Written: Aug. 7, 1998
Postcript Written: July 22, 1999.
The most important page that appeared in the Notices of the Amer. Math. Soc. after Oct. 1993 is the "Another Opinion" (p. 845, Aug. 1998) by Greg Kuperberg, David Morrison, and Richard Palais, informing the readers about the Los Alamos XXX archives.
This is the revolution initiated by Paul Ginsparg, (see his speech delivered to the UN) ), that is going to tumble the AMS with its pompous paper elitism and mentality, along with paper journals altogether. As a corollary, MathSciNet (and of course its paper version Math Reviews) will become completely redundant, and I bet that it would discontinue after 2010 (or sooner). Of course, we would need to archive the reviews between 1940 and 2000, but no new reviews will be necessary. Probably, all the math literature of the past would be put on-line, making even this unnecessary.
If you want to look up, say, the Mehler formula, all you have to do is use the on-line search-engine, and search for Mehler, and you would get right away all the articles that mention it in the title or abstract.
You might say, `how do I know whether the proofs are valid?'. After all, anybody and her sister can submit there. A `real' (paper or electronic) journal has `standards' and `rigorous' refereeing.
Baloney, no one (except Faltings reading Wiles) can be trusted with careful checking of logical correctness. I know of at least two RECENT papers, in Math. Invent. and Annals of Math., no less, that claimed to prove long-standing conjectures, and that were completely erroneous. The reason is that the referees are anonymous, and can afford to do a careless job.
The alternative is to ask experts in the field to read your article carefully and check for errors and mistakes, and to find out whether your results are new. Then, of course, you should give credit to these experts, and hence make them accountable.
The most rational solution is to stop submitting papers to journals (even electronic ones), and have your papers solely in your homepage and in the xxx archives, with the above-mentioned non-anonymous refereeing. Being a despicable and irrational human, with the human frailties of vanity and fear of the Joneses, and out of politeness to the paper journals in which I am a member of the editorial board (and not having the guts to resign from them, since I am flattered by the `honor'), and being aware that the Halmosian-Krantzian-Knappian desert-generation is not yet dead, I am not following this advice completely. But I plan to adopt it gradually.
For example, my very interesting paper A Heterosexual Mehler formula for the Straight Hermite Polynomials , has been carefully read, and approved, by Dominique Foata, and is exclusively published in my website and the xxx archives. A reader in 100 years will know that it can trust it, since Foata is a very critical and careful reader.
There is one fly in the ointment, it takes about two minutes to manually convert a TeX source file to the requested format required by math.xxx.lanl. Have no fear, if you are using AMSTEX, I wrote a nifty UNIX Shell program, called `doron' , that automatically creates a file called name.sub from the AMSTeX source file name.tex, (ready for submission, after that you checked that it looks OK), by typing `mailx -s put math.xxx.lanl < name.sub') ). So after you downloaded the above program (and saved it as `doron'), once and for all change its mode by typing: chmod +x doron. Then whenever you have a new paper, say rh.tex, all you have to do is type: `doron rh' (without the quotes), then go over the top matter, and type
`mailx -s put math.xxx.lanl < rh.sub'.
(you can even automate this by writing a 1-line script, call it, say, jane, that has in it:
`mailx -s put math.xxx.lanl < $1.sub'.
call that file jane, do, once and for all, `chmod +x jane', and from now on, to mail a name.sub file, all you have to do is type `jane name'. E.G. in the rh.tex case, you would type: `jane rh'.) In one momemnt or less you would get the response of the archives.
So roll over Transactions, Proceedings, Journal of the AMS, Annals, Inven., Acta, ..., Fibionacci Q., here comes the LANL XXX archives!
Another human remnant is not accepting .com submissions. So it is only open to the .edu `elite'.
Last but not least, the sites-administration staff is very nasty.
So, while it is good to have your article published in as many places as possible, including the xxx, it should be in addition, NOT instead, publishing it in your own website, where you are free to let your creativity reign, and one is not subject to the narrow-minded judgement of the so-called moderators.