**Decolonising Mathematics and Science Education**

C. K. Raju

(Professor, AlBukhary International University, Malaysia)

Extended Abstract

Colonial education teaches imitation of the West on the premise that the West is superior. This Western superiority was asserted by a whole host of racists from Hume and Kant[1] to Macaulay and Rouse Ball.[2] But their arguments were all based on a fraudulent history of science.[3] For example, on this fraudulent history, “Euclid” is declared the father of “real” mathematics. However, there is no evidence that “Euclid” even existed. My prize of Rs 2 lakhs for serious evidence about Euclid stands unclaimed, for several years,[4] and leading Western scholars admitted long ago that “Nothing” is known about Euclid.

In fact, during the Crusades, when the church changed to Christian rational theology by copying Islamic rational theology, it masked this process of stealing from the religious enemy by concocting the story of Euclid to claim ownership of reason.[5] What exactly is “real”mathematics? The related story about “real” mathematics ties it to a Christianised philosophy of mathematics as metaphysics which suits the post-Crusade theology of reason.

However, a completely different story emerges from the most superficial inspection of the manuscripts of the Elements[6] (the book which “Euclid” supposedly wrote, but which does not mention his name). Contrary to the innately absurd claim that the Elements was written to demonstrate metaphysical (deductive) proofs, its very first proposition uses an empirical proof, as does the key 4^{th} proposition, essential to the whole book. The book, therefore, cannot be about metaphysical proofs as the church and racist historians like Rouse Ball wildly contended. In an interesting case of persistent mass gullibility, hundreds of thousands of Western scholars who studied the book, over 7 centuries, failed to apply their mind to this elementary discrepancy between facts and story at the very first step. Eventually, when they did grudgingly admit the discrepancy, leading Western intellects like Russell and Hilbert[7] jumped in to do exactly what theologians do: they tried to save the story by piling on the hypotheses. That is, they retained the blind belief in Euclid and his intentions, and just changed the facts by rewriting the book from a formalist viewpoint, in their respective tracts on the foundations of geometry. Like its earlier Crusading reinterpretation, the formalist rewriting of the book fails to fit the real Elements. But that is how we teach geometry in our schools today, for we teach blind imitation of the West.

The Elements is actually written from the viewpoint of Egyptian mystery geometry (and “Euclid” was probably a black woman from 5^{th} c. Africa as depicted on the cover of my book[8]). This deeply religious view of mathesis, or arousing the soul to make it recollect its past lives, prevailed from Plato to Proclus both of whom explain it in detail, as in Plato's story of Socrates and the slave boy.[9] Proclus defines mathematics as the science of mathesis.[10] However, during the first religious war which it waged against “pagans”, the church cursed the related notion of soul and its past lives in the 6^{th} c.[11] (To respect that taboo, Westerners today only refer to that “soul arousal” by coyly speaking of the aesthetic value of mathematics.) However, the subsequent religious wars, the Crusades, which the church waged against Muslims, were persistent military failures (after the first Crusade, and beyond Spain). Hence, the church sought a non-military way of conversion. Hence, it accepted back mathematics, reinterpreting the Elements as concerned solely with rational persuasion, to align it with the post-Crusade Christian theology of reason, the better to be able to convert Muslims (who accepted the aql-i-kalam).

Theological “solutions” are inevitably half-baked. Proclus explained that mathematics contains eternal truths, and hence is especially suited to arouse the eternal soul on the principle of sympathetic magic that “like arouses like”. After the church cursed the related notion of soul and its past lives, there was no longer any systemic basis for this belief. Nonetheless, the belief (that mathematics contains eternal truths) lingered on as a superstition which has infected all Western thought about mathematics. During the Crusades, church-besotted Western minds added the further superstitious belief that mathematics, since it contained eternal truths, was hence the “perfect” language in which their god had written the (eternal) laws of nature.[12]

These superstitions about mathematics created severe difficulties for the West in understanding practical mathematics (arithmetic, algebra, trigonometry, calculus, probability, i.e., most of the math taught in schools today). Unlike the religious mathematics, earlier imported from Egypt, this practical mathematics was imported from India. This import of practical mathematics was spread over several centuries, first from Arabic books such as Al Khwarizmi's Hisab al Hind (from Baghdad via Cordoba in the 10^{th} c.), and then Arabic books translated at Toledo (12^{th} c.), and eventually directly (from Cochin, 16^{th} c.).[13] Western scholars (all priests) conflated the two distinct streams of mathematics: the religious and the practical.[14] This Western attempt to try and understand practical mathematics from a religious perspective (with which it was familiar) was a disaster.

Thus, because of their primitive Greek and Roman system of numeration, and religious ideas about unity, Westerners were perplexed for centuries even by a simple thing like zero. (The very name zero derives from sifr = cipher meaning mysterious code.) In the 10^{th} c, their leading mathematician, a pope, most blunderously got constructed an abacus for “Arabic numerals”,[15] thus exhibiting a fundamental misunderstanding of efficient arithmetic algorithms (the same one's which are today taught in primary school). This was a mistake about elementary arithmetic which posterity will forever laugh at. Howlers such as “surd” and “sine”, still in current use, tell the same amusing tale of Western blunders about mathematics during the Toledo translations, and this linguistic confusion was accompanied by fundamental conceptual errors, which persist till today, as in the very term “trigonometry”.

Backward Westerners found it impossible to understand the infinite series of the Indian calculus, though they quickly grasped that the resulting precise “trigonometric” values were of great practical use in navigation, then the principal scientific challenge facing Europe. Thus, Descartes objected to infinite sums or “the ratios of curved and straight lines”, as he called them, stating that this was beyond the human mind[16] (presumably meaning Western mind, with which he was familiar). This objection arose from his superstitious/religious view of mathematics as “perfect”. This was superstitious for with a different philosophy of mathematics the ratio of the circumference of a circle to its diameter was easily understood by both Egyptians, and Indians since the sulba sutra-s,[17] thousands of years before Descartes. It was, in fact, taught to children in the traditional Indian syllabus in mathematics.[18]

Newton shared that religious view of mathematics, but wrongly thought he had answered Descartes' objections and made calculus “perfect”, and that this perfection could be achieved through metaphysics. Hence, in his Principia, he proclaimed that time is metaphysical and flows equably[19] (this was a regress from his teacher Barrow who gave a physical definition of equal intervals of time[20]). In fact, Newtonian physics failed just *because* Newton made time metaphysical,[21] a conceptual error arising from his misunderstanding of the Indian calculus.[22] Though Newton's fluxions[23] (and his hopelessly absurd idea of “flowing” time[24]) were eventually rejected, this Western mistake about the Indian calculus persists to this day in a modified form (as in the current representation of time by metaphysical formal “real” numbers wrongly declared essential to define the derivative with respect to time). This continues to create many other problems for present-day science as I have explained elsewhere.[25]

That is, one may properly speak of “Western mathematics” as an inferior sort of mathematics which began when the practical Indian mathematics imported into Europe was repackaged to suit some Christian superstitions. This was a needlessly complexified version of the original imported version. However, this was the mathematics the West re-exported during colonialism just by declaring it “superior”on the strength of Christian triumphalist history. We never critically examined that claim of “superiority”. Specifically, the addition of those religious and metaphysical elements added nil to the practical value of mathematics: NASA today computes the trajectories of spacecraft by numerically solving ordinary differential equations, which is what Aryabhata did.[26] Formal real numbers are irrelevant to the computer programs NASA uses, for a computer cannot handle that metaphysics of infinity, and uses a different number system.[27] This is also true of all major applications of “national importance” today. The religious superstructure that the West added to mathematics did however create enormous learning difficulties in mathematics. The student difficulties with present-day math are a direct result of those Western perplexities in understanding imported mathematics, through religious blinkers. On the principle that phylogeny is ontogeny, those difficulties are repeatedly reproduced in the present-day mathematics classroom.[28]

The demand for decolonisation of mathematics and science education[29] is, therefore, firstly a demand for a critical re-examination of Western mathematics and the science based on it. Repeat, it is a demand for a better mathematics and a better science (not merely a better pedagogy). It is also a demand for a religiously neutral mathematics[30] shorn of Christian superstitions (which superstitions also creep into science through mathematics). What stands in the way of this demand is the indoctrinated colonial mind which is incapable of a critical re-examination of the West.[31] Its first reaction inevitably is to respond to any and all criticism in stock insular ways typical of Western theologians: e.g., accuse the critic in generic terms of being a Hindu or Islamic fundamentalist (no evidence of religious affiliations needed), misrepresent the critique in equally generic ways (“Don't reject everything Western”), etc. To avoid engaging with the specifics of the critique, it then just lapses into silence, pretending that that silence itself is “superior”! The real critique is never addressed, and no Western scholar dared address the above critique of formal mathematics in the last 15 years. (Obviously, like the church, they know their beliefs would shatter into a thousand pieces if they started honestly addressing the critique.)

The inability of the colonised mind to reject anything Western, howsoever inferior, is clear from the case of the Christian ritual calendar, which is manifestly inferior, unscientific, and detrimental to our economic interests.[32] Yet the colonised elite chose to define our secular national festivals solely on that religious calendar. As theology shows, there are always a thousand ways to “save the story”—any absurd story—and defend such bad decisions. The difficulties with mathematics and science are much harder to understand, especially since most Western educated are mathematically and scientifically illiterate, and just rely on “experts”, whose expertise they judge solely on the basis of their blind faith in Western certification.

The time has clearly come to leave behind the West and its minions and move on. An alternative philosophy of mathematics called zeroism (similar to sunyavada) has been around for the last decade. Zeroism is superior to formalism in many ways. Most practical applications of mathematics today involve computation, and zeroism is ideally suited to that. (Formalism just declares that everything done on a computer is erroneous.) Again, for example, conventional limits fail for the frequentist interpretation of (Kolmogorov) probability (since relative frequency converges to probability only in a probabilistic sense), but zeroism works very well in this situation.[33]

Further examples are provided by the fundamental problem of infinities arising from discontinuous functions in physics[34] (as in Stephen Hawking's creationist pseudo-science of singularities[35] in general relativity) or the renormalization problem of quantum field theory etc., but these are more technical. However, while Western-trained academics are unable to answer this critique, they are dishonestly unwilling to admit the possibility that a fundamentally different philosophy of mathematics, divorced from Christian traditions, may be superior. Hence, they just use the theological con trick of lapsing into silence and pretending that the silence is superior. In fact, as in Indian tradition, and in the present-day legal system, failure to answer objections is proof of the validity of those objections.

Another key advantage of this new philosophy of mathematics is that it presents a religiously neutral and practical understanding of mathematics, constitutionally appropriate to a secular country like India (and indeed to any country which is not specifically Christian). This also better suits the practical applications of mathematics to commerce and science, which is the reason why most people learn mathematics. Yet another key advantage is that, by eliminating trash Western theological beliefs in present-day mathematics, it enormously simplifies the pedagogy of mathematics as I have demonstrated in teaching experiments with 8 groups in 5 universities in 3 countries.[36]

Changing mathematics, and especially the Western understanding of infinity (inevitably intertwined with the Western theology of eternity) naturally changes science as I have explained in detail elsewhere. It would take too long to explain the decolonised physics which has been constructed,[37] but decolonised courses in physics and statistics have been explicitly outlined.

As stated in the beginning, colonialism was rooted on the strength of an education system which taught blind imitation of West on the belief in Western superiority. That belief in Western superiority was based on a fraudulent history of science, a natural outgrowth of Christian triumphalist history from Orosius to Toynbee. Therefore, to uproot colonialism, it is most necessary to teach a more realistic history and philosophy of science as I recommended in my booklet on *Ending Academic Imperialism*.[38] A new curriculum on history and philosophy of science was designed, following an international workshop,[39] and I taught it in two parts to two cohorts of international students as a regular university course.[40] The students came from some 50 countries, all victims of colonialism. The announcement of the course attracted the usual generic and unsubstantiated accusations which is the only response one expects from Western “scholars” from top universities. After that silence as usual. A video interview of the students was conducted by Claude Alvares and is freely available online from Multiversity TV.[41] Alternative syllabi are also being designed for the social sciences (apart from my course on statistics for social science).

The point now is to start introducing these curricular changes into mainstream education to end for ever the horror of colonial mind capture through education.

[1] Immanuel Kant, “Of National Characteristics, so far as They Depend upon the Distinct Feeling of the Beautiful and Sublime”, in *Observations on the Feeling of the Beautiful and the Sublime*, trans. John T. Goldthwait, University of California Press, Berkeley, 1991, pp. 110–1.

[2] W. W. Rouse Ball, *A Short Account of the History of Mathematics*, Dover, New York, 1960, pp. 1–2.

[3] C. K. Raju, *Is Science Western in origin?*, Multiversity, Penang, Daanish books, Delhi, 2009. Reprint Other India Bookstore, Goa, 2014.

[4] For a re-announcement of this prize in the presence of the then Malaysian Deputy Minister of Higher Education, see the video, “Goodbye Euclid”. (Links and other details are posted at http://ckraju.net/blog/?p=63.) This prize was naturally preceded by years of attempts to persuade insular Western scholars, as described in C. K. Raju, *Euclid and Jesus: How and why the church changed mathematics and Christianity across two religious wars, *Multiversity, 2013.

[5] *Euclid and Jesus*, cited above.

[6] This is true even of the massively doctored “original”, based on Heiberg's elimination of all manuscripts except one as “Theonine” since they mention Theon, not Euclid, as the author. T. L. Heath, *The Thirteen Books of Euclid's Elements*, Dover, New York, 1956, vol. 1 (2^{nd} edn.).

[7] C. K. Raju, “Euclid and Hilbert”, chp. 1 in *Cultural Foundations of Mathematics*, Pearson Longman, 2007.

[8] C. K. Raju, *Euclid and Jesus*, cited above.

[9] Plato, *Meno*, in *Dialogues of Plato*, trans. B. Jowett, Encyclopaedia Britannica, Chicago, 1996, pp. 179–180.

[10] Proclus, *Commentary* (falsely translated title: *A Commentary on the First Book of Euclid’s Elements*), trans. Glenn R. Morrow, Princeton University Press, Princeton, New Jersey, 1970, Prologue part 1, p. 38.

[11] C. K. Raju, “The curse on 'cyclic' time”, chp. 2 in *The Eleven Pictures of Time*, Sage, 2003.

[12] The belief in “laws of nature”, is another superstition which crept from Christian theology into science. See, e.g., C. K. Raju, “Islam and science”, Keynote address at International Conference on Islam and Multiculturalism: Islam, Modern Science and Technology, Asia-Europe Institute, University of Malaya, 5-6 Jan 2013, http://www.ckraju.net/hps-aiu/Islam-and-Science-kl-paper.pdf. In *Islam and Multiculturalism: Islam, Modern Science, and Technology*, ed. Asia-Europe Institute, University of Malaya, and Waseda University, Japan, 2013, pp. 1-14.

[13] C. K. Raju, *Cultural Foundations of Mathematics: the Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16 ^{th} c. CE*, Pearson Longman, 2007.

[14] C. K. Raju, “Math wars and the epistemic divide in mathematics”, chp. 8 in *Cultural Foundations of Mathematics*, cited above. An earlier version was presented at Episteme-1, Homi Bhabha Centre, Mumbai, 2005, http://www.hbcse.tifr.res.in/episteme/episteme-1/allabs/rajuabs.pdf, and http://www.hbcse.tifr.res.in/episteme1/themes/ckraju_finalpaper.

[15] For an image of the pope's apices from a manuscript of 976 CE, see *Euclid and Jesus, *cited above*, *Fig. 11.1, p. 119.

[16] R. Descartes, *The Geometry*, trans. D. Eugene and M. L. Latham, Encyclopaedia Britannica, Chiacago 1996, Book 2, p. 544.

[17] Apastamba sulba sutra 3.2, S. N. Sen and A. K. Bag, *The Sulbasutras*, IndianNationalScienceAcademy, New Delhi, 1983. p. 103. The same thing is repeated in other sulba sutra-s e.g. Katyayana sulba sutra 2.9 See also Baudhayana sulba sutra 2.9.

[18] This can still be done, since the string is a superior substitute to the ritualistic compass box, see C. K. Raju, “Towards Equity in Math Education 2. The Indian Rope Trick” *Bharatiya Samajik Chintan* (New Series) **7 **(4) (2009) pp. 265–269. http://ckraju.net/papers/MathEducation2RopeTrick.pdf.

[19] Isaac Newton, *The Mathematical Principles of Natural Philosophy*, A. Motte’s translation revised by Florian Cajori, Encyclopedia Britannica, Chicago, 1996, p. 8.

[20] C. K. Raju, “Time: What is it That it can be Measured” *Science&Education*, **15**(6) (2006) pp. 537–551

[21] C. K. Raju, *Time: Towards a Consistent Theory*, Kluwer Academic, 1994. Fundamental Theories of Physics, vol. 65.

[22] C. K. Raju, “Retarded gravitation theory”, in: Waldyr Rodrigues Jr, Richard Kerner, Gentil O. Pires, and Carlos Pinheiro (ed.), *Sixth International School on Field Theory and Gravitation*, American Institute of Physics, New York, 2012, pp. 260-276. http://ckraju.net/papers/retarded_gravitation_theory-rio.pdf.

[23] *Cultural Foundations of Mathematics*, cited above.

[24] This is hopelessly absurd because while things may flow in time, the idea of time itself as flowing is meaningless, for it requires a time 2 in which to flow. This point was observed by Sriharsa in his Khandanakhandakhadya, and later copied by McTaggart. See, “Philosophical time”, chp. 1 in *Time: Towards a Consistent Theory*, cited earlier.

[25] A quick summary of how science changes, if math does, is in the table in the day long talk in Tehran. http://ckraju.net/papers/presentations/decolonizing-mathematics.pdf.

[26] For an account of how Euler's method (for solving ordinary differential equations) is copied from Aryabhata, see *Cultural Foundations of Mathematics*, cited above. Of course, NASA uses more sophisticated methods of numerical computation today, but the issue here is that of formal mathematics, not the sophistication of the numerical algorithm,.

[27] For example, floating point numbers do not obey the associative law for addition. A quick account of the theory is in my TV lectures on C programming, and is uploaded at http://ckraju.net/hps2-aiu/floats.pdf.

[28] “Math wars and the epistemic divide in mathematics”, cited above.

[29] C. K. Raju, “Decolonising math and science”. In *Decolonizing our Universities*, Claude Alvares and Shad Faruqi ed., Citizens International and USM, 2012, chp. 13, pp. 162-195 Video is first 34 minutes of the one at http://vimeo.com/26506961.

[30] See, the “Petition to teach religiously neutral mathematics” which has now gathered the requisite 50 signatures, http://www.ipetitions.com/petition/teach-religiously-neutral-mathematics. Also, http://ckraju.net/blog/?p=94. A related paper was presented at the ISSA meeting in AligarhMuslimUniversity.

[31] The demand is for a critical re-examination (which the Western-educated mind inevitably confounds with blanket rejection), C. K. Raju, “Be critical: choose what is best”, *The Sun*, Malaysia, 29 Aug 2011, p. 16. Clip posted at http://ckraju.net/press/2011/the-Sun-29-Aug-2011-p16-clipping-ckr-respon....

[32] C. K. Raju, “A tale of two calendars”, in *Multicultural Knowledge and the University,* ed. Claude Alvares, Multiversity, 2013, pp. 112-119. http://www.ckraju.net/hps-aiu/ckr-calendar.html.

[33] C. K. Raju, “Probability in Ancient India”, chp. 37 in *Handbook of the Philosophy of Science*, vol 7. *Philosophy of Statistics*, ed. Prasanta S. Bandyopadhyay and Malcolm R. Forster. General Editors: Dov M. Gabbay, Paul Thagard and John Woods. Elsevier, 2011, pp. 1175-1196. http://ckraju.net/papers/Probability-in-Ancient-India.pdf.

[34] C. K. Raju, “Renormalization and shocks”, appendix to *Cultural Foundation of Mathematics*, cited earlier.

[35] * Eleven Pictures of Time*, cited earlier.

[36] A partial report is in C. K. Raju, “Teaching mathematics with a different philosophy. 1: Formal mathematics as biased metaphysics.” *Science and Culture*, **77** (2011) (7-8) pp. 274-79. http://www.scienceandculture-isna.org/July-aug-2011/03%20C%20K%20Raju.pdf. “Teaching mathematics with a different philosophy. 2: Calculus without limits.” *Science and Culture*, **77** (2011) (7-8) pp. 280-86. http://www.scienceandculture-isna.org/July-aug-2011/04%20C%20K%20Raju2.pdf.

[37] A partial account is in C. K. Raju, “Functional differential equations. 1: A new paradigm in physics”, *Physics Education* (India), **29**(3), July-Sep 2013, Article 1. http://physedu.in/uploads/publication/11/200/29.3.1FDEs-in-physics-part-..., and “Functional differential equations. 2: The classical hydrogen atom”, *Physics Education* (India), **29**(3), July-Sep 2013, Article 2. http://physedu.in/uploads/publication/11/201/29.3.2FDEs-in-physics-part-....

[38] C. K. Raju, *Ending academic imperialism*, Multiversity and Citizens International, Penang, 2011. http://multiworldindia.org/wp-content/uploads/2010/05/ckr-Tehran-talk-on.... Video at http://www.youtube.com/watch?v=zdvgH4gByfk.

[40] The formal curricula and lectures for the two courses are posted at http://ckraju.net/hps-aiu and http://ckraju.net/hps2-aiu/ . See also http://ckraju.net/blog/?p=89.

[41] See part 5 of the video series, links to which are posted at http://ckraju.net/blog/?p=73.