Suppose most mathematical research papers were freely accessible online. 


Suppose a well-organized platform existed where responsible users could write comments on any paper (linking to its doi, Arxiv number, or other electronic identifier from which it could be retrieved freely), or even ``mark it up'' (pointing to similar arguments elsewhere, catch and correct mistakes, e.g.), and where you could see others' comments and mark-ups. 


Would this be, or evolve into, a useful tool for mathematical research? What features would be necessary, useful, or to-be-avoided-at-all-costs? 


This is not a rhetorical question: a committee of the National Research Council is looking into what could be built on top of a World Digital Math Library, to make it even more useful to the mathematical community than having all the materials available. This study is being funded by the Sloan Foundation. 


Input from the mathematical community would be very useful.



Math Annotate Platform?
I think such a thing would provide immense value. In particular I can think of instances when the following sorts of comments would have saved me a great deal of time: 


(1) No need to read pages XX-XXX, here is a one paragraph argument.


(2) This result has since been strengthened, see ...


(3) The following claims are not quite right, here is a counterexample, and here is how to fix it.


(4) The following claims actually are right, even though the following might at first seem like a counterexample.


(5) What the author really means by [SGA] is [SGA N, page XXX]


(6) This result has the following interesting applications ...
(6a) What would be even better is an automated system where, not just can you see what papers cite a given paper as you can today, but you can even see where a given lemma or proposition is cited.


(7) The author has only cited the relevant papers of his friends, the following other work in the subject is closely related.


(8) This paper is actually much less / much more interesting than it sounds...


(9) The following seems to be a gap in the argument:


(10) This 200 page paper assumes along the way in places which are explicit but maybe you didn't notice the following conjectures...


I think it would be essential however to ensure that people post under their own names and other measures are taken to ensure responsibility and measure the credibility of authors, but I think at the present stage of development of the internet we know how to do that.


I also think items like (3), (4), (9), (10) will become increasingly important; already it seems that people who consider themselves sufficiently famous don't necessarily bother publishing in journals (and so are not subjected to the review system), or even if they do are perhaps sufficiently famous to override or intimidate the reviewers, perhaps by sheer number of pages, etc...


