C. K. Raju
of Advanced Study
Rashtrapati Nivas, Shimla 171005
Abstract: Many people laugh at the thought of decolonising mathematics. What is there to decolonise in 1+1=2 they ask? They have in mind the kindergarten images of 1 orange and 1 orange making 2 oranges. This is an empirical proof accepted in normal math. However, most people are unaware that colonialism changed math teaching from normal to formal math,1 which prohibits such empirical proofs,2 and demands axiomatic proofs instead.
This makes formal math extraordinarily difficult without adding an iota to practical value, as in the 378 pages needed by Russell and Whitehead to prove 1+1=2 in their Principia, which proof adds nothing to the practical value of arithmetic in a grocer’s shop. Going a step further, no one has yet met my Cape Town challenge to prove 1+1=2 in formal real numbers, from first principles, without assuming any result from axiomatic set theory. “Real” numbers are declared essential to calculus, though the practical value of calculus (in calculating, say, rocket trajectories) today involves computers, which use floating-point numbers and cannot represent metaphysical “real” numbers. (See footnote 2.)
The widespread ignorance of current math facilitates the imposition of formal math, by declaring it (normatively) universal, or epistemically “superior”. This is supported not by any reasoned debate, or critical comparison, but by (a) the fraudulent claim that such deductive/axiomatic proofs avoiding the empirical (a church technique) are actually found in “Euclid’s” Elements;3 (b) the myth that the book’s author was (a White, male) called Euclid who intended such proofs;4 and (c) the superstition that deductive proofs are “superior” since infallible. Actually, deductive proofs are more fallible, and manifestly inferior to empirical proofs.5
Though formal proofs are epistemically inferior, this method of reasoning without facts was glorified since it was politically useful to the church (and its theology of reason, as in Aquinas’ proof about angels on a pin6). Even today, formal math enables politics (including church superstitions) to be smuggled into “science” as in the creationism of Stephen Hawking’s singularity theory,7 which mimics Augustine.
Decolonisation of math seeks to eliminate the fraud, myth, and superstition associated with formal math, and reverts to simple, utilitarian, normal math with a philosophy of accepting inexactitude, called zeroism.8 Reverting to normal math makes math easy. It enhances practical value, and enables students to solve harder practical problems, as has been demonstrated in teaching experiments, across the last decade, in three countries, teaching calculus at university level,9 and geometry at school level.10
However, decolonisation of math results in the complete crash of the long myth of Western intellectual/racist superiority. But Western thinkers have been unable to respond intellectually to the critique, in public debate, in the last two decades. Hence, amusingly, various entities from an Oxford philosophy journal, to racist newspapers in South Africa, to an MIT science magazine, and the American Mathematical Society11 are repeatedly making scurrilous ad hominem attacks in complete desperation, to avoid loss of power and influence through decolonisation of math.
C. K. Raju holds a PhD from the Indian Statistical Institute, Kolkata, preceded by an MSc in mathematics and a BSc (Hons) physics from Mumbai. He initially taught and researched in formal math (advanced functional analysis and applications to relativity and quantum field theory) for several years. Later, he was responsible for porting large applications (space, oil etc.) on India’s first supercomputer, Param, and that experience led him to abandon formal math.
He has authored numerous research papers and several acclaimed books. In Cultural Foundations of Mathematics (Pearson Longman, 2007) he compiled evidence for the development of calculus in India (with a different philosophy, now called zeroism) and its transmission to Europe in the 16th c., where it was not properly understood. In Time: Towards a Consistent Theory (Kluwer, 1994) he earlier explained why Newtonian physics failed for theoretical reasons, and was replaced by relativity (by Poincare), because Newton (failing to understand the Indian calculus) had made time metaphysical. He went on to outline a new physics, using functional differential equations, forced after relativity, but which Einstein failed to understand. In the Eleven Pictures of Time (Sage, 2003) he proposed a new way to relate science and religion through time. He has developed and taught decolonised courses on math, and the history and philosophy of science. His shorter books include Is Science Western in Origin? (Multiversity 2010), Ending Academic Imperialism (Citizens International, 2011) and Euclid and Jesus (Multiversity, 2012).
He has wide-ranging interests: he has headed India’s largest computer science department, been editor of the Journal of Indian Council of Philosophical Research and Vice-President of the Indian Social Science Academy. He has received several awards. Currently he is an Honorary Professor of the Indian Institute of Education, and Tagore Fellow at the Indian Institute of Advanced Study.
Web, Writings and talks, Press, Videos.
1 How Colonial Education Changed Our Math Teaching | C.K. Raju, 2020. https://www.youtube.com/watch?v=Rm6d-bUmmGg. Sulba Sutra Geometry: Can We Teach It in Schools Today? | C.K. Raju, 2020. https://www.youtube.com/watch?v=rLI_UU6dfnE.
2 C. K. Raju, “Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the YuktiBhâsâ”,” Philosophy East and West 51, no. 3 (2001): 325–362. http://ckraju.net/papers/Hawaii.pdf. Abstract at http://www.ckraju.net/papers/Hawaii-abstract.pdf.
3 C. K. Raju, Euclid and Jesus: How and Why the Church Changed Mathematics and Christianity across Two Religious Wars (Penang: Multiversity and Citizens International, 2012).
4 C. K. Raju, “To Decolonise Math Stand up to Its False History and Bad Philosophy,” Conversation, October 24, 2016, CENSORED after publication; reproduced in C. K. Raju, “Was Euclid A Black Woman? Sorting Through The False History And Bad Philosophy Of Mathematics | Science 2.0,” October 24, 2016, https://www.science20.com/the_conversation/was_euclid_a_black_woman_sorting_through_the_false_history_and_bad_philosophy_of_mathematics-180581; also reproduced in C. K. Raju, “Black Thoughts Matter: Decolonized Math, Academic Censorship, and the ‘Pythagorean’ Proposition,” Journal of Black Studies 48, no. 3 (2017) 256–78; and in C. K. Raju, “To Decolonise Math Stand up to Its False History and Bad Philosophy,” in Rhodes Must Fall: The Struggle to Decolonise the Racist Heart of Empire (London: Zed Books, 2018), 265–70; see, also C. K. Raju, Mathematics, Decolonisation and Censorship, 2017, https://kafila.online/2017/06/25/mathematics-and-censorship-c-k-raju/.
7 C. K. Raju, The Eleven Pictures of Time: The Physics, Philosophy and Politics of Time Beliefs. Sage, 2003. Also, “The Christian Propaganda in Stephen Hawking’s Work.” DNA India, January 16, 2011, sec. Lifestyle. https://www.dnaindia.com/lifestyle/review-the-christian-propaganda-in-stephen-hawking-s-work-1495047. And, “Decolonising mathematics: how and why it makes science better”, http://www.ckraju.net/papers/palestine-extended-summary.pdf, abstracts of two invited talks at Palestine Technical University, aborted by Israel’s refusal to grant a visa. Also, “The politics of creationism from John Philoponus to Stephen Hawking”, http://www.ckraju.net/papers/Berlin-2020-abstract.html,
8 C. K. Raju, Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th c. CE (Pearson Longman, 2007); C. K. Raju, “Zeroism,” in Encyclopedia of Non-Western Science, Technology and Medicine (Springer, 2016), 4604–4610, http://ckraju.net/papers/Springer/zeroism-springer-f.pdf.
9 C. K. Raju, “Teaching Mathematics with a Different Philosophy. 1: Formal Mathematics as Biased Metaphysics,” Science and Culture 77, no. 7–8 (2011): 274–279, arXiv:1312.2099; C. K. Raju, “Teaching Mathematics with a Different Philosophy. 2: Calculus without Limits,” Science and Culture 7, no. 7–8 (2011): 280–285, arXiv:1312.2100. See, also, “Calculus without limits”, CUTS, Sarnath, Calculus without limits, CISSC, Tehran, “Calculus for social science”, Ambedkar University, Delhi, “Calculus without limits”, SGT University, Delhi, Institute lecture and workshop, IIT: BHU, etc.