We have absolutely no time for this, but we feel obligated to write something. In their latest issue, the journal Nature – yes, that Nature – has a double-banger contribution to the “decolonization of mathematics”. To begin, there is an unsigned editorial, Why we have nothing to fear from the decolonization of mathematics. Then, the main event is a long article by “math and science writer“, Rachel Crowell, Charting a course to make maths truly universal. Both pieces are, of course, ridiculous.
We’ve been here before, and we’ll be here plenty in the future. These freak arguments are breeding in universities, and too few academics are willing to poke their heads above the parapet to object. A couple months ago, we wrote about the UK’s Quality Assurance Agency, and their hamfisted plans for “equality, diversity, accessibility and inclusion”, and “decolonisation”, of mathematics. Nature‘s current offering is a very similar mix of absurdity and poison.
We’ll try to be brief. The Why Evolution is True guy has written the obvious in some detail, making for a very good critique of Nature‘s nonsense. There are a few aspects, however, that are so bad, and so annoying, they are worth re-hammering.
The editorial begins,
What’s the point of decolonizing mathematics?
Very good question, and of course the answer depends upon what one means by “decolonizing”. For the editorialists, decolonizing mathematics is presented as little more than throwing in a little history. The editorial notes the Arabic origins of algebra, Hindu-Arabic numerals, and the like, and contains little else of substance. The penultimate line of the editorial is,
So, to answer the question: what’s the point of decolonizing mathematics? It is so we can get a more accurate picture of the subject’s origins and development, and the variety of problems it helps to solve.
As if we white guy lecturers had never thought of including such colour in our lectures. As if it wasn’t by now entirely standard to reflect upon and to teach the multicultural origins of modern mathematics.
It is difficult to find anyone who objects to such history in mathematics subjects. Different lecturers may consider it more or less valuable in this or that undergrad subject, for all manner of valid reasons. But if there is any maths lecturer hostile to the idea of spending at least a little precious lecture time on humanising their subject, or is unappreciative of the fuzzy and complicated origins of most mathematics, we haven’t met them.
There is plenty of sting, however, in the editorial’s tail:
such questions [of decolonising mathematics] reprise aspects of an older, more academically focused debate on whether — or to what extent — scientific knowledge is socially constructed.
Huh?
The editorial’s “case in point” is algebra. Since Arabic algebra was rhetorical rather than symbolic, and was more geometric, and was focussed upon the solving of practical problems, this somehow proves algebra is a social construct.
This is absurd. Yes, Arabic algebra looked different. But the idea that it wasn’t the same basic stuff, quadratics and cubics and so forth, solved in fundamentally the same ways, is nonsense. Different civilisations did different mathematics, expressed very differently, for differing purposes and to very very differing degrees. But what they did, or didn’t do, is the same basic stuff. Mathematics is not a social construct. It is weird that it is not, but it is not.
The editorialists want this “social construct” thing, however, so they can pretend that mathematics is the contribution of many cultures much more than it is:
Decolonizing science is the antidote to exceptionalism, the idea that any single culture or civilization possessed special abilities in advancing science.
Well, we were talking about mathematics rather than science, but whatever. They’re still wrong. The word “abilities” is loaded, and “single culture or civilization” is a straw man, or straw person, or something. But for various reasons, some obvious and some mysterious, certain civilisations produced way, way more mathematics than others. The Babylonians did quadratics. The Arabs did quadratics. Indigenous Australians did not do quadratics. No social construction framing is going to change that.
The editorial ends by denying, hand on heart, that the decolonisation push could be in any sense a political exercise. They give the “last words” to the editors of Nature’s special issue on racism:
These are not political or ideological acts, but part of science itself — an example of science’s self-correcting mechanism in the pursuit of truth.
Those aren’t quite the last words. The very last word is “bullshit”.
Now to Crowell and the main event. This part will be brief, since Crowell writes almost nothing of substance on decolonisation. She writes plenty on good people doing good work in reaching students from poorer backgrounds and minority groups. She writes in depth about mathematician Edward Doolittle, who distinguishes “Indigenous mathematics” from “indigenizing mathematics”: the latter involves selecting examples from given cultures to be discussed in a standard mathematics subject, and the former involves “getting inside a culture and examining the mathematical thinking in it”. Sure, if there is sufficient mathematical thinking there to be examined, and if that’s what interests you and/or your students, go for it. Will that give your students a better training in mathematics? Maybe, maybe not. But, unless you prove it does, why should anybody else much care?
Beyond this, Crowell has some amazing lines. To begin,
Maths is built on a modern history of elevating the achievements of one group of people: white men. …
No. Modern maths, well into the 20th century was, by and large, the achievement of white men. It is what it is.
This means that the accomplishments of people of other genders and races have often been pushed aside, preventing maths from being a level playing field.
How many “other genders” are we talking about here? If you’re claiming it’s more than one, you need to bone up on your maths.
Crowell mentions a few mathematicians, seeming to claim, without evidence, that they have been “pushed aside”, and that they are somehow comparable to Cantor and Gauss and Poincaré. It is no reflection on the fine mathematicians she names, but this is embarrassing.
As to the difficulties of decolonisation, Crowell writes,
Sometimes it’s even challenging for mathematicians and other researchers to imagine how to decolonize a quantitative subject such as maths, because they’re not used to identifying how their curriculum might be affected by colonialist or racist mindsets.
Crowell provides no examples or evidence for such colonialist and racist mindsets, nor how they affect any curriculum.
Finally, hilariously, Crowell quotes John Parker, head of mathematical sciences at Durham University, on the awkward start to Durham’s decolonisation program, largely authored by a white guy. This and other aspects were criticised, and Durham responded:
Durham’s senior mathematicians felt that their curriculum-reform process had to be led by the students, because otherwise “we’re in the awful situation of deciding for ourselves what’s best for them”, Crossman says. That, Parker adds, would be at odds with the concept of decolonization, because colonization “was some group of people thinking they knew best for some other group of people”.
Yep, there are foolish teachers out there who somehow imagine they might know what’s best for their students. And such foolish practice is obviously comparable to colonisation.
The willingness of so many properly smart academics to put aside their critical faculties, to buy so completely into this nonsense, is as clear a sign as any of the insanity of our times.
What’s the point of decolonising mathematics indeed. I’ve wondered why it’s specifically mathematics (a universal subject if there is one, and one that can be so abstract as to be totally divorced from any human concerns like power relations) that is taken by these people to be steeped with inequity, and not any other subject. I believe it might be because mathematics is taken as a metonimy for “quantitative thinking” as a whole. (And also it is one of the few quantitative subjects taught in school, and with the emphasis some educationalists place on “STEM” teaching as part of mathematics education, it becomes even more the representative of quantitative reasoning and “white man science”.) So in the mind of these people, what, for example, allowed the US army to drop napalm over Vietnam? Math. Math did it. (Though we should also point out that this is not new; some mid-20th century mathematicians were adamant that their discoveries ought not to be applied, which in their mind definitely meant “ought not to be applied to military science”.
Hi Marty. Good work on the Nature things. It is amazing to me that Nature and Scientific America should both publish embarrassing rubbish these days. It’s remarkable that the Nature editors should extol a practice that has been virtually universal in Maths departments over the last three decades, since the appearance of the MacTutor History of Mathematics website. Perhaps their next editorial will tell us about this exiting new thing called the internet and tell us it’s our moral responsibility to use it?
Decolonizing maths seems like quite an industry these days, but I have yet to read anything vaguely substantive or interesting. Perhaps I am reading in the wrong places? Some authors simple argue that we just need to broaden what we mean by mathematics. This approach is evident in the “dance is mathematics too” idiotic nonsense. I don’t know how people can get funded to propagate such air-head notions, but there’s money in them-there-hills. Another approach I’ve seen is to just deny the importance of formal mathematics. There is a book “Decolonizing The Mind” by Sandew Hira that appeared this year which has a chapter of decolonizing mathematics (but be careful, there is more than one book with this title!). I haven’t seen this book, but I’ve seen talks by the author on-line. One of his “arguments” is that formal mathematics with axioms and definitions “creates phantasies” and “leads to invalid knowledge”. To prove this he gives a very short argument using high-school algebra (that any half-decent student could see through and involves dividing by zero!) concluding that 1=2. Anyway, snake oil salesmen aside, I do notice that there is to be a very high profile program later this year at Edinburgh’s International Centre for Mathematical Sciences (ICMS), entitled “Mathematics for Humanity”. The Scientific Committee for the program includes Terry Tao, John Baez and Nalini Joshi. The program has three themes, one being “Global history of mathematics”, which has a description that is critical of the current discipline of history of mathematics, seeming to claim that it has “contributed to alienating the majority of humanity from a sense of ownership of the mathematical tradition, thereby hindering education, scientific development, and international collaboration”. People are often naturally interested in the fact that ideas and results have occasionally appeared in different parts of the world, sometime even almost simultaneously, and sometimes very far apart in time, like Gaussian elimination. These things have been studied with enthusiasm in recent decades. It would be embarrassing if this program failed to produce something new of substance that matches its implicit damning criticism of an entire academic disciple. However, I notice that the ICMS advertisement for the program refers to “knowledge-driven #Activism”, so I fear it may just be responding to popular demand, which makes me skeptical about its outcomes.
Oh, God. Thanks Grant, sort of. I thought I was done with this nonsense, at least for now. But now I guess gotta go look at Hira and ICMS.
These people are clearly well-intentioned, and they’re definitely not stupid, at least not all of them. But they seem utterly incapable of being critical and honest about this stuff. The political agenda trumps sense.
This is a side note of a side note, but something I’m a little irked by: in your post above, you seem to say that there are only two genders. This seems to believe-away the existence of non-binary people. Was this deliberate?
Yes.
The claim that there are only two genders is factually incorrect without further qualification. The usual use of the word “gender” in modern-day academic literature refers to either gender role (i.e. social roles generally based upon biological sex) or gender identity (i.e. personal identification of one’s gender). Certainly there are societies with more than two gender roles (e.g. hijras in India, the Māhū in Hawaii), and certainly there exist people who personally identify as non-binary. While many Western cultures generally have a gender binary, even this is changing now in some places, with some countries (Australia included) even legally recognising third/non-binary genders in passports.
So there are certainly more than two genders, unless you add some additional qualifications such as “considering only gender roles in traditional Western cultures”. The articles are horseshit elsewhere, but the mere implication that “more than two genders exist” is not.
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In principle, I’m not against “decolonising mathematics” (or specifically, “decolonising the teaching of mathematics”, which is what these articles seem to really be about) if it’s done with proper consideration. The way history has panned out such that white men have made so many of the important higher-level discoveries is a terrible consequence of colonialism and sexism in the past, and I think it’s important to at least acknowledge and/or mitigate that during teaching. Curricula should be more diverse when possible, as long as this does not come at the expense of teaching more-impactful mathematical discoveries or more-efficient methods.
The real problem with that quoted statement, as you have rightly pointed out, is that at the university level in many modern branches of mathematics, there are considerably fewer accomplishments by non-[white men] of a similarly-revolutionary calibre to mention. This makes it difficult to actually find good changes that can be made in the first place, at least at the university level.
The least-objectionable changes would be to update the curriculum for historical accuracy; e.g. teaching that Pythagoras’ Theorem was independently discovered by many civilisations, or giving due credit to the Hindi mathematicians such as Bhaskara II who first solved Pell’s Equation hundreds of years before Fermat. Other very reasonable changes might be to include relevant examples from non-Western contexts, say, such as the classic “rice on a chessboard” to introduce the topic of exponential growth.
But I don’t think I’ve seen a single article on this topic properly lay out how a full curriculum should be changed, to the same amount of detail as a full curriculum. The people writing these articles should propose such a thing in detail (likely for a national curriculum at primary or secondary level, since I suspect that’s where the most reasonable changes can be made); only then is there anything concrete to actually discuss on its merits. Until then, we’re arguing at ghosts.
Well, I trolled myself, so I had it coming.
Thanks, edderiofer. I’ll reply in two parts. First, on the gender stuff.
The fact that a concept is generally accepted in modern academic literature hardly guarantees that the concept is clear or consistent, or that the concept reflects, much less clarifies, reality.
One aspect of the modern academic literature is the (reasonable) rejection of the opposition between nature and culture. I’m not convinced, however, that this rejection has been properly weighed, for what it ultimately means for the distinction between sex and gender. I’m far from convinced that the concept of gender would survive a proper critique.
Obviously, these questions are too complicated to resolve here. Decolonisation is more than enough work.
Thanks again, edderiofer.
I agree, that in terms of solid curriculum content there seems little substantial from the decolonisers to critique. Beyond that, however, I think you’re buying too much into their shtick, and I think you’re not acknowledging their bait and switch.
First, I think you’re way overstating the need that maths education “should be more diverse”. What does “diverse” mean? History is good, and historical accuracy is important, and that will naturally lend itself to the appreciation of various cultures’ contributions (while being totally silent about other cultures). But diversity as a goal is silly, and distracting.
I’m not a “Just the facts, ma’am” kind of guy. I like humanising the subject. I like talking about the surprising and nutty history of mathematics, and that Pascal’s triangle is really Chinese, and so on. But these are maths subjects. History is not close to the main game, and “diversity” should not be the game at all.
Secondly, you seem to be swallowing Nature’s editorial bait, that decolonisation is essentially about historical accuracy, about acknowledging the contributions of various cultures. But that is clearly not what decolonisation is fundamentally about. Decolonisation has a strong, and pretty nasty, political agenda, and its advocates are willing and happy to undermine the notion of mathematics in order to serve that agenda.
> Decolonisation has a strong, and pretty nasty, political agenda, and its advocates are willing and happy to undermine the notion of mathematics in order to serve that agenda.
What is that “nasty agenda”, and in how far is the notion of mathematics being undermined?
Thanks, Denny. I’m not sure I understand your question(s). I’ll try to answer.
I thought the Nature editorial was intellectually dishonest, and clearly, sneakily, intending to undermine the universality of mathematics. It was also straight-out denying the political agenda of decolonisation, which, whatever the worth of that agenda, is simply absurd. I thought the language in Crowell’s article was accusatory, implicitly but clearly enough suggesting those not on board with decolonisation were happy to continue a tradition of racism and colonialism. I felt the exact same way about QAA, where what mattered critically in mentioning a mathematician is whether they were a nazi, or were nice to their cats or whatever. it is fundamentally about judging the Goodness of people, which can easily turn any subject, or any article, or anything, into a purity test or a loyalty test. Seems nasty to me.
Far from being “socially constructed” mathematics is pushed forward by thinkers who are often far ahead of most of their peers. It advances under one-of-a-kind flashes of insight by pioneers, not a blind mob deliberating on each others’ belly-buttons until consensus is arrived upon.
Algebra is an excellent example of this. The development of the complex numbers. Archimedes. Aritosthenes. Hypatia. Einstein (well ok that’s mathematical physics). Ramanujan. Andrew Weil. The calculus (in this case TWO great thinkers more-or-less simultaneously but isolated from each other in different countries, during a pandemic, no less, which gave them time to be by themselves and to meditate at length. “socially constructed” my eye.
I’m a lazy publisher and have done a good 10 years of work on a subject in a corner of math nobody else is working on. I’ve shown glimpses in talks at a few conferences. Maybe it’ll be regarded as an advance after it is all out there and probably long after I’m gone. Or maybe not. But this is not an unusual situation — the frontiers of this subject requires people who go into their study, shut the door and think, think, think — and waste a lot of scrap paper). I won’t say most mathematicians are antisocial (I’m not, really). But a lot of us are socially … um how can I put this … “challenged”.
The decentering etc. madness has spread to, or spread from, physics education:
“Observing whiteness in introductory physics: A case study”
https://journals.aps.org/prper/abstract/10.1103/PhysRevPhysEducRes.18.010119
The paper, which I had thought or hoped was parody, even has a footnote (no. 1) wherein the authors explain their capitalization choices as based in social justice: “[I]n most cases we choose not to capitalize white and do choose to capitalize Black, Hispanic, and Students or People of Color. (The exception is when referring to Critical Whiteness Studies, which is a formal term that is capitalized in the literature.) This choice is informed by critical scholarship and activism[.]”
Don’t read the abstract shortly after eating.
ABSTRACT: “Within whiteness, the organization of social life is in terms of a center and margins that are based on dominance, control, and a transcendent figure that is consistently and structurally ascribed value over and above other figures. In this paper, we synthesize literature from Critical Whiteness Studies and Critical Race Theory to articulate analytic markers for whiteness, and use the markers to identify and analyze whiteness as it shows up in an introductory physics classroom interaction. We name mechanisms that facilitate the reproduction of whiteness in this local context, including a particular representation of energy, physics values, whiteboards, gendered social norms, and the structure of schooling. In naming whiteness and offering a set of analytic markers, our aim is to provide instructors and researchers with a tool for identifying whiteness in their own contexts. Alongside our discussion, which imagines new possibilities for physics teaching and learning, we hope our work contributes to Critical Whiteness Studies’ goal of dismantling whiteness.”
Thanks, Sanjoy. Yeah, I was aware of that one as well, and I read it (not shortly after eating). Of course it is crazy, and I had considered writing on it. But, it wasn’t maths, and it was smalltime clowns in a smalltime journal. When Nature starts it with this crap, however, something has to be said.