Written: Feb. 2, 2008.

Until three days ago, I was eagerly awaiting decisions regarding two submissions, to the journal Experimental Mathematics. The first one was an article about certain positivity conjectures, written in collaboration with Manuel Kauers, and the second one, about combinatorial games, written in collaboration with my brilliant student Thotsaporn "Aek" Thanatipanonda.

And What a coincidence! At the very same day, Jan. 31, 2008, came the two decisions from the "managing editor", and, for good balance, the first was accepted, and the second rejected. But both of these responses had one thing in common. Neither came with referee reports! When I inquired about this with the publisher, Klaus Peters, he told me that the previous editor-in-chief resigned suddenly a few months ago, and it took them some time to find a replacement (Yuri Tschinkel, currently at New York University's Courant Institute), and he was faced with a huge backlog.

So like the guys who "discovered" the organic transistor and the skin transplant, who were under
lots of pressure to produce results, and did some "shortcuts",
Prof. Tschinkel did something analogous with the editorial process. He simply said to himself,
that it is too daunting to request 200 referee reports, and send 200 Email messages, requesting
reviews, and then getting one hundred declinations, and having to find more referees, with
very slow convergence.
Wouldn't it be much more efficient if he set aside a few hours, and quickly glanced at
each submission, and decide by the "look" or "feel" of it, whether to accept or reject it.
He then probably asked the "managing editor", Ellen Ulvanova (who is a professional
publishing expert, but not a professional mathematician) to copy-edit the manuscript, and
look for typos. And indeed, while the acceptance of my paper with Kauers came with no
referee reports (Experimental Mathematics,in the past had **two** referees for each paper), it asked
to correct a few typos. The rejection of my paper with Aek, not only was unaccompanied
with even one referee report, but didn't ask to correct any typos, but that is fair enough.
If the paper is to be rejected, then why bother with typos.

When I complained to Klaus Peters about this "execution without fair trial", he
kindly forwarded my request to Prof. Tschinkel, and miracle-of-miracles, within less than
48 hours, came a fairly detailed
"referee report".
In defense of Prof. Tschinkel, he did not try to pretend that this report was
a genuine report solicited by him,
beforehand, from an independent expert, but simply tried
to show me that this paper so obviously "does not meet the standards of the journal".
The details of my rebuttal,
are really not relevant to the point of this Opinion, but what got me so mad was the
implication that he is **so** smart that he even knows, and is competent to judge,
research in combinatorial game theory, that is so far removed from his
expertise in algebraic geometry. The report made it clear that he
knows nothing about combinatorial game theory, and even less of
experimental-yet-rigorous mathematics, that is a whole different ball game than
the kind of experimental mathematics that a mainstream expert in algebraic geometry, like
himself, is familiar with.

But, that's also not the main point. One often gets rejected unfairly by supposedly "expert" referees.
But, a **necessary**, if not sufficient, condition for the proper handling of
a submission, is to solicit *expert* reviews.

Indeed, it is very unprofessional, and may I say unethical, to bypass the admittedly time-consuming, but necessary, peer-review process. Frankly, I am not at all worried about the rejected paper, but am rather nervous about the "accepted" paper. Who knows, perhaps it has a major flaw, which even such a smart person as Prof. Tschinkel can't detect in two minutes? The rejected paper will be resubmitted to another journal, and let's hope that this journal will not employ the time-saving devices of Prof. Yuri.

I have always admired Alice and Klaus Peters for their innovative publishing and great integrity. I hope very much that they will learn their lesson, and look for a more honest, if less "efficient", editor-in-chief.

Opinions of Doron Zeilberger