Dividing without dividing, the Bakhshali Manuscript, some Babylonian mathematics, and the Newton-Raphson Method

This talk will require only 12th-grade mathematics. The modern Newton-Raphson method can be derived using the concept of “the derivative” and simple algebra. We travel to many places when we apply this method to simple functions. However, we will dive only into three such realms.

Firstly, we will see how modern computers use the method to divide. Learning to divide means being able to divide without dividing.

Secondly, the Bakhshali Manuscript, one of the most important documents in the history of mathematics, uses an algorithm suggested by this method.

Lastly, the Babylonian mathematicians also unknowingly used this method to compute.

The talk blends history, mathematics, and applications.

Pre-reqs to enjoy the talk are:

The derivative of 1/x is -1/x^2.
The derivative of x^2 is 2x.

But these are not really needed!

This talk will be delivered by Dr. Sarmad Abbasi.

Some useful resources for the lecture

1. The Bakhshali Manuscript:
https://www.ams.org/publicoutreach/feature-column/fc-2018-06

2. The Babylonian method:
https://www.cantorsparadise.com/a-modern-look-at-square-roots-in-the-babylonian-way-ccd48a5e8716

3. A Nature article on finding square roots:
https://www.nature.com/articles/s41598-022-25039-y