Written: Feb. 10, 2021
For a long time traditional scholarly journals, including mathematical ones (starting with Crelle's) served the vital need of communicating information, using the print medium. In the 20th century, with the exponential growth of math (and science) and the growing number of specialties and subspecialties, the canonical organs of the math societies, e.g. the Transactions and the Proceedings, could not accommodate the flood, and commercial publishers started publishing journals. They did a great service, and the relationship was symbiotic.
Then came the internet, with infinite disc space, and mathematicians (and scientists) realized that they can do without the commercial publishers, and started a new trend "open access journals".
They introduced the following transform
Journal of X → X (journal)
[see e.g. here].
But "open access" is such a non-issue, nowadays, all papers are now freely available on the arxiv, and, very often, also in the authors' web-sites.
Much more important than "open-access" is open-mindedness, full disclosure and accountability. All refereeing and editing should be above board with the names of the accepting and rejecting referees (and editors, there are often quite a few "editors-in-chief"), made public. Anonymous refereeing is immoral, trashing people anonymously. Also authors should have the option to have their rebuttal published, and a truly open-minded journal should have a section "rejected papers" where the authors would have the option to explain why they believe that the rejection was wrong. Of course, this option should be optional! In fact I asked the journal mentioned in Opinion 178, to put a link to my rebuttal in their journal's web-site, but they refused.
It is also disappointing that these new "innovative" journals have the same protocol and policy as traditional journals, the only difference is that they are electronic, and do not cost money. But as I said above, this is such a non-issue.
It would be nice if these "innovative" journals would be truly innovative, and in addition to being open-access, and use zero-blind refereeing, would have the option for readers (and authors) to leave comments, putting links to follow-up papers, announcing the solutions of open problems made in the paper, and possibly pointing out errors, or alternative proofs. It would also be nice to be able to put a "like".
Let's have truly open journals. Being "open access" is a necessary condition, but very far from sufficient.