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I had submitted a paper manuscript to JAMS (J. of Amer. Math Soc) and recieved the following email 2 months after the submission. Can you help me interpret this email, as to what the situation is and what would be the best way moving forward.
Are there any positives/negatives that can be taken. I have not received any referee reports or any technical points on my work, which is what disappointing me. I would like to understand the circumstances/rationale behind this decision.

I am new to journal publishing. I want to know how i can take this decision moving forward, while choosing another journal for submitting. And also self evaluating my work from this. Is there anything to loose heart?

email : (names and references removed for privacy reasons)

Dear Professor XXXX,

This message concerns the manuscript

XXXXX by XXXX

submitted to the Journal of the AMS.

We regret to inform you that we cannot accept this paper for
publication in JAMS. The reviewers who evaluated this submission did
not think that it meets the acceptance standards at JAMS.

JAMS is the premier journal of the AMS, with extremely selective
acceptance criteria. A paper must be truly exceptional to obtain the
unanimous approval from the editors, which is required for
publication. We publish fewer than 30 papers per year in all of
mathematics. As a result, less than 10% of submissions are accepted
for publication, and many excellent papers are rejected.

One reviewer suggested that the discussion in your paper should
include a comparison with the following reference:

XXX, XXXX, XXX. XXXX: XXX.XXXXX XXXXX XXXX, Journal of XXXXX.
5555;5(XXX):5555-4444.

Sincerely,

XXXXXX, Editorial Assistant Journal of the American Mathematical
Society

--- Sent via EditFlow by JAMS Editor <journal.american.math.society@gmail.co

Dear Professor XXXXX,

The reviews we received were intended for the editors' eyes only, so
we are unable to send them to you.

Apologies, XXXX

There isn't anything between the lines. It's simply a rejection. The editor and reviewers feel that your paper is clearly not strong enough for this journal, and they're telling you so.

Note that JAMS is an extremely selective journal, generally considered one of the top four out of all the many hundreds of journals in mathematics. It is very very hard to get a paper published there. Most of the papers they publish will be major breakthroughs in an area, or solve a famous open problem. The "10%" is actually misleadingly high, because the vast majority of papers are never submitted there in the first place because the authors know they have no chance.

Such journals often do a quick first round of reviews, where the reviewers are only asked if they think the results are potentially important enough to warrant publication in JAMS. Only if they say yes does the paper go on to a full technical review. In this case, it sounds like they said no. You didn't receive a detailed report because they didn't need to do a detailed review of the paper to make a decision. Remember that their job is ultimately to make the decision; it's not their job to give you feedback or help you improve your paper. Sometimes that happens along the way, but when the decision is clear, they won't spend time on a paper that, in their view, can't be made publishable in this journal.

The reviewers can, as in this case, make comments about things they happened to notice as they were doing their quick review. That's why you got the note about the reference. You'll have to read the reference to determine exactly what was meant here; it may be that the reviewer thinks that paper may already contain your results, or at least that they are similar enough that you need to carefully explain the difference. But it sounds like the reason for rejection was the overall significance of your paper, and this was just something they noted in passing.

How to move forward: submit to a different journal. If you want feedback on your paper first, you'll have to get it from someone else, e.g. a mentor, PhD advisor, collaborator or fellow researcher. Such a person could also help you get some ideas of journals for which your paper might be better suited - where it would have a better chance of acceptance or at least a full review.

Top journals, and JAMS is at the very top (most mathematicians probably will not have ever seriously considered submitting there), typically have 2 first passes before a proper peer-review (referee): (1) editorial consideration and (2) "quick" opinions from experts. Which is to say, there are 2 common ways for a paper to be rejected before it is sent for a full peer-review: (i) the editor decides from the title/abstract/info that it is not appropriate, or (ii) the editor solicits experts for an opinion of whether it is worth the effort of a full peer-review.

Based on your letter, and since you didn't receive a referee report, I would say the most likely scenario is (ii), and this is not surprising because unless you have done something really spectacular (I don't know that you haven't, but playing the odds...), you shouldn't bother submitting to JAMS, Annals, etc. (It can also happen that a referee who is asked to do a normal review, just sends back a few lines in the case of recommended rejection, in which case a full report would not be passed on to you either.)

So my suggestion listen to the expert's advice and compare what you've done with what's in that paper. Then, if possible, ask some more senior people for advice for where is an appropriate place to submit your work.

Most likely is that your theorem is just not ground breaking enough. It is possible there are other issues with the paper (writing quality of the text or logic of the math). But we really can't tell because the paper was not deeply reviewed. Go to a lower tier journal (more specialized) and submit it there. This will either get published or at least give you better feedback on your manuscript.

Note even on the off chance that your discovery should be at that top level journal, it is still their choice and people make mistakes. Nothing is perfect. Move on.

Here's a positive from this experience that nobody's mentioned:

You got your answer in 2 months. This is actually quite fast for an answer on a mathematics paper. This is much better than waiting 12 months or more, then getting that same response.

You should address the cited reference (which may be duplicating some of your ideas), and resubmit to another journal.

The second paragraph of the mail is just boilerplate that everyone gets. The final recommendation is all you really need to be concerned with, but I'll guess that it is a big concern for the reviewers.

Is it the case, perhaps, that you missed an important earlier paper (the one cited) in developing your own? If so, you need to go back to your work and see how much you add to the earlier work. It may be that you only need a simple update before resubmission, but it is possible that you are left with too little that is new for you to proceed successfully without a lot of work.

But, no, nothing seems to be hidden or implied that isn't stated directly.

As for your comment about submitting (as is) to a different journal, they will likely have exactly the same reaction. Possibly even some of the same reviewers.