Twice a week, Tiri Chinyoka holds extracurricular classes for mathematics undergraduates at the University of Cape Town in South Africa. One October evening, a predominantly black group of first-year students gathered around whiteboards as they grappled with the intricacies of vectors and matrices, while on the wall behind them some oppressive history looked on: a mural spanning some 30 feet portraying students past, dressed in black gowns and mortarboards — all of them white.
Some academics are worried that the decolonization movement could disadvantage South African mathematicians in the global arena.
“Structurally, nothing has changed from the colonial era, whether you’re talking about human experience or you’re talking about the physical infrastructure,” says Chinyoka, sitting later in his office in one of the university’s classically inspired buildings that overlook the city. Sporting a black leather flat cap and dreadlocks, Chinyoka is not a stereotypical mathematician. “If you look at what we teach in the mathematics curriculum, it is almost irrelevant to the South African context,” he says.
Since apartheid ended in 1994, South Africa’s universities have struggled to transform themselves, leading to escalating student protests over the last three years — including the toppling of a prominent statue of Cecil Rhodes, an infamous colonizer who donated the land on which the University of Cape Town now stands. And as students and academics accelerate the process of decolonization across South African universities, the spotlight has fallen onto mathematics.
Exactly what decolonizing math would entail isn’t entirely clear: Curriculum revisions that promote non-Western contributions to the field, new teaching methods rooted in indigenous cultures, and greater openness to ideas outside the academic mainstream are all under discussion. Some want to go further, challenging the philosophical foundations of mathematics itself.
That notion strikes many mathematicians as odd. After all, the patterns and equations that underpin our knowledge of the physical world would seem to have little to do with power dynamics. Math simply is.
“It doesn’t inspire a lot in me,” Henri Laurie, a soft-spoken academic who has spent three decades teaching math at the University of Cape Town, says of efforts to decolonize math. “I can see that it has meaning in the creative arts and possibly even in history and law” but “when it comes to science and mathematics, we want to be part of the international community.”
Unlike the arts and humanities, mathematics is generally understood to be universal and objective. Necessary truths are discovered through a process of logical deduction — with proofs as the cornerstones of the discipline. “What makes mathematics valuable, what makes it powerful, is that you can communicate mathematics without any change to a huge range of cultures,” says Laurie.
He is among those who are concerned that the decolonization movement could disadvantage young South African mathematicians on the international stage if curricula were changed or alternative methodologies take hold. “We can’t cut ourselves [off] from mathematical developments in the rest of the world,” says Loyiso Nongxa, vice president of the International Mathematical Union, which promotes international cooperation among mathematicians. “Our intellectual project would be impoverished.”
In his evening classes, meanwhile, Chinyoka hopes to broaden students’ understanding of what they can do with the mathematics they are presented with in lectures — from engineering to academia to law. He believes that South African mathematics should be reframed around the challenges faced by South Africa, as well as other developing countries.
“We still have this more Westernized view: You sit in a mathematics class on topology or abstract algebra, with zero idea about which context it applies to,” he says. Pointing to the current water and energy crises in South Africa, he argues that math should be taught with concrete applications in mind, rather than purely theoretically, which is a luxury afforded only by the West.
“What is the use of teaching the Bantu child mathematics when he cannot use it in practice?” asked Hendrik Verwoerd back in 1953. At the time, Verwoerd was in charge of South Africa’s education system for black students, and later he became prime minister. His racist legacy persists today: Only 28 percent of black students achieved a mark above 40 percent in mathematics in the 2016 National Senior Certificate examinations, compared to 86 percent of white students.
Some argue that math should be taught with concrete applications in mind, rather than purely theoretically.
And while the number of black math graduates is increasing at South African universities, few continue into academia. “We are severely underrepresented as local Africans, and especially African females,” says Sudan Hansraj, a lecturer at the University of KwaZulu-Natal.
Growing up under apartheid, Nongxa of the International Mathematical Union experienced racism in the education system first hand. “I was only exposed to mathematics two years before I went to university,” he recalls. “There were very few African schools that offered mathematics.” Nongxa, who transformed himself from herd boy to professor of mathematics, is an outlier in his village.
The perception that math is disconnected from black lives may be perpetuated by the field’s distorted history, which often centers on the achievements of white men. “There was an erasure of contributions from the developing world and people of color,” says Fasiha Hassan, deputy president of the South African Union of Students. “We would acknowledge where it really comes from.”
Ethnomathematics is a global movement that recognizes non-Western contributions to the field. Founded in the 1970s by Ubiratàn D’Ambrosio, a Brazilian educator and philosopher, ethnomathematics seeks to include indigenous knowledge in math education. As an example, Xolisa Guzula, a specialist in multilingual education, points to a traditional southern African game played with stones called upuca that can be used to teach concepts such as number theory and estimation. In this way, she argues, mathematics is connected to a learner’s culture.
Teaching in indigenous languages alongside English (the dominant language of math education globally) has also been shown to improve mathematical comprehension by presenting concepts from different perspectives. “Multilingual people do not make meaning through one language — that again is a monolingual ideology,” says Guzula.
Yet ethnomathematics is generally used only to introduce math to students, who quickly switch to formal math, which has roots in the formalist philosophy of mathematics developed in Europe in the early 20th century. Formal math underpins both the academic discipline and how it is taught in schools and universities globally. And so while Asia and the Middle East have made significant historical contributions to mathematics — including algebra and the common number system — the methodological foundations of the discipline, as practiced by almost all mathematicians, remain Western.
C.K. Raju, an Indian polymath, is trying to change that emphasis. He has written provocative articles such as “Was Euclid a Black Woman?” and believes that many mathematical discoveries are falsely attributed to the ancient Greeks. But Raju goes even further, arguing that formal mathematics should be replaced with what he and others call “normal mathematics” — which has roots in Asian philosophy.
Formal math education was introduced in India, as in South Africa, by a colonial administration, Raju notes. “Colonial education replaced indigenous math without any critical comparison,” he said in an email exchange in which he promoted the benefits of his methodology in the teaching of such subjects as calculus and geometry. Over the last decade, he has led workshops in normal mathematics to teachers and university students in India, Iran, and Malaysia.
Centering mathematics around deductive proof, as formal mathematics does, is mistaken, according to Raju. He argues that an overreliance on pure reason can lead to false knowledge: if the premises from which the reasoning begins are false, then so too is the knowledge. Instead, in Raju’s normal mathematics, he places empirical knowledge alongside reasoning at the core of mathematics. It was unnecessary, he argues, for Bertrand Russell and Alfred Whitehead to write 378 pages of logic in their “Principia Mathematica” in order to prove 1+1=2 — when empirically it’s obvious. To Raju, this and much of formal math is “metaphysical junk,” and the only math of value is that which has practical application.
While the number of black math graduates is increasing at South African universities, few continue into academia.
But Raju’s ideas are highly controversial in academic circles. Last year, he lectured at the University of KwaZulu-Natal and at the University of Cape Town — where Henri Laurie sat on the discussion panel. “However interesting Raju might be, he’s also quite outlandish and he makes claims that cannot be supported,” Laurie says.
Fierce debate surrounded Raju’s appearance at the University of Cape Town, where he was accused of being a “conspiracy theorist” and a “charlatan” by senior academics. Others have called for universities to remain open to revolutionary ideas such as these.
“There is no flexibility to try to do things alternatively or to try to open up ourselves to interrogating new ways of thinking,” says Chinyoka, adding that allowing researchers to explore new directions in mathematics would not mean throwing out existing methods. “Some students may want to carry out research using these alternative theories and they should be allowed to do that,” he said.
Several early-career mathematicians and scientists at the University of Cape Town declined to discuss the subject of decolonizing mathematics with Undark, citing professional repercussions.
To most mathematicians, the value of the discipline remains embedded in its rigorous standards of deductive proof. “I do think that as a driver for mathematics it is very important, and that’s something we should hold onto,” says Laurie. Bernhard Weiss, a philosopher at the University of Cape Town, agrees that the necessary truths of pure mathematics are foremost: “Unless you see through the applications to the central core, then you’re not getting at mathematics.”
Yet an opposing view regards mathematics as an evolving work-in-progress whose truths are dependent on culture and invented, rather than universal and discovered. Mathematics, in this view, developed as a result of problems that needed to be solved: the development of geometry to help ships navigate, or the invention of statistics to support the insurance industry.
“Truths in mathematics are never absolute, but must always be understood as relative to a background system,” writes Paul Ernest, a philosopher of mathematics at the University of Exeter and a proponent of this ‘fallibilist’ understanding of mathematics.
The perception that math is disconnected from black lives may be perpetuated by the field’s distorted history.
In this sense, the teaching of mathematics’ history might demonstrate to students the erratic path of revisions and modifications that have brought the field to its current form. “For me it’s like evolution,” says Nongxa of the International Mathematical Union. “There are mathematical ideas that flourish and mathematical ideas that go extinct. And one cannot say that this branch will flourish and this other branch will go extinct.”
Given the dominance and success of formal mathematics, Nongxa and others acknowledge that it is a difficult climate for alternative methodologies — one made harsher still if the academic community remains closed to ideas outside the mainstream. “We are academics and intellectuals,” Nongxa says. “We are open to debate things that we might disagree with — let’s not have this debate polarized right at the beginning.”
Thomas Lewton is a science writer and documentary filmmaker whose freelance film and photography work has been featured on the BBC, VICE, and The Guardian.