Dear X,
We regret to inform you that we have decided not to proceed with publication of your submission
"Proof of the Collatz 3x+1 conjecture"
to The Electronic Journal of Combinatorics. Our journal receives a great number of high quality submissions every year, and we can only publish those few that in our estimation have the most substantial mathematical depth, importance, originality and interest to our readers. We thank you for submitting your paper to our journal. We would be happy to consider future papers of yours for publication.
Best wishes,
xxxxx,
Editor in Chief
PREAMBLE: It is not easy for a referee to base her/his rejection of a paper based primarily on the fact that, in their opinion, the paper is not of the highest quality. I was asked by the editorial staff to use what appear to be the "new" EJC criteria, as follows: Please apply very high standards, those of the best journals in combinatorics. A paper must be more than just publishable to meet our standards. In particular, it would be useful if you could comment on the importance of the research in this paper and not just look at it for correctness.
STRATEGY I EMPLOYED: 1. I browsed through the published papers in the last two issues of EJC, using them as representatives of the quality now desired by the journal. 2. I fully believe the proof is correct but I found the method of proof uninspiring, since it relies heavily on computers. Even worse, the proof is not direct, but reduces the 3x+1 conjecture to the so-called Four Color Theorem, by exhibiting a planar map (with more than million vertices and three million edges) that would need five colors, if the Collatz 3x+1 conjecture is false. While most people accept the computer proof of the Four Color theorem, I still don't like its proof, since it is just "experimental math".
REASON FOR MY RECOMMENDATION: The proof of the 3x+1 conjecture is the holy grail in the area of recreational mathematics, that mainly attracts amateurs, many of them crackpots. There is no punch line, however, and no new insight, except the fact that the 3x+1 conjecture is now proved to be true. So I rate this work as high-class experimental math (interpreted in a broad sense), but definitely not of the quality demanded by the Electronic Journal of Combinatorics.
I am not sure where to recommend the author resubmit. He may try "Journal of Recreational Mathematics".