I have been following a professor whose research I really like. To simply illustrate the impact of his research, let me quote a quote from Quanta Magazine:
[He] says he usually gets two responses: “You’ve opened up a whole new theory, and you’re an idiot.”
We have exchanged many emails, and I have nailed my proposed research to the point where I believe that it suits his research very well. I am really satisfied with this.
However, I lack 5 points in TOEFL to reach the minimum requirement of this school. So I have to apply to other professors in other schools. Because he has opened up a new theory, other professors research doesn't have that much in common with my proposed one. I have no complain about that, and I think I would still be happy to work on a research that deviates from my proposed one. The next professor who has research similar to my proposal, has refused me because he doesn't have intention to admit more student this year (but he says he will be glad if I apply next year).
Q: If I really want to work on this research, can other professors advise me well? In my knowledge, I also need to work for them, to enrich their research, so chances are that I have to work on a different research. And if I do have to change my proposed one, which one is more advantageous, accepting it or waiting another year to apply? It's kind of a shame to spend a whole year preparing for grad school, then suddenly have to wait for another year; but I can deal with that.
Answer
Don't put all your eggs in one basket.
Until you've actually been admitted somewhere, it's a really bad idea to pin your hopes on only one advisor, only one school, or only one set of research directions. Sure, there may be one particular advisor that you seem to "click" with more than any others, but you should not think of that as your only option until you actually know that it's an option at all.
Even under optimal circumstances, there is a good chance that you won't be admitted to a particular school, or that a particular advisor isn't taking new students, or that your newest grant proposal won't be funded by a particular agency, or that your latest paper won't be accepted by a particular journal, or that your latest experiment will fail, or that you won't be able to hire a particular student into your research group. It doesn't matter how hard you want it, or how much you deserve it; you will never get everything that you want.
And you are applying under less than ideal circumstances—your TOEFL is below the minimum requirement for your first-choice department. Unless you can improve your score before they make admissions decisions, it's safe to assume that you will not be admitted. Don't worry about it; don't be afraid of it. Accept it and move on. But don't withdraw your application!
Meanwhile, cultivate other options. One of those options might be to spend a year improving your language skills. Another might be to apply to other advisors in the same department (although that's unlikely to work given your TOEFL score), or to other departments. Yes, that might mean changing your proposed research, but your research career will span decades; there's plenty of time to go back to your initial proposal later. Or you might be able to find other advisors who will work with your original proposal.
How do you know which option to pursue? You don't. Try them all.
I generally advise undergraduates in my department who are interested in graduate school to apply to 5-10 different departments and simultaneously to apply for industry jobs. Apply to options that you think you might be a good match. Remember that any particular application has a small chance of being accepted, especially at top schools like Berkeley. Play it as a numbers game — your goal is to set up enough options, with a wide spread of probabilities, that you can reasonably expect to get a couple of offers.
Once you have those offers, then start making a decision about which one to accept.
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