Some identities of Monishwaran Maheswaran

During the summer of 2017, Monishwaran Maheswaran showed me some amazing mathematical identities. He found them experimentally and shared them with me over the course of the summer. They show extraordinary creativity and talent to find new structure. Monishwaran is currently a high school student in India. He took some engineering class at the Harvard summer school.

Here is a draft of Minishwaran with some of this theorems of August, 2017:
Photo of July 31, 2017. Monish explaining an identity on the blackboard. Below is my writeup of some of the theorems found by Monishwaran.