C. K. Raju
Indian Institute of Advanced Study, Rashtrapati Nivas, Shimla 171 005
Mathematics is NOT universal. Indian ganita was practical, hence accepted facts, and empirical proofs, as does science. But Western mathematics was religiously oriented, since Pythagoreans and Plato who explicitly related math to mathesis and the soul, and declared this religious math to be “superior” to practically-oriented math.
church transformed this religious understanding of math in two ways.
During the Crusades, it (a) accepted “reason”, as part of
Christian theology (mimicking Islamic rational theology). Its aim was
to use “universal”
reason to convert Muslims (who accepted reason, or aql, but rejected the Bible as corrupted). It reinterpreted a (Neoplatonic) math text to to declare that math was solely about the immediate church requirement of using “universal” reason for persuasive proofs (to convert Muslims), and used this text (“Euclid”) to teach reasoning to its priests (e.g. in Cambridge). Further, the church (b) rejected facts as “inferior” to un-testable (metaphysical) axioms, to save its numerous dogmas which were contrary to facts. Few understand the confusing church doublespeak about “reason” (meaning “reason minus facts”), commonly confounded with “reason” in the usual sense of “reason plus facts”. In fact, ganita (normal math, reason plus facts) differs from Western math (formal math, reason minus facts).
The church allied with the colonial state to conquer colonised minds through colonial education: its key propaganda was about Western “superiority” and non-Western “inferiority”. Hence, colonial education propagated the myth of “Euclid” and his axiomatic proofs declared “superior” and infallible. However, there is nil evidence for Euclid. There is ample counter-evidence that “Euclid’s” Elements was a book by another author from another time written for a different reason (it was a Neoplatonic book on math as mathesis). And the fact is that the Elements does not contain a single properly axiomatic proof: contrary to what ALL Western scholars superstitiously believed for centuries, under church tutelage. When the absence of axiomatic proofs in “Euclid” was finally admitted, B. Russell and D. Hilbert rewrote the Elements to fit the facts to church myth and superstitions, and invented formal math. Today, our NCERT still teaches Western formal math to children on (1) the myth of Euclid, and (2) the church superstition that axiomatic (“deductive”) proofs are “superior” to proofs based on facts. Few understand that this metaphysics makes math difficult without adding to its practical value: they just ignorantly imitate what they believe to be “superior”.
The correct response is (1) to keep demanding primary evidence for these church myths, and (2) to PUBLICLY debate on (or demand elimination of) the church superstitions packaged with (colonial) math teaching today, and (3) to teach math strictly for its practical value, setting aside all bogus claims of superiority since Plato. Geometry teaching in schools can be changed back to normal math; this is practically advantageous, and easily possible. A textbook (Rajju Ganita) is ready, even at the school level, as the next talk will explain. (The calculus too can be taught without the metaphysics of limits, and that benefits science, but that is another story.)
C. K. Raju, Euclid and Jesus: how and why the church changed mathematics and Christianity across two religious wars, Multiversity, Penang, 2012.
C. K. Raju, “Eternity and Infinity: the Western misunderstanding of Indian mathematics and its consequences for science today”, American Philosophical Association, Newsletter on Asian and Asian-American Philosophies, 14(2) (2015) pp. 27-33. http://ckraju.net/papers/Eternity-and-infinity-Pages-from-APA.pdf.
C. K. Raju, “Decolonising mathematics” (why deduction is MORE fallible than induction), AlterNation 25(2) pp. 12-43b. https://doi.org/10.29086/2519-5476/2018/v25n2a2. Based on a keynote address at the 11th Higher Education Conference, University of Kwazulu Natal, Durban, 2017, video at https://www.youtube.com/watch?v=cpS6MfzJr2E.
Abstract for first of #Srijan Talks, Delhi, 23 Nov 2019.