Soft Question about International Graduate Schools Hello members of this site! I hope this question isn't too bothersome, but I need to ask some professionals who know what they're doing. Furthermore, I know that this is supposed to be a more technical exchange but I ask you patience with this post. 
Too long, won't read: Does it really matter where I go to get my PhD in terms of Job opportunities as well as equipping me for a career in pure research?
So to start, I'm a unique case: I'm 17, about to be a senior in High School and simultaneously about to be a Junior in college. I'm currently a mathematics major with a minor in physics and I'm on track to get my degree in two years, and I'm positive that I want to pursue a Ph.D. in Math and do pure research for basically the rest of my life. I really love doing math and I enjoy every second of it. 
However, I'm still confused about the whole graduate school thing. Obviously I'm not one to stay on the beaten path and I've been  looking into overseas graduate programs in Japan that are taught in English. I love Japan almost as much as I love math, but I really want to receive the best education possible for my Ph.D. which I'm not so sure these programs can offer, after all, the universities that host these programs rank in the 150-200 range compared to American universities that rank in the 1-100 range in terms of quality (According to the QS ranking system). 
I really, really want to study overseas (which isn't an option for my undergrad. studies because of the program that is paying for my college education). But I also want to make sure that I get the best education and that if I do go overseas  with an advanced degree from a Japanese university, there will be job opportunities waiting for me when I get back.
Will certain doors be opened for me if I attend a school that I don't necessarily have my heart set on (i.e Princeton or MIT or CU Boulder), over attending one where I know for a fact that I will enjoy my term there (i.e. Tohoku University with the IGPAS)? Is studying abroad for a math PhD unfeasible and silly to even think about?  
--Thank you all for your time!
 A: First, I would like to clarify that I am not a Ph.D. in mathematics. I am a masters student in a top 100 university and what I am telling you is what has been told to me by very many successful mathematicians with careers in Academia.
It is important to note that getting a job in Academia is tough. It is particularly tough in fields such as Mathematics and Philosophy. There are many people who get PhDs from top 10 universities in pure mathematics, yet cannot find jobs in Academia. A general rule of thumb is that to get such a job, it is good to have three enlightening publications. Pure mathematics is perhaps one of the most competitive fields. You may be brilliant, but never stumble onto something in time. You may be less than brilliant and hardworking, but quickly stumble onto something. Do not forget that there is a considerable amount of luck involved. Academia is not today what it was 20 years ago in terms of finding a job.
However, if you get a PhD, do not fear. You will most certainly find a job in a STEM field. However, more applicable PhDs such as statisticians and computer scientists will get their first choice. 
One benefit of a job in academia is that upon granting tenure, there is very much stability.
A question you should ask yourself is if you are willing to work in industry. If so, then I recommend getting your PhD in Japan. If not, I recommend aiming for the best program you can. You have to decide which is more important. A job doing pure mathematics for the rest of your life, or expanding your horizons by studying abroad and detracting somewhat from the probability of being able to do pure mathematics as a career.
Another possibility is that you accept that even if you are brilliant, your chances as a pure mathematician are slim given the nature of the system. You could, in this case, decide on a more practical route and pursue a PhD in applied mathematics, statistics or computer science. Then you have higher chances of academia and industry.
