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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 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. I my idea true? I know none of our institutions and universities in top 200 of the world ranking. Please give me some idea on it and sufficient resource such that I can make me convince.

Suppose I have completed a PhD in India. Will it be accepted internationally. When? Why and Why not?

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Are you interested in pure math or applied math? –  Faheem Mitha Feb 14 at 18:05
    
M.Sc. in applied mathematics. I have no proper answer, as I not concentrated in a single part. –  Dutta Feb 15 at 2:31

3 Answers 3

up vote 9 down vote accepted

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:

  1. Indian Institute of Science, Bangalore
  2. Indian Statistical Institute (Kolkata, Delhi, Bangalore, Chennai)
  3. Tata Institute of Fundamental Research (Mumbai, Bangalore)
  4. Indian Institute of Technology (KGP, Kanpur, Delhi, Mumbai, Chennai)
  5. Institute of Mathematical Sciences, Chennai
  6. 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.

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Bright sides of the bright institutions are written properly. Some of bright proofs are shown. But sometimes I have seen empty list of publications of professors of those top institutions. They are maximum in number. Can you explain it. Next those institutions except IITs accepts vary less number of applicants (it is single digited always, but number of applicant is triple digited at least). I do not kow why. –  Dutta Feb 15 at 2:42
    
There are multiple reasons for this. First, professors may not update their websites regularly. This can be mitigated by searching in google scholar. Second, some old professors only teach and don't do research. This is rare-ish in the top schools but present. The younger crop is usually excellent at research communication and publication. –  Shion Feb 15 at 3:43

In terms of information, I doubt I can improve on Shion's answer. However, I'll add some comments.

First, a disclaimer. I don't know much about Indian academia, but I was a grad student in math for a while, a long time ago, at TIFR. It did not go well. I also know (knew, perhaps) a fair number of Indians who doing research mathematics.

First India nominally has a lot of universities. However, the vast majority of them are not research universities. At least in mathematics, my impression is that most of them don't count for much on an international research scale. That, of course, does not necessarily mean you will get a bad mathematical education there. It all depends on personal experience, including ones advisor (sometimes out of the way places have good research people), the local atmosphere, plus the internet, with sites like mathoverflow, is definitely having a levelling effect.

In any case, the important places for mathematics, as Shion says, are the handful of (mostly government sponsored) research institutes. There are also the various IITs, which do have math departments, which for the most part are better than the "regular" universities, and probably not as good as the research institutes.

If you go to study at the research institutes, I think you can get quite a good mathematics education there. I don't think it is any worse than the education you would get at a good Western university, and in some ways it may be better. For one, thing you will experience less distractions. See below. For example, the School of Maths at TIFR was, and I expect still is, quite a high powered research place, and has good connections with the international research community. There are regular visitors from abroad to give talks and visit. TIFR Faculty travel abroad freqently on visits, giving talks, taking sabbaticals and so on.

However, some caveats.

First, as Shion says, they are mostly smaller places (though I think the TIFR school of maths is quite substantial). Second, as a math student, you are likely to find yourself extremely socially isolated. These places pay very badly, regardless how good a mathematical education they impart. They also tend to be located in expensive metropolitan areas. For example, the TIFR is located at the tip of South Bombay. Bombay is possibly the most expensive place in India. You won't have enough money to do much of anything. Plus, of course, you'll be very busy studying.

These institutes are additionally typically not part of a university campus, so you aren't surrounded by the considerable variety of people and happenings you experience in a regular university environment. You'll be stuck with your fellow students, postdocs and faculty, for the most part.

These issues are to some extent true of a mathematics student anywhere, but they are, in my opinion, more extreme in India. I was a grad student in the US, and it was not nearly so isolated.

There are some advantages for an Indian citizen to being in an Indian research institute as opposed to say a European or US university, however. First, you won't have to put up with being treated like a third-class citizen, and being constantly pushed around by government and university bureaucracy. Second, you'll have all the time in the world to do your research. Indian research institutes, unlike Western universities, don't bother their students with things like teaching duties. Since they aren't regular universities for the most part, they don't have much by way of students anyway. There will probably be opportunities to teach courses if you want, though, if only at neighboring colleges.

So, to summarize if you don't mind going years at a stretch doing not much but study maths, you'll be fine.

A final word about areas represented. I think the math research institutes skew heavily towards theory. I think there is some CS, but again theoretical. The TIFR for example is entirely theoretical, though I believe there are some people there who do consulting. My impression is that the IITs are more applied. If you are interested in things like machine learning, those might be better places to look at. Areas like statistics are also poorly represented. There is ISI, but not much of anything else at the level of statistics graduate study.

Some of this may be factually inaccurate. I am sure some of it is biased. Factual corrections appreciated; I am always happy to learn.

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Just one note. PhD students (or junior/senior research fellows as they are called in India) are quite well paid now after a recent salary shuffle. This makes the cost of living quite manageable. Usually, you will also live on campus in hostels - the costs of which are either included or negligible in many of these places. –  Shion Feb 14 at 20:26
    
@Shion Can you give approximate pay ranges for PhD students? Thanks for the comment. –  Faheem Mitha Feb 14 at 20:50
    
It starts from Rs. 16000 a month. –  Dutta Feb 15 at 2:43
    
"you won't have to put up with being treated like a third-class citizen, and being constantly pushed around by government and university bureaucracy": I am an Indian citizen studying pure math in the US (through college, grad school, and soon a postdoc), and while there are some number of hoops to jump through I would definitely not go so far as to say that I have been treated like a "third class citizen", although I expect that some of this has been due to my undergraduate education in the US. –  Aru Ray Feb 15 at 6:18
    
In addition, teaching experience (at least some teaching experience) is essential if you are looking for a postdoc/faculty position at a US university (presumably UK/European as well), certainly in mathematics. –  Aru Ray Feb 15 at 6:22

This may be institution dependent rather than "country dependent". If the university or other institution publishes a lot of international publications, these works will probably be known for the foreign scientists reviewing your potential future application (they must be competent in the area!). In other words, you need to care more about the status of your institution, laboratory and supervisor rather than about the general status of the country.

It is possible to see problematic laboratories and unsuccessful research projects everywhere. No country is protected.

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Thank you for your interest. A developed country may had a bad university and a good university may be located in the third world. So as a student one should consider the status of the university. I was trying to compare the status of mathematics in India and in other countries. –  Dutta Feb 17 at 15:13

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