The title is copy-pasted from the following question by Ingrid Daubechies, on mathforge.org [I added some links]:

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.

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* UPDATE:* David Roberts points to the fact that Daubechies asked the same question at mathoverflow before asking at mathforge. The answers are much more welcoming there, interesting read.

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Notice: “a World Digital Math Library”, not “the World Digital Math Library”. Concerning the involvement of the Sloan Foundation, that would be great, let me cite again the Conjecture 4 by Eric Van de Velde, proposed in MOOCs teach OA a lesson:

OA is not sufficiently disruptive. Hoping to minimize resistance to OA, OA advocates tend to underemphasize the disruptiveness of OA. Gold and Green OA leave the scholarly-communication system essentially intact. When presented in a minimalist frame, they are minor tweaks that provide open access, shift costs, and bend the cost curve. Such modest, even boring, goals do not capture the imagination of the most effective advocates for change, advocates who have the ears of and who are courted by academic leaders: venture capitalists. This is a constituency that seeks out projects that change the world.

There seems to be two camps in the discussion about comments for articles as a tool of mathematical communication:

- the cons: few, very vocal, are using the straw man argument that comments to articles are like comments in blog, therefore unreliable. It is my interpretation that in fact this is motivated by fear of authority loss. Maybe I am wrong, anyway their argument is blown away by one fact which I shall mention further.
- the pros: they are not disputing the utility of the tool, they would like to have more details instead, about what exactly will be comments for: a kind of online perpetual peer-review, will be them considered as original contributions, where do comments sit in the continuum between the original article and its peer review and, most important, how to motivate mathematicians to seriously participate.

I think the formulation of the question by Ingrid Daubechies is precise and very interesting. Accordingly, mathematicians from both camps could take some moments to think about it.

Is this the kind of disruptive idea which could make the people dream about, concerned about, and also, very important, which could be considered as world-changing? I certainly hope so.

Let me close with the funniest argument (in my opinion) against the idea that comments are bad, because they are like comments in blogs. You see, there is an elephant in the room. Who invented blogs? Why, a mathematician, John Baez with his This Week’s finds. And what exactly is the content of Baez’ first blog in the world? Well, dear naysayers, it is about comments by John Baez of mathematical (and other) scientific articles.

John Baez participates to the discussion initiated by Ingrid Daubechies with this:

I would like some way for me to be able to easily read lots of comments on people’s papers. Right now to find these comments I either use Google or trackbacks on the arXiv. But I think there could be something better.

To be honest, I mostly want to read my own comments on people’s papers, because I wrote a lot of them in This Week’s Finds, and nobody else writes nearly enough. I don’t have much trouble finding my own comments: I use Google, and use keywords that single out This Week’s Finds. But it’s harder finding comments when I don’t know who wrote them or where they are.

Congratulations John Baez, you are an example for many of us!