it makes math so easy so why don't we teach it?

C. K. Raju

*Indian
Institute of Advanced Study, Rashtrapati Nivas, Shimla 171005*

**Summary**

Did you find math
difficult? In this non-technical talk, I will explain why math became
difficult and how to correct it.

Briefly, it is not
because we teach math wrongly but because we teach the *wrong math*.
We are proud of ancient Indian mathematics, but do not teach it
today. Why not? Because colonial/church education changed our math
teaching. It indoctrinates the student to believe that everything
non-Western is inferior, and everything Western must be blindly
imitated. Hence, we never critically compared ancient Indian math
with current formal math to decide which is actually
better.

Ironically, most present-day school
math—arithmetic, algebra, trigonometry, calculus, probability
and statistics—was transmitted from India to Europe between the
10^{th} to the 16^{th} c. Since Europeans, then, were
backward in math, they struggled for centuries to understand even the
arithmetic algorithms, today taught in primary school. Especially,
the Indian calculus and its infinite series did not fit the European
(religious) belief that mathematics is exact (since eternal truth).
Hence, they invented a metaphysics of infinity (formal real numbers,
formal set theory) to make formal math exact in a fantasy world. This
was declared “superior” and given back to us through
colonial education. The added metaphysics has nil practical value,
and all practical value of math still comes from the original normal
math, or inexact calculations in the real world, as done in ancient
India, or as today done on a computer. But the added metaphysics
makes even 1+1=2 enormously difficult: so difficult that Russell
needed 378 pages to prove it.

Math becomes very
easy if we revert to the original. I will explain this with examples
from (a) my geometry school text for class 9, *Rajju Ganita*,
and (b) my university-level course on calculus without limits. Making
math easier *adds *to practical value: it enables students to
solve harder problems, as has been demonstrated in pedagogical
experiments over the last decade. (It also improves science, but that
is another story.) So, why don't we teach it?

**About
the author**

Professor
C. K. Raju holds an honours
degree in physics, an MSc in math from Mumbai, and a PhD from the
Indian Statistical Institute. He taught and researched in formal math
(real analysis, advanced functional analysis) at Pune University for
several years, before playing a lead role in the C-DAC team which
built the first Indian supercomputer, Param. In *Time:
Towards a Consistent Theory *(Kluwer, 1994) he proposed a new
physics, using functional differential equations. In *Cultural
Foundations of Mathematics* (Pearson Longman, 2007) he proposed a
new philosophy of math, now called zeroism, and compiled evidence for
the origin of calculus in India and its transmission to Europe, where
it was misunderstood. In the *Eleven Pictures of Time* (Sage,
2003) he proposed a new way to relate science and religion through
time perceptions. In 2010 he received the TGA Award in Hungary. He
has developed and taught decolonised courses on math, and the history
and philosophy of science, in three countries. His school text, *Rajju
Ganita*, aims to show how the geometry of the śulba-sūtra
can be effectively taught in school today. He is currently a Tagore
Fellow at the IIAS, Shimla, and an Honorary Professor at the Indian
Institute of Education.

(Talk at Environmental Science Department, Pune University: 11 Oct 2019, 4 pm. See map at http://www.unipune.ac.in/university_files/campus_map.htm. )