Formal metaphysical mathematics of the kind currently taught in schools and universities can and should be decolonised and uncoupled from its Western roots, and doing so would make it easier to teach and learn.
This controversial take on modern mathematics was expressed by Dr Chandra Raju, an Indian computer scientist, mathematician, educator, physicist and polymath researcher associated with the GD Parikh Centre for Excellence in Math at the Indian Institute of Education at Mumbai University, during the University of KwaZulu-Natal’s 11th annual Higher Education Teaching and Learning Conference held in Durban, South Africa, at the end of September.
Earlier in September, Raju also participated in a panel discussion at the invitation of the University of Cape Town’s Curriculum Change Working Group and spoke on the topic of decolonising science. His invitation to the discussion and the views he expressed drew criticism from a range of academics, including Jeff Murugan, an associate professor in the University of Cape Town’s maths department. Local media reported that Murugan had described his ideas as “fringe”.
“Much of what Raju says either reflects a very shallow understanding of the nature of science or, when they are correct, trivia,” Murugan is reported to have said.
Murugan is also reported to have said he was concerned that the changes that Raju advocates in his decolonising mathematics project amount to a neo-bantu education that, if implemented in South Africa, would see students unable to compete in the global marketplace of ideas.
Central to Raju’s argument is that mathematics and science are generally believed to be universal and objective, which, according to him they are not and can never be.
Present-day mathematics, known as formalism, due to British philosopher Bertrand Russell and German mathematician David Hilbert, reduces mathematics to metaphysics, and it is common sense that metaphysics can never be universal, he argues.
In the abstract to his UKZN conference paper, he writes: “Calculus with add-on metaphysics makes math very difficult and was globalised during colonialism. Eliminating redundant metaphysics in math makes math easy to teach.”
At the conference, Raju said it is now well-known that calculus and its infinite series originated in India across a 1,000-year period starting from about 470AD and was essential for agriculture and overseas trade, India’s two key wealth sources. Both monsoon-driven agriculture and navigation required a sound calendar, which called for good astronomy and precise trigonometric values.
He said Europeans were then backward in navigational skills and between the 16th and 18th centuries, governments offered large prizes for those solutions. This saw the Jesuits translating Indian texts en masse.
“However, like Indian arithmetic earlier, Europeans did not understand Indian methods of summing infinite series using non-Archimedean arithmetic, and a different philosophy now called zeroism – they tried to fit [the Indian translations] into their religious beliefs about mathematics as perfect and error-free,” he says.
He said the difference between normal mathematics and formal mathematics is that the former accepts empirical evidence (1+1=2 because one chair and one chair makes two chairs), while Russell required 378 pages to prove the same equation because formal mathematics prohibits empirical evidence.
“Science uses math – Changing math changes science,” he said, criticising the view that the formal mathematics community is solely authorised to decide what mathematics is taught.
He said decolonising mathematics means curricula decisions are made locally, are transparent, and they enable teachers to be accountable to their immediate society and ensures teachers can publicly explain why they teach what they do.
Calling for a #FormalMathMustFall campaign, Raju said science and engineering accept empirical proofs and thus normal mathematics is a professional gain as students can solve more difficult problems. For example, typical university calculus does not teach non-elementary elliptic integrals when this is taught in decolonised calculus.
“If the purpose of teaching math is for its practical applications to science and engineering, we should teach normal math. However, normal math begins with axioms invariably laid down by Western authority, so [it] means a loss of authority for the West,” Raju said.
He said colonial higher education had its roots in church education and the early universities like Oxford, Cambridge, Paris and Bologna were established during the Crusades to “mass produce indoctrinated missionaries”. The institutions were wholly church-controlled until the 20th century, so colonial and church education was designed to indoctrinate its products to fanatically trust authority against commonsense.
Decolonising education means fundamentally redesigning education to free people’s thought processes and analysis. The alternative mathematics, worked out by the Multiversity Group over the past decade and tested among eight groups in five universities across three countries, demonstrates the effectiveness and application of normal mathematics in the modern context.
Founded by Vijay Bhatkar in 1998, the Multiversity Group advances the application of information technology in education, governance and services.
“There is ample material for decolonised courses, but [university authorities] must decide whether to use it – you choose whether academics remain subordinate to the West and create indoctrinated slave minds or wait until students burn down your institutions,” Raju concludes.
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