I am currently a senior year student at Hansraj College, University of Delhi. I have completed my 2-month summer internship at IISc Bangalore recently. During my stay, I got to interact with a lot of Pure Mathematics Ph.D. students. I have come to know lately that many BS and MS students leave even the topmost schools like IISc, IISER's, TIFR etc and go for Ph.D. in pure Mathematics abroad.

Although the standard of research in pure Maths is pretty good in India. See this post here

I have the following questions and some associated assumptions/facts:

Question 1. So, why do these top students leave these exceptionally good schools that are almost at par with the elite US universities for a Ph.D. in Pure Maths?

Assumption 1. Since they were already a part of the school, it is unlikely that the small department size is a factor behind this. However, unlike US schools, TA's are not common in India.

Assumption 2. The recent pay increase should have improved the financial situation as well.

Question 2. What is something that Indian grad schools lack when it comes to theoretical Mathematics or in general that drives students out of India?

I am going for a Ph.D. soon, so I think this is something I should know.

Thank you.