Gievn that I myself am a non-native English speaker, I tend to have more tolerence to the writing from a non-English speaker. Y. Zhang may not be a good example in this case. He went to the US in 1985 and received PhD in math in the US. He has lived in the US since then. From what I know, Zhang has no problem in English while the OP may have serious English language problem. I agree with many parts in your answer, though.

@scaaahu: Not being able to speak English well is not a character flaw. It is however a problem if English is the language that you're writing your papers in. There is also a distinction to be made between speaking a language imperfectly and expressing yourself poorly. In my answer I tried not to harp much on issues of grammar and usage.

Well, in His/Her supervisor(s) accept the work and they published it in a highly known journal, my guess is that the word published could be the misuse of the word submitted.

@scaaahu: Sure, the OP has used entirely the wrong word here. Again, this is not a crime, but doing this in one's academic work could certainly lead to its lack of understanding and thus rejection. Look at it this way: wouldn't it be nice if language issues were most of the source of the OP's difficulties? If so, they can be overcome provided they are acknowledged and addressed. Not to tell someone when their writing is unclear is not doing them a favor, in my opinion.

@scaaahu If you think you are going to earn millions of dolloars with your paper, why not spend a couple hundred on a professional editor for polishing language?

@Raphael I don't know the OP's location so I cannot answer this question for him. I would find professional ediors to help me if I were him. I think language is only one of his problems. There may be other issues as well.

@Raphael I looked at the OP's questions on other SE sites. The one on Signal Processing SE looks okay(I am no expert. I just parsed the English). The questions on TCS SE look pretty awfully bad. The one on Math SE is too short but it hit the key to the problem. I am confused. I think he can write English to some extent. My comment above was meant to say English is probably one of the problems he's got.

"He found the Holy Grail or some other famous cup" - fantastic phrase.

Congrats, you've (unintentionally, I'm sure) convinced the OP that if he fixes his English all will be well :) (see his comment on my answer)

@Selfishness: "[I]f a person is not known and has done very good thing, they will ignore his work (at first at least)." Given that my answer contained a specific, recent, clear counterexample to this, I'm not sure what further to say in response.

@ff524: Yes, that was not my intent, but I think it's okay: whether or not language issues are the entirety or the brunt of the problem, it will still be advantageous for the OP to address them. (In fact, only by doing so will s/he be able to figure out whether this is actually the case.)

suspect this answer is so highly rated partly because respondent is so highly qualified to write it, working/established in academia "the hard way". here is some bkg & a large collection of refs on the Zhang twin prime breakthru & refs on what its like to work in academia & the challenges there & interview with Zhang etc

I, at least, rated it highly on content -- not having recognized the author, and not bothering to chase the pointer now.

It might be worth noting that most Journals I have thus far submitted accept only anonymised papers. Hence, the argument whether people unknown to the community are treated unfairly does not have any weigh in an argument for or against rejection.

@EricTobias this varies widely by field. In theoretical computer science, single-blind reviews are the norm.

I wasn't sure whether to +1 for the laughs at "Holy Grail or some other famous cup", or to -1 for the wrath I shall surely face after awakening the whole floor just now with hoots of laughter.. In the end I decided -1+1=0, but +1 for the patient advice.

If the person's first language isn't English, why can't they first publish in a journal in their native language? There ARE non-English and non-US academic publications

@DVK: If your English skills are not strong enough and you are not experienced writing in English, writing your paper first in your native language is probably a good idea. However, when it comes to publication, the number of languages in which reputable math/TCS journals accept papers is by now quite small: you can submit a paper written in English or French virtually anywhere; some prestigious international journals accept German papers [though most native German speakers now write all their papers in English].

There are countries with tremendously large and strong mathematical communities -- China, Japan, Russia -- in which virtually all serious researchers publish their papers in English or French. There are some journals which publish papers in other languages -- but these papers are then usually not read by the larger community. If you just want to publish something, ok; but if you want recognition for solving a famous problem, this type of publication is problematic: see e.g. newscientist.com/article/….

Also, you mention in all capitals that there are non-US academic publications: who are you talking to? More than half of all my publications are in journals which are either based in countries other than the US or are not even fundamentally based in any particular country.

@PeteL.Clark - there are countries outside USA. Russia has math publications (at least used to have them back when i cared to check). I'm sure so does China. I didn't say it has to be international publication.

@DVK: If you don't "care to check" what the current situation is on mathematical publications in languages other than English, why are you commenting on it? I explained why for the purpose of solving a famous problem, publishing in a language that the experts in the field can read is important. You do not convince people you aren't a crank by publishing a paper that none of the experts will read. If your point is merely that "There are countries outside USA": I promise you, I know that.

@PeteL.Clark - you're implying that his only option is to publish in perfect English. Unless the native language is of some rare tribe in Amazon, that's NOT the case. He can publish in his native country, and if it really is a valid paper, then have it professionally translated. There ARE experts in the field that read in languages other than English, let me assure you.

@DVK: I am not implying what you're suggesting. Moreover, what I have given is my sincere advice for how to best get taken seriously for solving a difficult problem. I gave you a specific link to someone whose work is not getting taken seriously for this exact reason. As your recent comments are not engaging with the nuances of my responses, I will stop responding to you on this point. But if your advice is different, please feel free to leave an answer. The best advice is supported by external evidence and personal experience, so I would be very interested to hear about that.

Speaking about english and text clarity, OP's question came across to me as an hypothetical question "What if someone..." instead of "I claim that I have...", this answer seems to assume that OP is indeed dealing with the issue he represented, rather than asking about how things go in this situation (for other people).

@Mefitico, I don't know if your reputation is enough to see the original version of the post, but in the first version, the OP states "P.S. This is a $\textbf{real}$ situation."

"No professional reviewer will say something is wrong lightly." Not true in my experience. I have multiple times gotten claims that a proof is wrong when it clearly isn't (and I subsequently published it elsewhere). Even very short proofs. It seems to manly happen at highly-ranked journals too. Perhaps because they're the most inundated with bad submissions that to guess something is wrong based on your gut, while lazy and unacceptable behavior, is probably a good guess.