Another Breakthrough in Feminist Mathematics

I have written many pieces over the years about the massive attempt to enroll more women in STEM fields, noting in one essay here that “Readers of the higher education press and literature may be forgiven for supposing that there is more research on why there are not more women in STEM fields than there is actual research in the STEM fields themselves.” Now comes a new book, Inventing the Mathematician: Gender, Race and Our Cultural Understanding of Mathematics (State University of New York Press), by Sara N. Hottinger, interim dean of arts and humanities and a professor of women’s and gender studies at Keene State College, suggesting that the problem may not be with women but with math.

In a revealing, just published interview with Hottinger, “Hidden Figures: Women’s studies meets mathematics in a new book arguing for a more inclusive cultural notion of numeracy,” Inside Higher Ed notes that her book’s “ultimate goal is to deconstruct our individual and cultural ideas about math — then build them back up again in a more inclusive fashion.”

Here are some highlights of that interview in which Prof. Hottinger mounts a vigorous challenge to conventional understandings of women and math. I have numbered these selected nuggets to facilitate later discussion of them.

  1. During my senior year of college, I did an independent study on psychoanalytic theorist and philosopher Jacques Lacan and ended up writing my final paper on the connections between mathematical topology and Lacanian theory. I wrote my women’s studies senior thesis on feminist pedagogies in the mathematics classroom and the ways in which feminist approaches to the teaching of math allowed marginalized students to understand and work with mathematical knowledge in innovative new ways.
  2. … the content of any science is profoundly constrained by the language within which its discourses are formulated; and mainstream Western physical science has, since Galileo, been formulated in the language of mathematics. But whose mathematics? The question is a fundamental one, for, as Aronowitz has observed, “neither logic nor mathematics escapes the ‘contamination’ of the social.” And as feminist thinkers have repeatedly pointed out, in the present culture this contamination is overwhelmingly capitalist, patriarchal and militaristic.
  3. I continued this work in my doctoral dissertation, where I made the epistemological argument that mathematical ways of knowing are shaped within communities…. And, now, in this book, I consider the cultural construction of mathematical subjectivity and argue that mathematics plays a significant role in the construction of normative Western subjectivity and in the constitution of the West itself.
  4. … recently, feminist and poststructuralist critiques have demystified the substantive content of mainstream Western scientific practice, revealing the ideology of domination concealed behind the façade of “objectivity.”
  5. In much the same way that feminist education scholars have shown, via discourse analysis, the incompatibility between femininity and mathematical achievement, both Walker and Stinson show the complex ways successful black mathematics students must accommodate, reconfigure or resist the discursive construction of a normative white, masculine mathematical subjectivity.
  6. The teaching of science and mathematics must be purged of its authoritarian and elitist characteristics, and the content of these subjects enriched by incorporating the insights of the feminist, queer, multiculturalist and ecological critiques.
  7. Because mathematics is understood to be the ultimate manifestation of the human ability to reason, mathematical achievement is a clear marker in the construction of an ideal subjectivity. If these multiple associations — between reason, masculinity, subjectivity and mathematics — are teased apart, we can better understand why mathematical subjectivity and the ability to succeed in mathematics is so difficult to achieve for those in marginalized groups. For example, if mathematical subjectivity and the ability to reason is constructed within Western culture as masculine, then women will continue to find it difficult to see themselves as mathematical subjects. Women will have to choose between being good mathematicians or being “proper” women.
  8. See Ginzberg (1989), Cope-Kasten (1989), Nye (1990) and Plumwood (1993b) for lucid feminist critiques of conventional (masculinist) mathematical logic.

I suspect Minding The Campus has few readers who will be persuaded by this deconstructionist argument. Indeed, many readers may find it disconcertingly familiar while others will suspect I’m perpetrating some sort of hoax.

Right on both counts!

Paragraphs 1, 3, 5, and 7 are, as I claimed, from Prof. Hottinger’s interview with Inside Higher Ed. But paragraphs 2, 4, 6, and 8 are quoted from NYU Physicist Alan Sokal’s famous 1996 hoax published in Social Text, “Transgressing the Boundaries: Transformative Hermeneutics of Quantum Gravity,” which claimed that “physical ‘reality’ … is at bottom a social and linguistic construct.”

Sokal’s “Ridicule Didn’t Work,” James Piereson and Naomi Schaefer Riley wrote recently in the Weekly Standard. “The trends that Sokal spoofed remain trendy in academic liberal arts. “‘You might have thought that humanities scholars, and particularly those working in subfields of cultural studies, would have been mortified with embarrassment, like a pretentious man who got caught mistaking his son’s finger-paintings for Jackson Pollock originals,’ says intellectual historian Wilfred McClay. ‘But they weren’t much embarrassed, and those fields have not suffered noticeably.’” In fact, their influence is even greater than before, “because highly ideological fields such as gender and race studies have broken out of the academic hothouse and into the mainstream of American life and politics.”

Thus what Sokal spoofed remains true of much of contemporary social science, especially cultural studies attempting to deconstruct, reconstruct, or otherwise transform our understanding or race, gender, sex, etc.: it’s often hard to tell the parodies from the real thing.

12 thoughts on “Another Breakthrough in Feminist Mathematics”

  1. Having read the interview, I think Rosenberg’s characterization of Hottinger’s position, and comparing it with the Sokol hoax, is unfair. Her goal is to change mathematical pedagogy (not the practice of mathematics) to avoid alienating potential women and minority mathematicians. This is laudable. If the way mathematics is currently taught does discourage minority and women students, it seems reasonable to try and address this problem while maintaining rigorous mathematical standards.

  2. Ha ha! I liked how you snuck in Alan Sokal’s prank. How funny and original. Let me try this game, too, by quoting some other nonsense:

    1. In all other cases treated previously… one has been able to define them only relative to a given language, and for each individual language it is clear that the one thus obtained is not the one looked for.

    2. Even elementary mathematics contains , first, formulas to which correspond contextual communications of finitely propositions… and which we may call the real propositions of the theory, and, second, formulas that… in themselves mean nothing but are merely things that are governed by our rules and must be regarded as the ideal objects of the theory.

    3. The fundamental idea of my proof theory is none other than to describe the activity of our understanding, to make a protocol of the rules according to which our thinking actually proceeds.

    4. a purely logistic view of mathematics was inadequate; … mathematical propositions possessed a variety of interpretations, of which the logistic was merely one.

    5. It would not be advisable to let the reform take the form of a cast-iron logical system into which all the mathematics of the future are to be expressed. No democratic mathematical community would stand for such an idea, nor would it be desirable. … it is not desirable to try and put mathematics into the straight-jacket of a logical system

    1 is a quote from Kurt Gödel. 2 and 3 are by David Hilbert, and 4 and 5 are by Alan Turing, all morons who thought that mathematics is founded on human practice and language.

  3. What’s particularly amusing to me about the failure of Sokal’s hoax is that Sokal is an outright Marxist who felt this crap undermined the great undertaking.

    He didn’t notice the failure of Marxism any more than his targets noticed the failure of deconstructionism.

    When I realized Sokal’s goals, I had a very hearty laugh.

  4. I’d love to see some examples of this new feminist mathematics. Then I would suggest that feminists use only stuff built according to their new discipline, while they should avoid those bad products created following the evil constructs of capitalist mathematics.

  5. It is an established fact that the number 11 is a sexist construct imposed upon disenfranchised members of the minority community by misogynistic xenophobes. Ditto number 37, and of course, 143.

  6. You — and, a fortiori, Dean[!?] Hottinger — should give a nod to Eugene Wigner’s “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”

    Until a feminist “mathematician” demonstrates that feminist “mathematics” is at least as effective as “normative white, masculine” mathematics, I doubt any mathematician, scientist, or engineer will pay any attention to it — except, of course, as another demonstration of the fundamental silliness that defines the humanities today.

  7. The funniest part of this is that the paragraphs taken from Sokal’s parody seem less absurd on their face (and less reliant on silly academic buzzwords) than the paragraphs that were written seriously.

  8. Mr. Rosenberg’s argument — if we can call it that — is impossible to follow as he continues to insist on using both 1) ‘words’ as they are traditionally, oppressively & artificially constrained by historically colonialist, hegemonic patriarchal, so-called ‘dictionaries’… and 2) Unreconstructed Aristotlean UnQueered, Syllogistic, so-called ‘reasoning’ to link those ‘words’ together into some sort of linear patterning which refuses to acknowledge the debt owed to what we now know is nothing more or less than Intersectional Victim Circus Circle Dancing.

    ‘Nuff said; must go visit my Safe Space!

  9. I’ll believe in “feminist mathematics” when you can design an aircraft or a spacecraft using them. And, it has to be a BETTER aircraft or spacecraft than one designed using “patriarchal” mathematics.

    Because ENGINEERING doesn’t care about masculine or feminine. Engineering only cares that the bridges and buildings and aircraft don’t fall down.

  10. The first thing to know about trans identity, like all identities, is that it is a social artifact.

    Your identity and self-image is but a reflection of what society thinks about you. This is especially true of feminine and black identity.

    Obama, in “Dreams from My Father,” goes into this at length. He recognized that black self hate is but a reflection of what society thinks about blacks. He began to doubt the effectiveness of focusing on black self esteem as a basis is for political action.

    Racism is built into the culture. We are all racists and sexists. We can’t help it.

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