C. K. Raju

Mathematics is
compulsorily taught in school to millions each year. Therefore, it
sets a very healthy democratic precedent to decide the nature of math
education by a public debate which James Glover has initiated in his
response (*Hindu*, 15 October) to my article (*Hindu*, 3
September) on “Nothing Vedic in Vedic math”.

The claim that “It
is ancient, hence Vedic” holds no water. For, how do we *know*
it is ancient? Our actual source is a modern one: Krishna Tirtha. He
never produced the relevant
parishishta, even when challenged to do so by the late Kripa
Shankar Shukla. How strange that not a single mathematician from
Baudhayana, Aryabhata, Brahmagupta, Bhaskara, Varahamihira,
Vatesvara, Uday Diwakar, Parameswaran, Madhava, to Nilkantha noticed
or commented on these aphorisms for over two thousand years. Such
faith-based history—based solely on the word of one
person—should be clearly separated from history based on
evidence. Else we only damage the credibility of the glorious
history of mathematics in India, for which there *is* solid
evidence.

Second, if *everything*
ancient is Vedic, what about the *anatmavada* of Buddhists or
Carvak? Accepting the denial of *atman* as “Vedic”
knowledge damages the core philosophy of the Upanishads. Thus,
stretching the meaning of the word “Vedic”, just to save
Krishna Tirtha's story, has disastrous implications for Hinduism.
Hence, that quibble about the meaning of “Vedic” should
be rejected.

Besides, why is that label “Vedic” important? Is Vedic math to be taught because of the label “Vedic” or because of its practical value? If the latter, the misleading label “Vedic” should be gracefully dropped. If the former, or both, that would be a religious imposition.

A recent petition, signed by fifty people, addressed to top educational administrators, asks that mathematics should be taught in school only for its practical uses, and in a religiously neutral way. India is secular; therefore, religious propaganda should not be slipped into state-controlled education, even under the cover of its correlated practical value. Decisions on such issues concerning a vast mass of people should not be taken behind closed doors, just by some people designated “experts”. These “experts” must declare any conflict of interests, and publicly explain the reasons for their decisions.

A cocktail of practical
value and religious propaganda can have obnoxious consequences. Post
colonisation, math teaching in India blindly apes Western practices.
That is a pity because most of that school mathematics (arithmetic,
algebra, “trigonometry”, calculus, and probability),
actually originated in India for its practical value. Europeans
imported it also for its practical value. However, contrary to
popular belief, the understanding of mathematics is *not *universal.
Indian *ganita* accepted empirical proofs. This differed from
the European understanding of math as metaphysics. Hence, over
centuries, the West adapted the imported Indian math to fit their
metaphysics, linked to church theology. During colonisation, it
exported back this religiously coated mathematics, which is now
taught globally. That metaphysical veneer is irrelevant to the
practical applications of math, but instills religious biases in
millions who learn math for its practical applications.

What exactly are those
religious dogmas in Western mathematics? The very word mathematics
derives from “mathesis” which means learning. In Plato's
*Meno*, Socrates demonstrates an untutored slave boy's innate
knowledge of mathematics. He then argues that, since the boy did not
learn mathematics in this life, he must have learnt it in a previous
life, so he has proved the existence of the soul! Socrates concludes
that all “learning” involves the soul recollecting its
eternal ideas. In Plato's *Republic*, he rejects the teaching of
mathematics for its practical value, but prescribes it on the grounds
that it is spiritually uplifting, like music. That notion of soul
was, however, cursed by the post-Nicene church; how the links of
religious belief to Western mathematics evolved subsequently is a
complex story told for the layperson in my book *Euclid and Jesus:
How and why the church changed mathematics and Christianity across
two religious wars*.

Mathematics was considered especially suited to arouse the eternal soul since it was believed that mathematics contains eternal truths, and “like arouses like”. The belief in eternal truths, in turn, led to the Western belief that mathematics is “perfect”, and cannot tolerate the smallest error (for it would be exposed sometime during eternity). It was further thought that this perfection could be achieved only through metaphysics and not empirically: a real dot on a piece of paper can never be a “perfect” mathematical point howsoever much one may sharpen the pencil! Today, mathematics is 100% metaphysics on the philosophy of mathematics known as formalism, initiated by Bertrand Russell and others, and used to teach math in our schools and universities.

The belief
that math is perfect is certainly *not*
universal: Indian tradition accepted mathematics as non-eternal, and
imperfect. The *sulba sutra*-s
explicitly speak of *anitya*
(impermanent) or *savisesa*
(with something left out), and Aryabhata speaks of *asanna*
(near value), while Nilakantha explains why the “real value”
(*vastavim samkhya*)
cannot be given. Tiny imperfections are inevitable and of little
consequence for the practical applications of math. Most practical
applications of mathematics today, such as sending a spacecraft to
Mars, are done using computers which do math “imperfectly”.

Other
aspects of Western metaphysics too are not universal. For example, on
post-Crusade church theology, logic binds God but facts don't. That
is, God cannot create an illogical world, but can create the facts
of his choice. Hence the Western belief that logical (deductive)
proofs which bind God are “stronger” than empirical
proofs which don't. But *which*
logic binds God? Contrary to naïve Western beliefs, logic and
reasoning are *not*
universal. Buddhist *catuskoti*
or Jain *syadvada* are
systems of logic which are not 2-valued (or even truth-functional),
so teaching 2-valued logic as “universal” involves a
religious bias. To avoid this bias, one can possibly choose logic on
empirical grounds, but that would destroy the very basis of
formalism that logical proofs are superior to empirical proofs.

Teaching
Western metaphysics spreads other biases. All systems of Indian
philosophy, without any exception, accept the *pratyaksa*,
or empirically manifest, as the first means of proof. This also
applies to *ganita*,
e.g. Aryabhata declares that verticality is tested by a plumb line.
Science and engineering, too, prefer empirical proofs to metaphysics.
So if math is done for its practical applications it is better to
accept empirical proofs in math. But present-day math teaches that
such proofs, hence all Indian philosophy, is “inferior”.
This is like compulsorily teaching Lokayata which rejects *anumana*
(inference) as fallible, and would hence dismiss all Western
philosophy as inferior.

Does any
of this make a difference to 2+2=4? Yes. *Why*
is 2+2=4? Putting together two pairs of apples to show four apples is
*erroneous* on formalism
which disallows reference to the empirical. Formalism posits that
2+2=4 can be “rigorously” deduced only metaphysically
from, say, Peano's axioms. Most people don't know how to do that or
even what Peano's axioms are. Thus, most Western educated never even
properly learn 2+2=4! Since they are taught alongside that all other
systems are inferior, they are compelled to rely blindly on Western
authority for every little thing. This is by design. To put an end to
this mental enslavement through indoctrination, education must be
decolonised. India lags behind in decolonisation of education, and
the new government ought to focus on that.