What do you think about an idea of getting a PhD in an "better then average institution" to get tons of experience to get a second PhD (in the same field) from top institution?
I'm now getting a MSc degree in applied math from one of the top Russia institutions, but I still feel like I don't have enough experience, and publications, and general "coolness" for applying to places like MIT or Stanford or other top universities - but I would really want to work with people there! Moreover the problem I've came up with for my thesis is somewhat "non-mainstream" (that's why I don't really have a thesis adviser and I'm guiding myself through it, so it turned out to be slower process than I expected).
I've been thinking of getting a first PhD in some good place in Europe, getting few publications, gaining more experience there and only after that applying into top institutions. From your own experience, does that seem to be a good idea? (I mean, having a completed PhD in some other institution seems like a great advantage from the lab's perspective - right?)