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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.

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    Migration from India to the US/UK is not specific to math PhD students and I imagine the reasons are also not specific. – Thomas Nov 5 '18 at 2:09
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    @Thomas Well in other fields, I can understand, the first world has better labs, facilities, infrastructure etc. But pure mathematics is immune to these factors. What causes theoretical mathematicians to leave these exceptionally good schools is beyond my comprehension. – yasir Nov 5 '18 at 2:12
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    Prestige and international name recognition matter in academia. No one looks to universities in India and allows them the same prestige internationally as Harvard, Stanford, Princeton, Oxford, etc. – Vladhagen Nov 5 '18 at 5:06
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Disclaimer: I'm European student at decent Math PhD program in the US.

Sorry, but it seems that I'm going to disillusion you...

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

Although I don't doubt that India have a couple of decent universities with relatively strong mathematics department, they are by no means "at par with the elite US universities". If they really were, I would expect crowds of applicants both from prospective grad students and faculty from Europe and North America to study/work there, but in fact there is quite opposite trend. You have mentioned "topmost schools like IISc, IISER's, TIFR", but without prior web searching I have absolutely no idea what all these abbreviations mean. The same true for overall level of Indian born mathematicians -- they are simply not on par with US, France, Russia and UK in math, just check recent and overall numbers of Fields medalists and ICM speakers. Please do not take it like something offensive, but realizing that is essentially an answer to your question.

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?

Just in my opinion, they lack

  • Transferable degree recognition and world renowned top notch researchers like I tried to elaborate above, that is crucial for graduate school, because grad school is essentially about research.
  • Job prospects after graduation. It goes without saying that Europe and especially North America region (US + Canada) have more attractive job market both in terms of available positions, research prospects and salary than India. In general relocating to grad school is easier than relocating to postdoc or faculty position, this is why Indian students willing to have a shot at American or European job market trying to get in local grad schools.
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    Although I appreciate your criticism, I feel some ignorance on your part. The sheer fact that IISc is unheard for you speaks for itself. It is the top research institute of India numbered 11 in terms of citations all over the world. I put this question just to look for the gaps Indian grad schools have and your second answer is spot on. And the fact about field medalists is also true. There has been no Indian recepient of Fields medal till date. – yasir Nov 5 '18 at 1:53
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    There are aspects of this answer that are probably correct, but overall it seems to jump to conclusions (no references) and be a unnecessarily harsh. – Thomas Nov 5 '18 at 2:01
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    I too have never heard of any of the "top tier" Indian universities. Had to Google search for meanings. – Vladhagen Nov 5 '18 at 5:07
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    Your claim about the overall level of Indian-born mathematicians seems much more arguable than the overall prestige of Indian institutions. (Fields medalists are a very small sample.) And it's not relevant to the question being asked. Other than that point, I agree with this answer. – user37208 Nov 5 '18 at 15:11
  • I had certainly heard of TIFR before (though not the acronym) from their research reputation. – Noah Snyder Nov 6 '18 at 13:34
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Though I have more knowledge of the Physics scene, the most important thing for research is not "physical" (facilities, salary etc), but having access to a strong, open, inclusive, active and sufficiently numbered community of grad students, post docs, professors, researchers and visitors. You learn from people around you.

In India, this is definitely not comparable to the top in the world. Do you know that there have been times when TIFR has not taken a single grad student for Math?(Was informed by existing math grad students on these facts). What does this say? How do you get a community then?

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I think you are wildly underestimating how strong the top US/UK universities are.

TIFR is a strong math department. For example, it looks like they have around one ICM invited speaker per ICM and most faculty publish regularly in top-20 journals. On the other hand, there are no Fields medalists or comparably famous people (in fact, no one whose research I was aware of before looking them up, though that might be reflective more on me or my field), and most faculty don't have publications in the top 5 journals. From this data it seems to me like they are comparable to a US math department ranked somewhere between 30-80. (I hesitate to try to nail it down further because I'm just not that knowledgeable about their department, and because rankings are pretty subjective anyway. Plus the lack of teaching at TIFR means faculty have more time for research.) But they are pretty obviously not comparable in research profile to a top 10 US math department, where typical faculty are publishing frequently in top 5 journals and many are famous at the level of Fields medalists.

As far as I can tell all the other universities in India combined had only a handful of ICM speakers in the last 16 years. I looked at a random other university you listed, and people are doing good research but they don't seem comparable to Tata Institute or to top 50 US math departments.

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I can not answer the specific question about Indian students, but I can give some perspective related to Russia, and some bits of my answer may also apply to your situation.

As you may know, Soviet Union had a strong reputation for the quality of its education and research in physics and mathematics. After the collapse of USSR, Russia inherited the majority of academic institutions and research groups.

The next thirty years are the story of almost continuous brain drain, with a lot of groups and individual researchers leaving Russia for the US, UK, EU, China, etc. Obviously, government is trying to keep people by raising salaries and providing research grants, and in some places the funding is on par with US standards.

However, what modern Russia lacks is stability. Government initiatives are usually a short-term response to a certain political situation. There is a strong feeling that the priorities may change and financial support can be re-directed to other areas of economy. Also, there is a fair amount of corruption, nepotism and sexism in Russian academia, making it less attractive and forcing some students / young researchers to seek luck elsewhere.

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    Quite a lot of the brain drain that Russia and other Soviet countries faced was due to Jewish intellectuals leaving at the first opportunity available. Similarly many people who had any options to leave satellite countries (Czechoslovakia, say, as my advisor did) tried to flee ahead of various invasions. It left behind a gap that isn't easy to fill. I taught a lot of Russian students, mostly Jewish, and found them uniformly very smart, though not always as hard working as they might have been. Another effect of the Soviet system, perhaps. Not the same problem that India might face. – Buffy Nov 6 '18 at 13:59
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    @Buffy Partly true, but brain drain was (and remains) a continuous process, and the effect goes far beyond a couple of years right after the collapse. – Dmitry Savostyanov Nov 6 '18 at 18:18

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