The latest issue of Nature, one of the world’s most prestigious scientific journals, has a long (4-page) feature about the “decolonization” of mathematics. As we’ve learned to expect from this kind of article, it points out gender and ethnic inequities among mathematicians, ascribes them to structural racism existing today, and seen as ubiquitous in math, and and then proposes untested ways to achieve equity in math (proportional representation of groups) by infusing the teaching of math with aspects of local culture.
The problem with this paper, like similar “decolonization” screeds, is that while it certainly means well (I agree that everyone should have the chance to learn math), and is sensitive to differences among cultures, it gives no evidence that “decolonizing” mathematics (that is, removing its “whiteness” and “Westernness”, and using as math subjects features of the local culture) actually works. It’s a gift package of suggestions and assertions wrapped around, well, nothing. This doesn’t meant that the suggestions are not worthwhile, but there’s nothing to be gained by blaming inequities, which could be due to a number of factors, to existing bigotry and racism in math, for which it offers no evidence. More important, the “course” they chart has to be shown to actually lead to more understanding than alternatives.
Here’s where blame is affixed. You don’t have to be a rocket scientist to know that it adheres to white men.
Maths is built on a modern history of elevating the achievements of one group of people: white men. “Theorems or techniques have names associated to them and most of the time, those names are of nineteenth-century French or German men,” such as Georg Cantor, Henri Poincaré and Carl Friedrich Gauss, all of whom were white, says John Parker, head of the mathematical sciences department at Durham University, UK. 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. It has also squelched wider access to rich mathematical ideas developed by people of different backgrounds — such as Chike Obi, James Ezeilo and Adegoke Olubummo, a trio credited by the website Mathematicians of the African Diaspora with having pioneered modern maths research in Nigeria. Another example is Mary Golda Ross, a Cherokee mathematician and engineer who was a founding member of ‘Skunk Works’, a secretive division of the US aerospace manufacturer Lockheed. There, she developed early designs for space travel and satellites, among other things.
Where is the evidence that high quality and non-white mathematicians, of which until recently there were very few, are now being pushed aside by racism? I don’t doubt that there was discrimination in the past against women and minorities, but even then I keep thinking of the Indian Srinivasa Ramanujan, an immensely talented autodidact from Tamil Nadu who in 1913 sent a bunch of his theorems and proofs to G. H. Hardy at Cambridge, who instantly recognized the man’s talent and arranged for him to study at Cambridge. I can’t imagine anyone more “minoritized” in the UK than Ramanujan, dark of skin, poor, and humble of origin. And yet people helped him, and he’s still regarded as a giant in the field. Would people push him aside today—or anyone like him? I doubt it, just as I doubt that mathematics is presently rife with structural racism—that the playing field is still “far from level”. If “level” means “equal opportunity”, then I’d say we’re pretty close. If it means “equal outcoms”, I’d say, yes, it’s not level. But that’s not what a tilted playing field means: it means that right now there is not equal opportunity. Yes, the pipeline needs to fill up after a past of sexism and bigotry, but the article gives evidence for “structural bias” or “system bias” at the pipeline’s distal end.
Here’s what the advocates of decolonization advocate to replace the kind of math teaching we have today:
Edward Doolittle, a mathematician at First Nations University of Canada in Regina, contrasts Indigenous mathematics with the mainstream, global way of teaching maths, in which instructors essentially present the same content regardless of where they’re teaching.
Doolittle, who’s also a Mohawk person from Six Nations in southern Ontario, says that calculus courses are structured so similarly that he could teach the subject “anywhere the students speak English”, and even take over teaching a course midstream.
By contrast, he says that Indigenous mathematics involves getting inside a culture and examining the mathematical thinking in it. He draws a further distinction between Indigenous mathematics and the practice of what he calls “indigenizing mathematics”, which, he says, involves searching for cultural examples to use in courses taught in the global version of mathematics.
Indigenizing mathematics tweaks the curriculum when it isn’t feasible to fully immerse students in ideas from an Indigenous culture, Doolittle says. “It’s very hard, if not impossible, to break out of” the global mathematics system, he notes. By indigenizing mathematics, instructors can stay within the parameters of what they’re required to cover while broadening the cultural scope of their curriculum.
Using that approach, “we have respected the knowledge of Indigenous people and are furthering our ties with Indigenous people” while still teaching students core topics, he says. For example, when teaching statistics courses, Doolittle has discussed a simplified version of the Peach Stone Game, which is based on making wagers and is played in his community. “You can analyse this in terms of a binomial probability distribution,” or the chances of two outcomes over time, he says.
“I would like to encourage many of my colleagues to engage in indigenization efforts, and hopefully to turn up interesting examples from their local area,” Doolittle says.
As for how to “indigenize” math, the article gives a couple of examples beyond the Peach Stone Game: teaching about Polynesian navigation to Hawaiians in Hawaii and using aspects of local culture to teach math in five African countries (“the next Einstein will be African” is the motto of this five-nation consortium, the African Institute for Mathematical Sciences, or AIMS). And that’s about it. There is a lot of noise, but, as of yet, little to show that this kind of training produces results better than “non-indigenous” training. If it does work, more power to them. So far, most of the “indigenizing” appears to be mainly trying to increase the diversity of people going into math. That’s great, too, but it’s not a revolution in teaching math.
And even some of these endeavors involve bringing in mathematicians who aren’t indigenous. Here’s what AIMS does:
Faculty members at the centres are hired from African countries, often through partnerships with local universities. AIMS also hosts visiting lecturers from outside Africa who teach courses that range from a few weeks to two months in length. Bringing in outside researchers exposes students to top talent while they continue to expand their roots in Africa’s mathematical communities.
But isn’t it counterproductive to bring in “top talent”, probably white people, who undoubtedly teach math in decidedly non-Indigenous ways?
It’s clear that while I have no strong beef against using local culture or examples to teach math—or any form of science—this will go only so far (what happens when you get to really high-level math?), and if you’re going to do something like this, it’s better to start by showing in pilot projects that it really works. Blaming whiteness or the West on holding down math education in places like Africa (where whites are actually a minority), is no longer tenable, and even counterproductive.
But here’s the part I most object to. Durham University in the UK is itself mounting a decolonization effort that involves Ric Crossman, a statistician, and John Parker, head of Durham’s maths department. Here’s their philosophy of education:
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”.
What an AWFUL situation! It’s certainly feasible for some students to tell you the best ways they can absorb mathematics, but this will certainly differ among students, and not every student knows. But to put the curriculum and all the teaching methods in the hands of the students, ignoring the experience of teachers who have spent years finding out which forms of pedagogy work in general, is a recipe for disaster. It’s simply invidious to denigrate the expertise of teachers by comparing it to “colonizers.” But such are the rhetorical tactics that progressives have learned to use.
h/t: Carl
Maths is maths independent of your race, ethnic group or gender. Indeed perhaps the greatest mathematician of the 20th century was the Indian mathematician Srinivasa Ramanujan who died too early at the age of 32.
It is humanity’s universal language and should not be co-opted for political purposes.
Indeed. There’s a long list of Indian mathematicians alone: https://en.m.wikipedia.org/wiki/List_of_Indian_mathematicians
My latest approach is to look for preconceived notions.
Here, well, in every such piece like this – I see the preconceived notion that equal opportunity is expected to produce equal numbers of blank-slate “races” from the globe.
OK, two preconceived notions.
Tech note : email update isn’t working.
I think this is the main reason why research about race and IQ is considered taboo nowadays. More than any other line of research, it has the potential to undermine the main assumption that these projects to politicize STEM fields are based on.
As was mentioned here some days ago, Luis Leyva (Vanderbilt) has argued that math education represents a space which is “white and cisheteropatriarchal” and thus hostile to BIPOC and gay students. Anyone interested in the brilliant Ramanujan is likely to enjoy Kanigel’s The Man Who Knew Infinity (biography) as well as Leavitt’s The Indian Clerk (novel).
Hostility to gay students is odd given that Alan Turing, arguably one of the greatest mathematicians of the 20th century, was gay.
Who killed himself over the hostility felt toward to gay men.
…or he may have been careless with cyanide vapours in his makeshift home laboratory. Whatever, the posthumous recognition of his secret service to the nation was well deserved. The entire Ultra cryptography secret was not revealed until the 1970s. It was an astounding revelation. Homosexuals at the time were sincerely believed to be security risks. It was not simple mean-spiritedness that hounded them out of secret work. Kim Philby and his gang of five were all homosexuals, which was thought surely proof of something or other.
I would have thought that the fact that ‘he could teach the subject “anywhere the students speak English”, and even take over teaching a course midstream’ is actually rather a good thing.
They don’t mean well.
“As we’ve learned to expect from this kind of article, it points out gender and ethnic inequities among mathematicians, ascribes them to structural racism existing today, and seen as ubiquitous in math, and and then proposes untested ways to achieve equity in math (proportional representation of groups) by infusing the teaching of math with aspects of local culture.”
When I was at college (roughly 25 years ago), I noticed that in most of my quantitative classes, the professors were a) foreign and b) non-white, usually east-Asian. My impression from this is that us Americans don’t do math very well.
So when this data about racial inequities is asserted, I wonder what it would look like if national origin and ethnicity as well as race was taken into account. I would suspect that foreign born, non-white people are overrepresented in quantitative subjects at most colleges as both instructors and students.
Also, on the universality of math…some of you may remember Jaime Escalante, the famous high school math teacher on whom the movie Stand and Deliver was based. Long story short, he immigrated to the US after teaching in his native Bolivia, initially knowing almost no English, and thereby having to take on work far below his education level until he learned the language better. In one instance, in order to get a menial job, he had to pass a math test, which he finished rapidly and absolutely aced. But his English was so poor at the time, he was unable to communicate to the proctor that he was finished with the test so early!
The success of Mr. Escalante, and then later of his low income students that he so famously mentored (his students set records for scores on the AP Calculus exams in the 80s), seems utterly buried now in the dustbin of history. What he did should have been the catalyst for how to teach math to low SES kids…instead it seems to have been rejected wholesale by the educational establishment.
A very sharp critique Jerry!
You’re doing God’s work! Please keep it up 🙂
Yes.
Seems to be the fastest path to underachievement for everyone. I despair.
If I wanted to undermine the scientific competitiveness of the US, I could not think of a better approach than to infect STEMM in this way.
“Once is happenstance. Twice is coincidence. Three times is enemy action.” — Ian Fleming
Because Edward Doolittle gets a complimentary mention in Nature, here is a 2018 talk he give on Indigenous Mathematics at University of Manitoba:
https://www.uwinnipeg.ca/indigenous/weweni/weweni-2018/what-is-indigenous-mathematics.html
(I put this in according to Da Roolz but the formatting seems a bit different, so apologies if the embedded video comes out wrong.)
He discusses the Peach Stone Bowl game as a ceremony incorporating the Mohawk creation myth beginning 6:54. (Historical note: peaches are not native to the New World.)
In the Cree creation story, “we don’t know” {said with a breathy theatrical flourish apparently to indicate profundity) who was created first, man or woman. Thus the anticipation of Heisenberg’s uncertainty principle.
His remarks on the differences in approach to mathematics between indigenous cultures and post-contact settler culture begin at 29:20.
I should note that he is indigenous in the same sense that Barack Obama is black: his mother is a white settler. Unlike Mr. Obama, he holds her culture against her in impeding his way of knowing even though he spent much of his childhood reading in settler libraries.
Trying again.
https://www.uwinnipeg.ca/indigenous/weweni/weweni-2018/what-is-indigenous-mathematics.html
If you have a system of counting, you can do mathematics, it doesn’t matter.
Mathematician here, or at least I’m allowed to call myself one, since I got a doctorate. I couldn’t bear to finish the article but did read about the Arabic influence in the developmental of Algebra and should point out that this Arabic influence is something every mathematician is aware of and justly celebrates. It’s no big secret, and not something that is suppressed, purposely or not. Many universities offer a History of Mathematics course for their majors.
It’s nice to see Ramanujan’s name brought up. “The Man Who Knew Infinity” is exceptionally written and very highly recommended. As best he could, Hardy made Ramanujan welcome and nurtured him. Hardy was the preeminent and most respected British mathematician of the time and considered Ramanujan to be the equal of Euler or Jacobi. In a similar vein, Hilbert insisted that Emmy Noether be given her just due.
I think it is time for serious scientists to stop publishing in Nature Group journals. There are plenty of other perfectly fine places to publish.
They lost me a few months ago when they published an article advocating economic degrowth.
The practice of having the pilot and co-pilot run an airplane is obviously in need of decolonization, for “colonization ‘was some group of people thinking they knew best for some other group of people’ ”. I expect the Progressive thinkers at Durham University to recommend turning the cockpit of all airflights over to the passengers—or perhaps only to those passengers who have filed correct Post-Colonial Theory Statements.
On the other hand, maybe Progressive thinkers at Durham University haven’t heard about airplanes. Durham does claim to be the third oldest university in Britain, although UCL
has apparently made the same claim.
Durham University was founded in 1832, so while it may be the 3rd oldest in England, there’s 4 Universities older than it in Scotland.
I know little to nothing of mathematics, but these proposals sound to me like elaborate, sophisticated versions of rewriting story problems. Instead of John having two apples and Mary having three, we have Hosa and Catori catching fish. We are de-colonializing mathematics.
I’m assuming there must be more to it than that.
This may be one of the most accurate and concise descriptions of what the average person who’s jumped on board a Progressive Social Justice agenda believes “colonialism” to be. Thinking you know what’s best for someone else is right up there with telling them you’re right and they’re wrong. Who are we to judge?
“By contrast, he says that Indigenous mathematics involves getting inside a culture and examining the mathematical thinking in it.”
Cool. If a community has some problem or custom that is helpful in teaching math, identify it and fit it into the local curriculum where it’s most helpful. But why fragment the study of something as universal as math? Publicize that example that was helpful so that math worldwide can learn of it and, if practical, add that example to their syllabus. The last thing we want is for something as obviously universal as math to be customized like language dialects in each subset of society.
Indeed, Bob.
I found Prof. Doolittle’s attempts in the talk linked above to show there was a unique indigenous mathematical culture unconvincing. His extended digression on the Peach Stone Game failed to show how it is different from any other simple game of chance except that it is freighted down with creation symbolism, played ceremonially at mid-winter “and at other times of the year”(!) (Did he just make that up on the fly? I can imagine the stern rebuke from the university that would be delivered to a student who dared to ask such a question. Indeed, at another talk, Frances Widdowson was in fact censured for posing a non-snarky question along the lines of, “How do you know what you know?” to an indigenous shaman-elder who claimed mystical knowledge. Much like what Jerry and others routinely ask creationists.)
The well-known difficulty that pre-literate cultures have with abstraction was nicely illustrated in a ratio problem given to Alaskan Native students. “If two king salmon are as big as three red salmon and the fish-drying rack has room for 6 red salmon, how many king salmon would fit on it? You may draw your answer in the space below.” Doolittle said that when he, as an adult researcher in math education, discussed the problem with his father, the father said, “That doesn’t make sense. Often king salmon are bigger than red salmon but sometimes they’re not. You just have to compare what you caught that day.”
So merely using familiar exemplars like salmon instead of, say, apples and melons, may not help make the leap of abstraction needed to get the essence of the problem. Instead of seeing this as a barrier to indigenous learning that had to be surmounted — which framing the problem around salmon seemed intended to do –, Doolittle celebrated it as evidence that indigenous people had superior ways of looking at the complexity of real-life problems than the reductionist settlers. But, dammit, you still have to be able to solve for x in x/6 = 2/3 !
In the obligatory swipe at residential schools, Doolittle said that an elder, a “survivor” of a IR school, told him that the two big things they learned there were English language arts (literacy) and mathematics. He says, “English, we all know what that was for but she said, ‘Math, that was where they really got us!'” No elaboration. Ironically, many successful Indigenous people in Canada credited the residential schools, uneven though they were, as giving them a start that they would never have got otherwise. “Getting” math was part of that. These positive experiences were disavowed and recanted when it became necessary to stick to the party line in order to maximize payouts for abuse that the government is still trying to settle.
My take from the whole video was that the concept of distinctly indigenous mathematics is simply grievance politics. For Nature to be giving credence to this sort of thing shows how far it has declined as a serious scientific journal.
A nice quote from T H Huxley, one of the founders of Nature: “science commits suicide when it adopts a creed”.
“By contrast, he says that Indigenous mathematics involves getting inside a culture and examining the mathematical thinking in it.”
There already is such a thing, and it’s called “anthropology.” It offers some interesting insights into different cultures, but doesn’t offer much insight into math.
The reason for that is that theorems are generally named after the first person to prove them*. For whatever reason, until the era of easy global communication, Europe was where most of the advanced mathematics was being done. It’s hard to be at the cutting edge of mathematics if most of the other mathematicians’ work is several months away by sailing vessel. Most people in Europe are white. This naming issue is nothing to do with racism, it’s just a fact.
*Fermat’s last theorem should really have been called Fermat’s last conjecture until 1995 when it became Wiles’ Theorem.
While the number of mathematical and scientific ideas that can be rigorously proved is probably infinite, the amount of foundational/truly impactful ones is limited.
These ideas are relevant by their potential use and often, by serving as basis for defining whole new types of science.
The people figuring out/creating these ideas deserve recognition by having their name attached to them for eternity. And this regardless of their race and gender.
For whichever reasons, unfair or not, the scientific education lagged in places other than Europe for a while, and the educated were mostly men, but trying to hide the existence of these great thinkers just because of their race and gender is completely wrong. I find it disturbing and similar to the tendency of some people, trying to destroy any memory of people like Columbus, while their very existence might be due to their very actions.
Well, I guess it will blow peoples’ minds then to know that Wiles actually settled the Taniyama-Shimura Conjecture – not a European or white man in sight there: Fermat fell out as a corollary.
I read the book and my mind isn’t blown. Could you tell us what your point is: that Taniyama and Shimura should get the credit and the theorem be renamed? Sorry, but they don’t get the credit, nor did the proof of Fermat’s last theorem fall out after the T-S conjecture was proven; it took years of work afterwards. I read the book on this recently, and, except for your assertion that Taniyama and Shimura were Japanese (presumably implying that they were using “Indigenous Math”, you’re just wrong.