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While searching for universities to do my Ph.D. in mathematics, I noticed that most top universities in India use incredibly competitive entrance exams (much more difficult and time constrained than the GRE/TOEFL/Subject GRE) and only after you've cleared those and based on your ranking in those do they ask you to provide them the transcripts, recommendation letters, Statement of Purpose etc. indicating that the results of those (mostly objective) entrance exams are considered more important than the other three components of your application, mentioned above. The exam is usually followed by an in person interview which is equally rigorous. Even if they don't conduct the exam themselves, they rely on some other national level entrance exam as a screening tool and/or as a way to create a merit list to offer admissions.

However, in the US and most of Europe (I suppose) universities only require you to have done well in some (comparatively) easy exams like the GRE/TOEFL/Subject GRE and many even waive that requirement off. A university there using their own entrance exams and interviews as a screening process is unheard of and the admission decisions are made based on transcripts, recommendation letters, Statement of Purpose etc. The qualifying exams before one is allowed to officially begin their Ph.D. allow a couple of years of preparation thorough coursework in the university and though tough, I think they allow some flexibility in terms of when the student wants to take the exam and what electives he's opted for. Even if one fails to clear these exams some universities allow the student to terminate the program early after the coursework with just a master's degree. (I'm not 100% sure about the last few sentences.)

My question is that what are the possible reasons for such a drastic difference in the admission process?

ZSMJ
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    See this canonical question, which, unfortunately, doesn't yet include India: https://academia.stackexchange.com/q/176908/75368. In particular, admission in the US isn't by exam. – Buffy Sep 27 '22 at 14:39
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    If you have a lot of knowledge about doctoral admissions in India, I suggest you supply an answer to that question with the process (processes?) used in India. – Buffy Sep 27 '22 at 14:42
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    I don't know if the situation now is much changed from when I applied to graduate programs (several times in the 1980s), but the GRE and GRE subject tests were mainly hurdles that anyone reasonably competent would clear and they were primarily used for the awarding of university department (not national, such as NSF grants) merit scholarships, especially in lower ranked universities. I also don't recall anyone paying attention to them (such as actually preparing/studying for the tests) other than showing up at the appropriate time, at least among the (possibly atypical) students I knew. – Dave L Renfro Sep 27 '22 at 14:57
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    As far as I can tell, it's a cultural difference. India seems incredibly scared of processes that allow individual decision making because of a fear of corruption. – Alexander Woo Sep 27 '22 at 15:28
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    Putnam Competition scores (as self-reported by applicants or reported by recommendation letter writers) do play a role in graduate admissions in math - at most top departments they're definitely more important than GREs. Of course, they're voluntary and only available for US and Canada undergrads. – Alexander Woo Sep 27 '22 at 15:30
  • @Buffy That's a very helpful post. I'll try to add to it once I have a more thorough understanding of the admission process. – ZSMJ Sep 27 '22 at 16:34
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    The question seems to assume that PhD admissions work quite similarly in the US and Europe, but that's far from true. On the one hand, it doesn't make much sense to talk about "academia in Europe", since the systems differ considerably between various countries. On the other hand, for some countries in Europe there is no such thing as "PhD admission". (Example: In Germany, you essentially need two things to do a PhD: a Master's degree in a related subject (with some caveats), and a professor who is willing to supervise you. The main problem is to find funding to make for a living.) – Jochen Glueck Sep 27 '22 at 16:40
  • In general there are strict admission requirements when a certain funding body restricts the available fundings. It does not matter if you have 10'000 skilled applicants, you want to scream out the best 10, because you have money for 10. I think it is non-sense, because there should be a criteria on the minimum requirements, rather than this scientific darwinism, but I still wonder if it is the case that India is investing a lot in highly epxensive program (i.e. bringing the man to the Moon) preferring 2 PhDs position there instead of 200 PhDs position in other fields? – EarlGrey Sep 27 '22 at 20:19

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The main reason is the number of applicants. I know PhD applicants and Phd students from both India and Europe. I have also been part of interviews to select students from both.

European countries are struggling with a declining (young) population and offer other jobs that pay much better than doing a PhD with long term prospects. This is kind of the opposite for India (only in some limited sense). If you post an open PhD position in Europe, not a lot will show up. That is in contrast to India. There is a need in India to filter more aggressively and that is the reason for what you elaborate on.

Addendum to the answer (opinion): My answer is for the Physics community. The point you are missing is what happens once you are selected. In Europe, you are asked to bring a lot of independence. The supervisor will not see you every or every other day. Maybe once a week at most. In fact, your regular (or 'daily') supervision will be from a postdoc. In contrast, from what I know, Indian PhD students are not (but are expected) to be that independent. I have seen PhD students asking their supervisor (time and again) to solve a rather trivial problem they are facing.

quantacad
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    Also the national exam route makes it at least seem ‘fair’ across all social classes. – Jon Custer Sep 27 '22 at 16:06
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    'Daily'? First, they're your advisor, not your supervisor, and, second, you meet with your advisor once a week, maybe even less. – Alexander Woo Sep 27 '22 at 16:45
  • @AlexanderWoo This varies significantly from culture to culture (field of research and/or location). – N.I. Sep 28 '22 at 15:23