All we can do here is think critically about our personal lives, our culture, and the places where we live and work and consider how we might make them more equitable—from making meaningful efforts to hire, admit, or represent the historically underrepresented to establishing norms that ensure they can be heard and respected. (, The New Republic, July 6, 2020)
A few weeks ago I promised to continue the previous post, which described two alternative visions of antiracist mathematics, which can be described briefly, but in reverse order, as:
(b) “To change mathematics itself” — presumably including the content of mathematics, and not just racist practices and bad attitudes — “so that it actually serves Black and Indigenous communities” and at any rate does not “cause irreparable harm.”
(a) “Business as usual” as far as content is concerned, but with more Black people, along the lines suggested by John Rice in The Atlantic, which I quote again:
(1) acknowledging what constitutes thirddegree racism so there is no hiding behind a lack of understanding or fuzzy math, (2) committing to developing and executing diversity plans that meet a carefully considered and externally defined standard of rigor, and (3) delivering outcomes in which the people of color have the same opportunities to advance.
I’ve spent much of the last two weeks puzzling over what option (b) entails. Here I should acknowledge belatedly that the title of this threepart post was already used, before COVID, before George Floyd was murdered, by Tian An on the AMS inclusion/exclusion blog. The question in the middle of An’s essay
what kind of “pure” mathematics might be useful for antiracist mathematics?
bears on option (b) but only as interpreted by the word “useful”; it does not address the contents or the forms of reasoning or the underlying conceptual structures that compose what is currently understood as pure mathematics.
This is not the first time I’ve come up short when trying to imagine a thorough metaphysical transformation of algebra, or even the simpler task of replacing the standard introductory sequence in the training of a pure mathematician — abstract algebra, various kinds of analysis, differential geometry, topology — with something different. James Baldwin warns that the challenge is not to be taken lightly:
Any real change implies the breakup of the world as one has always known it, the loss of all that gave one an identity, the end of safety. And at such a moment, unable to see and not daring to imagine what the future will now bring forth, one clings to what one knew, or dreamed that one possessed. (James Baldwin, “Faulkner and Desegregation“)
At the height of the Science Wars authors called the very notion of scientific objectivity into question and treated it as a form of domination, a convenient alibi for racist, sexist, and neocolonialist power relations, or at the very least an unwarranted claim on university resources. Very few of these authors wrote about mathematics — this is probably why mathematicians’ memories of the Science Wars usually involve French philosophers. The main text of the time that dealt with mathematics is contained on pp. 4852 of Sandra Harding’s The Science Question in Feminism. The arguments are worth reading for their helpful reminder that the meanings of mathematics are not immutable. But they are of little help in imagining how one might “change mathematics itself,” and that’s because Harding was trained as an analytic philosopher, and as such is subject to the professional confusion between the mathematics practiced by mathematicians and the Mathematics that exists only as a topic for speculation by philosophers. So when she writes “no conceptual system can provide the justificatory grounds for itself,” she is denying the possibility of precisely one of the main kinds of Apologies that MWA dismisses as irrelevant to the concerns of practicing mathematicians (except, of course, during the brief period of the Foundations Crisis which is when analytic philosophy and mathematics last engaged in fruitful exchange).
The logic of that last sentence is rather convoluted, so if you read it quickly you probably missed the point. In fact, if you believe that mathematics has a special duty to justify itself then you disagree with the main thrust of MWA. This first epigraph to an influential text by Rochelle Gutiérrez, entitled Living Mathematx, is closer to the mark than the philosopher’s concern with “justificatory grounds”:
We need to be constantly considering the forms of mathematics and what they seek to deal with. As society presents new demands, new technologies, new possibilities, we must ask ourselves whether our current version of mathematics is adequate for dealing with the ignorance that we have.
The allusion to the “current version of mathematics” is a gesture (nearly 10 years old) in the direction of option (b). But the author of MWA is uncomfortable with the vision of mathematics as a shortorder cook to which “society presents… demands,” not least because “society” doesn’t speak with a single voice — chapter 10 of MWA invites readers to draw their own conclusions about the “demands” of funding agencies, for example. Anyway, once we have agreed that “society” is (among many other things) racist, or at least is not spontaneously and effectively antiracist, then we are entitled to treat its spontaneous “demands” with a good deal of caution.
I can tell I’m going to have to return to option (b) and its “demand” for a transformed mathematics, but if I continue to follow this particular stream of consciousness I’ll never get back to the dreary and dispiriting mechanics of the hiring process, which is what we’ll need to understand if we’re going to disregard Hazel B. Carby’s warning, in her chapter in the book Identity Politics in the Women’s Movement, about the “contradictory nature of the Black presence in the academy”:
Do existing power relations remain intact? Are the politics of difference effective in making visible women of color while rendering invisible the politics of exploitation?
and fall back on option (a). Anyway, maybe the creation of this Task Force by the AMS, whose stated goals are to

help the mathematical community understand the historical role of the AMS in racial discrimination; and

consider and recommend actions addressing the impact of discrimination and inequities to the AMS Council and Board of Trustees.
already counts as a step toward transforming mathematics as required by option (b).
The AMS will inevitably have its role to play in either option, because the composition of mathematics departments in North America will be mediated for the foreseeable future by MathJobs, the AMS website that provides a unifying structure for the job market. (In the absence of a social revolution, jobs will continue to be allocated by a market.) And I was planning to devote most of this post to an analysis of how using MathJobs may or (more likely) may not help mathematics become antiracist. But once again this post has gone on too long. So I will have to sign off before getting to the point; and I promise that I will not allow myself to be distracted in Part III from the discussion of option (a) and the hiring process.
This is an interesting issue i’ve thought about a bit. (I found this blog from your article in Science for the People , a group I had some interactions with of mixed quality (so i dropped out) when it was in ‘hiatis’ before this current revival; I was also on the Sftp list which had quite a few conspiracy theorists, etc on it . )
In college, I sort of wanted to do math —I was into theoretical biology (so E Fox Keller —mentioned in your SfTP aritcle —is a famous name in that field —the kellersegal model —though she dropped math after that. Interestingly in my math and biology courses none of these models were mentioned (eg the Turing model of morphogeneis, of which KellerSegal is a variant, nor Lotka Volterra equations of ecology (they may have been mentioned in an appplied math book. I was actually taking the course because they were required—and only got interested in math when i found J Theoretical biology in the library).
(Also, regarding your SfTP article, I am also familiar with the more recent issues about the person kicked out of Oxford–i think discussed by Noah Carl and others; and the ‘Sokal Squared’ hoax. Both of these have been recently discussed in medium —one by Massimo Puglicucii (a philosopher) . I sort of have tried off and on to write a more modern version of S J Gould’s mismeasure of man. His book hasn’t convinced most behavior geneticists, who still use the math methods of 2050 years ago. I don’ t really have the skills but i think there are more recent models based on nonlinear dynamics which are more applicable. Whether these are worth doing is an open question but the main point would be that what traditional behavior geneticsts view as closed cases (eg Ropbert Plomin, and related stuff by S Hsu) is not the only story or theory.)
Speaking of S Hsu –physicist at U Michigan who was recently releived of his deanship because he also does alot of iq/behavioral genetics research and has associqted with solme racist tperes—i think he is likely a top notch physicist but i also think his dabbling in the iq/genetics field really does approach scientific racism’ —his data anlyses may be correct, but his interpretation likely is not.
(Just because blacks are more represented in prisons in USA doesn’t mean they have a gene that leads them there—excpet maybe indirectly—melanain–but thats sturctural racism .)
Anyway Hsu asked if people good at math are also good at music—and he said he thinks so.
(I don’t). But I have wondered whether people who are good at math, are good at all kinds of it—algebra, geometry, nonlinear dynamics, physics, set theiory, comibinatorics,graph theiory, category theory, etc.
My view is ‘maybe not’. The same may be true of sports.
This may be one way ‘math can be racist’ , ‘sexist’, etc. People have different backgrounds and itnerests, so some kinds of problems appeal to them, and others don’t. They may work hard on and become good at problems that interest them, but less so at others.
Their different interests are likely mostly due to culture—just as with music. (Its possibly teaching classical music to someone raised on jazz, while possible, and not uncommon, often may not work—and a musical culture that uses one criteria for music or math, built up over decades, may exclude people not raised in that culture.)
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I think the ‘mainstream math world’ does have a sort of set of problems (and associated curricula) that interest them and which have devaloped over history, and primarily by white males occupation. So it may be the math problems that interest them are not found as interesting to people who are not in that dominant math culture.
(I know the kind of math, physics, biology, and mathematical social problems that interest me are not the kind most people find interesting— nor the kind you see discussed in most classes or journals. This is one reason I dropped out of formal programs.
(The dominant fields I was steered into in math biology was molecular biology/biotech/big data/drug development. I was interested in ecology, evolution, and social science, but I was basically in the wrong place for those .)
Its likely or possible that I really am only minimally competent at math (I know that is the case now—sort of forgot alot of it –and if you dont use it you lose it. (Nowadays i just try to look up answers in wikipedia. )
But i think its also possible that any abilities I had were stifled—itts like saying some wild animal is lazy or can’t really do any physical activity because it refuses to be a domesticated pack animal.
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The local public school system which i attended long ago as a white minority, and which is predominantly ‘people of color’ (when i went it was predominantly black, now it has many latinos) , is very poor functioning in math (and language). . So racism is always an issue—i think its mostly dealing with poverty and ‘culture’ (drugs, violence, bad diets, etc.) , racists would say its genes, and others say somehow the current math is ‘culturally biased’.
I partly agree that it may be culturally biased—but thats part of the environment.
People raised in different environments may not see the same patterns, nor find the same ones interesting. They also may not like the same music. (I grew up hating sports but loved hiking; in a sense the curricula was antinature people and hikers—we were supported to love sports.)
( For a slightly different ‘politically incorrect’ analogy , one could say or imagine current math is ‘melanin sensitive’—current equations like certain frequencies of light more than others, perhaps so they can retain their supremacy over other equations.
Other equations may prefer different amounts of melanin.
To attract more diversity, one needs to use for bait other kinds of equations.
(I wonder if there are any statistical differences between the choices for research topics by male versus female mathematicians, or black and white ones, or asians and others.
Do female mathematicians prefer pink equations, while males prefer blue ones?
Of course there may be a ‘leveling off affect—i.e. all professors of whatever background who are at an elite university will resemble each other more than they do the culture of their parents or grandparents whatever their socioeconiomic status. So thir preferences for pink and blue are the same, as for classical and hip hop for music.) .
(I like this reverse anthropogenic reasoning—i,e. people do not choose what equations, musics, paintings , or shapes they like—rather its the reverse.
The art and science that surive are the forms which are found to be most attractive to humans. So math and art ‘dress for success’.
Sort of like agricultural plants—eg corn and wheat spread because they noticed humans would eat them and plant more. So the corn and wheat chose humans over other snimals—a form of specieism.
I wonder if computer science may replace most math.
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