Math Questions about mathematics, physics and education

[MWH]

I've got quite some questions of which I've been curious to find clear answers, so I hope you can help me!
Especially since a few years I've been very interested in mathematics and physics and reading about these sciences, after which I've had a favour over mathematics. I'm also really interested in theoretical physics and mathematics in this field, so I'm sure I want to start a career in these fields. Could I get some advice about whether it's important to study mathematics and physics if I want to end up studying theoretical physics or if I can just do mathematics and specialize myself later on, given the fact that I'm more interested in mathematical physics?
I've lived in the Netherlands since my birth, but I want to study abroad, probably in the USA, for my English to develop much better and because the (university) education here as regards to mathematics and physics quite concerns me. What makes top universities like MIT and Princeton so much better than similar education in the Netherlands and is it necessary for me to sign up there and try to pass the largely hard to pass admittance, if I want to be at the front of my field?
About admittance, in what way exactly can or should I make them convinced about me, considering I've got a certificate in 'Havo' with the right chosen set of courses, higher general secondary education, rather than 'vwo', pre-university education (I was quite a different person back in the year in which it was determined what my level of education would be), a not yet proven proficiency in English and a long term motivation to stay focused on my study? And what would I have to do at a Dutch university to become transmitted?
It seems very expensive to go to a top university, such as Harvard. How exactly do things go with the costs, how can people actually afford to enrol if they have to take care of the costs themselves? Is it possible to borrow the required sum needed from a bank?
Lastly, it's said there is a lot of competition in the field of mathematics and physics. How sure can one be of his future in this field? Moreover, is it necessary for anyone to have a nobel prize-winning mentor, or is it also possible to become something solely on your own, and would this be possible at a Dutch university?
I'd be pleased if you would correct my possibly wrong view on all this.

Thanks in advance!

 

[mathwonk]

My impression is that Nijmegen, Utrecht, Amsterdam, Leiden, and other Dutch universities are among the best in the world, certainly in mathematics. many Dutch mathematicians are world leaders. You might speak to some of the people at those places about your plans.

 

[Ryker]

I've lived in the Netherlands since my birth, but I want to study abroad, probably in the USA, for my English to develop much better and because the (university) education here as regards to mathematics and physics quite concerns me.

Really, why is that? As far as I can tell, Netherlands has some top notch universities, just think of Leiden, Eindhoven and Utrecht, for example. Granted, you probably won't find a program as good as those at top US schools, but if your only reason for wanting to go to the US is being scared you won't get a good education in Netherlands, I think your fears are unwarranted.

 

[MWH]

Really, why is that?

As far as I know, such education is worth much more in the USA, e.g. the amount of physics/mathematics students is very thin here and someone that would become a shrub here, would become a large tree in America, e.g. because there are like a throng of mathematics professors and because much more money is involved in the education of a person studying physics/mathematics in America. Or am I not right/does this not matter at all?

 

[Ryker]

Well you raise good points, but don't fool yourself into thinking all is gold that comes from the US. I don't want to sound hypocritical, as I am in fact doing my second degree in Physics in Canada, and I might want to go to grad school in the US if I'm lucky enough to get in. But I'd choose this path because of wanting to move there, not because it's so much better. Maybe some people with more experience within this field will correct me, but I'd say if you don't get into, say, a top5 or top10 US school (in the particular area you want to research), you will NOT get better education than back home. There are, however, multiple other reasons why one would want to change the environment they study in, and doing grad studies in the US, even if you don't want to move there, would certainly be a great opportunity and experience. But strictly from the education perspective, the US is hyped up. Again, people might disagree, but if you follow research, you will see new discoveries and breakthroughs come from all over the world, and yes, from Holland, too. But obviously, there are some "powerhouses" that seem to have more money pumped into them, and that therefore churn out heaps and heaps of quality research. So by all means, go to the US or Japan or the UK or Canada or Singapore or whatever, but don't automatically exclude Dutch universities. Look at the research they're doing and then decide.

 

[MWH]

I see, thanks for your reply! It is however not that I automatically exclude Dutch universities, nor am I trying to say that Dutch education is so much worse than similar education in the USA/Oxbridge, I 'sort of' know about the history and current situation of the Netherlands concerning this and whom it has brought forth. But if I have to believe what I know, I'd say one who is very interested in and motivated about a lifelong career in mathematics (and physics) will have greater opportunities enrolling in one of the best universities in this field, especially for non-native speakers like me, who want to get more internationalized and be familiar with English mathematics and physics jargon. I don't know how much greater though, neither do I know if and how much motivation could reduce this gap in eventual outcome. As of I want the very best for myself, I'd seriously want to consider whether or not I should attempt to enroll in a university like Oxbridge or another, even if Dutch universities are not - and they, indeed, probably aren't - much worse than those at mathematics and physics. So why do you think I should or shouldn't try to get into one of the world's best universities as regards to mathematics and physics in general, given what I said before and some (otherwise possible future) issues regarding my studying, e.g. I'd probably be more distracted from my studying here? Furthermore, what exactly do they expect from me if I want to get accepted, as only like 5 percent gets through at Cambridge? I'd be pleased with any criticism.

@mathwonk I understand. I'm trying to contact certain people, but I'm not quite sure about whether or not, in my case, also studying physics would be (much) better at a top university at it's field, considering I've also got some different reasons to study abroad.