Mathematics research status in India I am an Indian student. I am not related to any kind of mathematics research. So I do not have proper idea about it. I may join in as a PhD after a few months. I want to get a picture of the research status in India.

India has several mathematics research centres, institutions and universities. I want to know the status of mathematics research in India. How many and which of them are of international standard? What about the impact factor of their mathematics publication? What is the status of computer science, which is almost neglected by Indian Mathematicians. Is my idea true? I know that none of our institutions and universities in top 200 of the world ranking. Please give me some idea on it and sufficient resource so that I can convince myself.

Suppose I have completed a PhD in India. Will it be accepted internationally. When? Why and Why not?
You have a lot of questions all interspersed within your question block so I will try my best to answer. Here is a disclaimer:

Disclaimer: I am a past graduate student of the Indian Statistical Institute

Mathematics research, especially in theory, is pretty good in India. The top institutions (in no order of ranking) are:


Indian Institute of Science, Bangalore
Indian Statistical Institute (Kolkata, Delhi, Bangalore, Chennai)
Tata Institute of Fundamental Research (Mumbai, Bangalore)
Indian Institute of Technology (KGP, Kanpur, Delhi, Mumbai, Chennai)
Institute of Mathematical Sciences, Chennai
Chennai Mathematical Institute, Chennai


All of these are quite good internationally and attract the best Indian students. The entrance exams are quite tough and many of the BS, MS students go on to do PhDs in top world institutions. Those who stay, are also quite good and publish papers in the usual top journals. The problem is neither funding nor red tape in my opinion. 

The problem is that compared to most "top" mathematics departments, these institutes are rather small (i.e. ISI Bangalore had ~only 20 full time faculty in my time and of those, 10 published regularly). You see, its only in recent years, that regular publications have become quite the norm and its usually being driven by younger faculty (usually those who have done their PhDs from US or Europe).

Please see him, him and him for reference in theory and on the applied, computing side, him [He is my MS thesis adviser] This is one small example from one school. I can assure you that the situation is similar in the other schools that I mentioned.

Most Indian PhDs go on to do postdocs internationally. Why just last year, we had a postdoc (who finished his PhD in ISI Kolkata and was joining IIT Bombay this year) in the ML lab here. He was great and very smart.

In conclusion, if you get a PhD in Mathematics in India and do good research while you are at it, I don't see why you shouldn't get international postdocs. Tenure track job positions will be restricted to the Indian subcontinent and south east Asia because USA and Europe have their own PhD glut problem. But, thats cool because most of these schools I mentioned are hiring very well. In fact, I plan to apply for several tenure track positions in CS departments in India when I graduate.