation”, see p. 36).

Are these practices a relic of a more aristocratic period in the life of our species, and can we look forward to a future mathematics that is more inclusive, in the vision expressed by David Pimm and Nathalie Sinclair and quoted on p. 33 of MWA:

Asking “[I]n  what sense … can mathematics be considered a democratic regime…” open to all,  Pimm and Sinclair quote  … Henri Poincaré to the effect that “only  mathematicians are privy to the aesthetic sensibilities that enable” the decision of “what is worth studying.”  The article, published in a journal for educators, is  motivated by the “view that mathematics can do something for me in a  humanistic sense that repays the careful attention and deep engagement it may  require; one that may expose students to a fundamental sense and experience of  equality … and provide them with another sense of human commonality.”

Or is it the case, as Chapter 2 suggests, that “the content of mathematics is bound up … with a hierarchical charismatic structure”;  so that if Weber’s “intellectual aristocracy” lose control of the editorial boards of the “great journals” will mathematics be voided of its content and collapse into a sort of intellectual gray goo?

Philip Davis and Reuben Hersh, in The Mathematical Experience, famously claimed that “the typical working mathematician is a Platonist on weekdays and a formalist on Sundays.”  I would consider substituting “social constructivist” for “formalist” in that sentence; that would make clearer the unsettling radicalism implicit in Harron’s critique.  For my part, while my (routinized) charismatic bargain leaves me the freedom to be a social critic on the weekends, when I write things like this blog entry and Mathematics without Apologies, on weekdays I carry out my middle-level managerial tasks of maintaining the charismatic hierarchy — writing letters of recommendation, sitting on hiring committees, refereeing journal articles, all the “Traditional Rituals” (in the language of sociologist Bernard Gustin) without which the system would not be a system.  I’m a gatekeeper, in other words.  Not only that, I fulfill my functions with sincerity and commitment, and that should go without saying, otherwise my charisma would be unceremoniously withdrawn.

So am I contributing to the preservation of an oppressive system?  It’s easy to point to out that our professional autonomy is conditioned by one might call its limited sovereignty, the fact (but this is one of the themes of Chapter 3) that we are dependent on Powerful Beings for the external goods without which the profession ceases to exist.  The Elsevier boycott of 2012 brought home to me just how little leverage we have, as mathematicians, over the profession’s material conditions, even those one might expect to be most dependent on our charismatic consent.  Our professional associations enjoy a fair amount of moral authority but lack the personnel, the organizational structure, the money, and the executive power to put up substantial resistance to the Powerful Beings on whom we depend.  Rereading the comments on Piper Harron’s blog, it occurs to me that the people to whom they are addressed, namely her readers, are not in a position to do much of anything about the issues raised there, beyond trying to answer questions like the one in this post’s title.