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If, after 28 months of waiting and the third request, I within a few hours receive “Reviewer # 1: Sorry that this review took so long. However, this paper does not contain any results of value”, I know that the referee read only the author's name and, possibly, the title of the article.

If I get the message "How about you try to establish a reputation for yourself on several less serious questions before claiming to solve * both * the Goldbach and Twin Prime problems?", Then I begin to think that the solution of these problems is reserved for the author of this message And he was promised to show “the Book". Is it ethical to give such advice?

If they write to me “Yes, I will not accept this work. ... From very general considerations, I believe that you have a mistake in your work. Formally, of course, I have to specify it, but I do not want to do it because of saving my own time”, I understand that they read the work, they did not find any mistakes and refuse, just in case.

Of course, the referee can save two hours of his time, and as a result, the author loses months, years, and sometimes, and all his life. Obviously, in order to recognize the results of my work, courage is needed. But, if “Reviewers' comments: ... I suggest rejecting it on grounds that it does not meet the standards of mathematical correctedness practiced by our journal”, I do not understand what is more important, form or content. I’ve always believed that the result is more important.

Sometimes they refer to feelings (“the referees felt given the methods you are using, it is hard to imagine that the results you claim are valid”), or belief (“I'm sure that your "elementary evidence" of Goldbach and the twins have mistakes, many years of experience does not allow me to believe in them, but I also can not spend time searching for them”).

But I'm not interested in the feelings of referees who did not even get acquainted with the proposed method and, I did not ask anyone to take my word for it. I offer the proof.

This is only part of the disclaimer, but there is not a single review or indication of an error. Is it ethical for judges to make a conclusion about a job without reading it, but only on the basis of their feelings and assumptions about what is written in the article?

Is every referee a priori smarter than any author to such an extent that in several phrases pulled out of context, can determine where the author's thought can turn? Should not the referee read the article at least until the first error and point to it? And if the error is not found, recognize the work as correct. Otherwise, he should declare himself incompetent and ask the editor to transfer the article to another referee Really all mathematicians not only do not see, but also do not want to see beyond their nose?

How can the author get an honest, unbiased assessment of his work in this situation?

  • Comments are not for extended discussion; this conversation has been moved to chat. – eykanal Jun 23 '17 at 19:58
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I think most of this question should be closed as a duplicate, and I would strongly recommend the OP read all of the highly upvoted answers here before commenting further:

I believe I have solved a famous open problem. How do I convince people in the field that I am not a crank?

However perhaps the last part of the question can still be answered:

How can the author get an honest, unbiased assessment of his work in this situation?

Have your work reviewed by a close colleague who knows you better than the strangers your work goes to through peer review. Ideally, this is what an academic advisor is for, but other people can act as surrogates in some situations. The person should be someone close to you, who is willing to spend some time reviewing your work because of that relationship, but who has the academic abilities, rigor, and qualifications to review your work.

Impress upon this person that you fear your work has some error, because otherwise it is a very important finding, and ask for their assistance in finding the error. Make it clear that you are not looking for praise or affirmation, but want to find the error. Don't tell them how long you have worked on it or say anything else that makes it seem like you have some personal need to feel good about this work: you only want to find the error.

If together you actually find no errors, and given you have followed my advice about finding someone qualified, then, given the importance of your finding, I would expect this person to make every effort to help you with explaining the work to others.

  • I hase appealed in the Department of Number Theory of Mathematical Institute. Professor rolled up his sleeves, brewed some coffee, and tells his graduate student to read the paper and report back to him. It was absolutely pointless. With the same success, I could turn to anyone on the street. – Andrei Allakhverdov Jun 19 '17 at 22:45
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    Are you close to that professor? Does he have any stake in your success, trust or knowledge in your abilities, or owe you a favor? If no, then you didn't read my answer thoroughly. He has no obligation or reason to give you time beyond his own interest and curiosity. – Bryan Krause Jun 19 '17 at 22:49
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    "No conjectures and assumptions are a criterion for the correctness of the work" Huh? What is that in response to? (also, have you already read the linked question and all of the answers?) – Bryan Krause Jun 19 '17 at 22:53
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    "How does science develop?" - By, as Newton referred to, "standing on the shoulders of giants." Did you come here looking for an answer to your question, or did you come here looking to rant and complain about people not taking you seriously? (note: you said before in a comment you needed truth rather than politeness) The rest of your comment: "That's what I wrote about" I still don't understand what you are referring to. There is a lot of back-and-forth here so it would be helpful to be explicit. – Bryan Krause Jun 19 '17 at 23:02
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    It is easy to make a claim. Making a claim in itself does not incur debts on the part of others, experts or not. I'd recommend that an author think in terms of persuasion of expert readers, in particular, to be transparent enough, and write in a style palatable to them, so that those secondary issues are not the problem. And, especially, when one claims extraordinary results/progress, such persuasion is all the more critical. To complain that expert readers are not persuaded is function-less, if your goal is to persuade expert readers. – paul garrett Jun 20 '17 at 0:41

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