Modern mathematics: Did the Greeks inherit the Earth?

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On 19 September 2017 University of Cape Town (UCT) Transformation Deputy Vice-Chancellor Professor Loretta Feris and the Curriculum Change Working Group invited Professor Chandra Raju, vice-president of the Indian Social Science Academy, and a panel of discussants to speak on decolonising the mathematics curriculum.

The speakers

Raju, a mathematician and computer scientist, believes that the traditional, ‘Western’ science based on the perspective that science is objective and universal has little relevance in a post-colonial world.

UCT’s Dr Henri Laurie and Professor Bernhard Weiss and Stellenbosch University’s Professor Lesley le Grange were also invited to present their perspectives on Raju’s beliefs.

Laurie is an applied mathematician whose research uses mathematics to sharpen debates in plant ecology. During his many years as an educator, he has emphasised the meaning of mathematical statements to cultivate enthusiasm for mathematics as a useful activity.

Weiss is a specialist philosopher of mathematics. Le Grange is a Distinguished Professor of Education and has more than two decades of experience in higher education. He is currently vice-president of the International Association for the Advancement of Curriculum Studies (IAACS); has an excellent understanding of higher education systems, particularly the South African higher education system; and has done work for the Council on Higher Education (CHE) in South Africa for more than a decade.

Raju’s rendition

Here is my summary of Raju’s views based on my notes, the incomplete released video and some extended quotes from his writings.

Raju rejects the “myth” that Western maths is universal. Its “superiority” over other ways of doing maths rests merely on some anti-scientific church dogmas born of hate politics. His preferred “other way” of maths is the religiously-neutral Indian ganita (together with the explicit philosophy of zeroism).

Further, most maths taught in schools today (arithmetic, algebra, trigonometry, calculus, probability) historically originated as ganita, but was “perverted” by Greeks and other Western Europeans who “inherited” it.

Selecting ganita over formal maths preserves practical value, while eliminating the false history and bad metaphysics. Indeed, practical value is enhanced: eg by eliminating Newton’s conceptual confusion about calculus and Einstein’s inferior theory of gravity.

Attributing the origins of “real” geometry to an unknown early Greek called Euclid was not only the stock church method of falsifying history, it helped to impose this theologically correct reinterpretation.

The imported ganita was wrapped in a false history (eg that Newton and Leibniz discovered/ invented the calculus) to deny its non-Christian origins – a denial powerfully motivated by the Inquisition.

Contrary to the text-book assertion that computer calculations are all erroneous compared to the “perfect” mathematics of formal reals, realistic “zeroism” rejects the idealistic claims of formalism as erroneous and a delusion.

Newtonian gravity is perhaps the most ironic example of how the Western metaphysics of maths hindered science. Newtonian physics failed because Newton, as the “second inventor” of the calculus, did not even understand it (both charges which he correctly made against Leibniz).

Intensely religious, he thought mathematics was the “perfect” language in which God had written the eternal laws of nature (revealed to him). Hence, he tried to make calculus “perfect” by making time metaphysical.

The conclusion is that Western metaphysical prejudices about maths, which were a veneer added on to an imported ganita, are not needed for its practical applications to science. On the contrary, their metaphysics actually hindered the development of science, and led to blind alleys.

Hence, it must be discarded, and we must abandon formalism. What is needed for science is to accept ganita (and zeroism), and its method of calculation.

Pedagogy

Perhaps the greatest beneficiaries of such a move (to accept ganita and abandon formal maths) will be schoolchildren. The statement that 2+2=4 admits of a simple understanding in natural language (which implicitly employs zeroism), where the abstraction “2” is understood ostensively by empirical referrants, exactly like the abstraction “dog”. However, formalism turns “2” into a very difficult abstraction, disjoint from experience, and involving set theory.

Since axiomatic set theory is too difficult to teach to children, they are today taught set theory without defining a set! Naturally, many students reject the lack of clarity in such “teachings”. Hence, most abandon maths before reaching calculus. They wrongly blame themselves or their teachers, when what is at fault is the subject of formal maths, with all its useless metaphysics.

Teaching school maths the way it actually originated in the non-West makes maths easy, as has been demonstrated by Raju’s pedagogical experiments, particularly the five-day course on calculus, which enables students to solve problems too hard to be solved by those equipped by a course in university calculus.

Teaching ganita the way it historically developed in the non-West, minus the veneer of confused metaphysics it acquired in the West, also has the advantage that it makes maths easy and intuitive, and leads to a better understanding. Hence, we must henceforth adopt ganita (together with zeroism) and reject formal maths.

Finally, he rejects the colonial myth that to validate knowledge it is necessary to obtain the prior approval of Western authorities, who will judge it in secret (secretive “peer” review). Secretive review was a church technique to preserve myths by using pre-censorship to prevent the public articulation of dissent.

This means: “Don’t submit your research to respected scientific journals and anonymous peer reviewers! Fight things out through oral debate.”

Since March 2015, we know what that means at UCT.

In short, ‘current’ “formal” mathematics is derived, inferior and perverted ganita. It should be abandoned and replaced by the easy-to-learn ‘kosher’ ganita. This is music to the ears of radical Fallists.

Since the ‘official’ video of the event fails to cover the panellists’ comments and questions from the audience and comments on it are disabled, this event could be interpreted as an attempt to validate Raju’s views (which would make radical decolonists ecstatic) and censor those of ‘others’, especially UCT’s mathematicians and physicists.

The ‘evidence’ I’ve been able to garner since the event is as follows.

A UCT mathematics lecturer standing (the room was packed) next to me left in a huff five minutes into Raju’s presentation commenting: “Snake oil salesman”.

One of the world’s foremost mathematical scientists wrote to me: “He’s a crank and rejects the views of qualified people.”

A non-mathematician senior administration employee wrote: “These [Raju’s] claims seem hardly credible – it appears that the university has suspended all incredulity. That such a charlatan is welcomed to UCT by a deputy vice-chancellor while Flemming Rose is shunned does us no credit.”

A UCT physicist specialising in CHED-like academic-support education wrote: “He must be either really smart or a fraud or deranged. It’s not clear to me whether we need to stop using our GPSs and gravitational wave detectors while we wait for the revolution to happen.”

I have forwarded this segment of the manuscript to the heads of the departments of Mathematics and Applied Mathematics, the DVC for transformation and the executive director of the Communication and Marketing Department to elicit formal and more authoritative comment and the release of the ‘missing’ part of the event video.

Since doing this, Part 2 of the “Raju Event” has been posted by UCT.