This grievance concerns the 9th standard mathematics textbook produced by the National Council of Educational Research and Training (NCERT). The present grievance is restricted to chapter 5 of that text titled “Euclid’s geometry”, available in electronic form at http://ncert.nic.in/textbook/textbook.htm?iemh1=5-15, and related material (Appendix 1) in this and the NCERT class 6 mathematics text.
Mathematics is a compulsory subject at the level of class 9, and the text is prescribed for students across India. Hence, the NCERT must ensure the accuracy of the texts. However, the said chapter is grossly inaccurate, and involves numerous lies.
A detailed note is posted online at http://ckraju.net/geometry/NCERT-grievance-detailed-note.pdf.
FALSEHOOD 1: NO EUCLID
Chapter 5 of the class 9 math text is titled “Euclid’s geometry”, but there is no evidence that “Euclid” existed. The NCERT has been made aware of this since 2007, and a prize of Rs 2 lakhs been publicly offered for serious evidence about Euclid. The NCERT has no evidence, and denies the need for evidence, hence does not change the text. In effect this amounts to insisting that all Indian school children MUST believe without questioning, which was a goal of colonial education. NCERT must (a) either supply evidence, or (b) change the school text, or (c) make public its policy of demanding blind belief.
FALSEHOOD 2. “ONLY GREEKS USED REASONING”. NO. INDIANS TOO USED REASONING
The NCERT text says that though everyone did geometry, in all the world only Greeks used reasoning. This is false. Indians too used reasoning, and reasoning was explicitly accepted by most schools of Indian philosophy. Indian mathematicians deduced the earth was round. Children must be taught the truth.
FALSEHOOD 3. “GREEKS GAVE AXIOMATIC (PURE DEDUCTIVE) PROOFS OR USED REASONING IN A SPECIAL WAY AS IN PRESENT-DAY FORMAL MATHEMATICS”
Greeks did NOT give any proofs in the manner of present-day formal mathematical proofs which exclude the empirical. Specifically, propositions 1 and 4 of ‘Euclid’s’ Elements involve empirical proofs, and the proof of proposition 47 (“Pythagorean theorem”) depends on these. Hence, there is not a single axiomatic proof in it. Children must be told the truth.
FALSEHOOD 4. “FORMAL (AXIOMATIC) MATHEMATICAL PROOFS ARE SUPERIOR: DEDUCTION IS SUPERIOR TO INDUCTION, DEDUCTIVE PROOFS ARE SUPERIOR TO EMPIRICAL PROOFS”
This is false and contrary to elementary common sense. Deductive proofs are always inferior to inductive or empirical proofs. This has been most recently explained in detail in the article on Decolonising mathematics, in AlterNation 25(2) 2018, pp. 12-43b, https://doi.org/10.29086/2519-5476/2018/v25n2a2. This church superstition is the basis of formal mathematics.
FALSEHOOD 5. HIDING THE CHURCH CONNECTION
The attribution to Greeks hides the church connection. The church regarded early Greeks as its sole friends, and church history claimed that most knowledge was due to Christians and friends (the Greeks).
Since church dogmas shatter against facts, the church glorified the prohibition of facts, and metaphysical or faith-based reasoning as “superior” to fact-based reasoning. Since persuasion (for conversion) was the sole concern of the church, it reinterpreted Greek works on geometry as having the same intent. Actually, the (Neoplatonic) “Greeks” said mathematics was a way to arouse the soul (which involved a notion of soul cursed by the church).
A HOTCH-POTCH OF INCOMPATIBLE GEOMETRIES
The NCERT texts hence teach a hotch-potch of distinct and mutually contradictory geometries such as (1) church religious geometry falsely attributed to “Euclid”, (2) Hilbert’s synthetic geometry, (3) Birkhoff’s axiomatic metric geometry, and (4) compass-box geometry which is empirical and metric. Instead NCERT should teach a single coherent system of (empirical) geometry of practical value.
THE ALTERNATIVE
The rope used in traditional Indian geometry is superior to the geometry box.
C. K. Raju