### Mathematics in ancient India and its contemporary applications: 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 10th to the 16th 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?