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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    $\begingroup$ Prof. Daubechies, I add my welcome to MathOverflow to Teo B's welcome. While I agree that something can be learned from the MathOverflow experience regarding collaborative editing, I think that a more strongly moderated version is more appropriate for (my idea of) the system you propose. Teo, you might find that Prof. Daubechies has some history of studying and asking "a few deep math questions" . Gerhard "Looking To See What Happens" Paseman, 2013.02.17 $\endgroup$ Feb 18, 2013 at 2:43
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    $\begingroup$ Similar questions: mathoverflow.net/questions/51056/… "Are there any good websites for hosting discussions of mathematical papers?" mathoverflow.net/questions/13619/… "Is a free alternative to MathSciNet possible?" $\endgroup$ Feb 18, 2013 at 12:33
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    $\begingroup$ Instead of building something "on top" of the World Digital Math Library, one should first build the World Digital Math Library, since it is just a web page with few links to free online math sources (like NAMDUM and GDZ Göttingen, which are valuable). It seems that WDML webpage was last updated around 2005. $\endgroup$
    – Misha
    Feb 19, 2013 at 19:50
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    $\begingroup$ Just to mention that, from what I have heard, some of the participants to the episciences project (see episciences.org) are thinking about integrating this kind of feature to the platform. $\endgroup$ Feb 19, 2013 at 21:48
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    $\begingroup$ The question was (as mentioned on an answer) reasked here publishing.mathforge.org/discussion/163/math-annotate-platform where there is quite a bit of discussion going on. In view of this, and even more so due to the fact that the answer that suggested this got accepted by OP I vote to close this question as 'no longer relevant.' Sign-up on that other page is easy and instant, at least was when I did it; it is just like our meta. (This is not even so much that I do not want the question here, but that it seems unfortunate to have the discussion split in parts.) $\endgroup$
    – user9072
    Feb 20, 2013 at 10:21

6 Answers 6


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...

  • $\begingroup$ Ha, I'm sure [SGA] was not a random example. I hate when people cite a dense, multi-volume work with no indication of where in its many pages one may find the result … which often isn't exactly as cited anyway! $\endgroup$
    – LSpice
    Aug 4, 2021 at 14:23

I think that such a platform would be extremely useful, but it also would need strong moderation to remove misuse, perhaps only initially. The moderation effort is not at all trivial as the experience of the arXiv moderators shows.

  • $\begingroup$ Peter, so much intellectual creative energy goes into any good Ph.D. thesis, and so little into making social decisions, how depressing! Moderation may be considered a pragmatic solution, but one should search relentlessly for solutions which do not violate the basic ethical principles. One should believe that ethical solutions exist, then one will find them. One thing is when I avoid reading X because I freely follow Ms/Mr A--that's fine; another is when A decides for me that I will not read X. My other authority, B, may advice me to read X, but A has prevented me from doing so--terrible. $\endgroup$ Feb 19, 2013 at 5:09

If this forum were a mathematical discussion forum, your question would be welcome, encouraged, and anticipated. I would be happy to provide input from a public citizen point of view.

This forum is meant more for answers, references, and perhaps derived questions. While I hope you get some appropriate input from here, I instead encourage setting up a wiki or participating in a forum like publishing.mathforge.org, which has been discussing related issues for a while.

I believe (after gathering a few search terms from suggestions about to appear) that you will find a lot of the discussion extant on various weblogs and related fora, and that you will see a number of issues to be avoided at some cost.

As with most community efforts, you will find the greatest success coming from a dedicated subcommunity which understands and represents the core values of the effort. Assemble that, and much of the rest will follow. It is my hope that what you propose will permit and benefit from contributions from the interested public.

Gerhard "Not A Professional Mathematician (Yet)" Paseman, 2013.02.17

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    $\begingroup$ If the system had a team of reviewers to vet and submit all postings (including corrections and comments), one could have a quality output. Trusted contributors could then provide content which could be reviewed after online publishing, rather than before. Gerhard "Been Thinking About This Too" Paseman, 2013.02.17 $\endgroup$ Feb 18, 2013 at 2:18
  • $\begingroup$ There is no server at publish.mathsource.org. Could you post a correction? Thanks! $\endgroup$ Feb 18, 2013 at 2:26
  • $\begingroup$ Good catch, Paul. Thank you, although community wiki should encourage corrective editing from all. Hopefully I got it right this time. Gerhard "Absolutely Nothing Will Go Worng" Paseman, 2013.02.17 $\endgroup$ Feb 18, 2013 at 2:30
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    $\begingroup$ Thanks -- I did not know about publishing.mathforge.org, and have now posted the question there $\endgroup$ Feb 18, 2013 at 2:55
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    $\begingroup$ Just for reference, here be the question posted on publishing.mathforge: publishing.mathforge.org/discussion/163/math-annotate-platform/… $\endgroup$ Feb 18, 2013 at 13:11

Having read and followed numerous discussion on the subject, it seems that possible downsides arise from having comments or discussions unwanted by the authors of the article.

However, enabling the authors to moderate all comments themselves would seem to address those concerns. That is, when the authors would receive the comments first and then decide whether to make them public. Of course, that would include the possible decision by the authors not to receive any comments at all, a decision that they should also be able to reverse at any time in the future.

Basically, since the authors are the ones who wrote the paper, they should own all the corresponding rights, including any comments and moderation.


Git is a version control system which is commonly used by programmers. While it is useful for managing ones own individual projects, it really starts to shine in collaborative situations. While it was designed to help programmers, it is really a great system for anyone trying writing any text based project. This includes math papers.

The advantages are numerous:

The entire history of the document is stored, so that information is never lost by writing over a document.

The contribution history is clearly documented, so you can see who is responsible for different parts of the work. This very nicely solves attribution issues.

The workflow for working together collaboratively is wonderful. If you and another person are working on different parts of the same document, or making changes to different files altogether, git will merge your work without any effort on your part. If there is a conflict between the work done, git alerts you to this, and allows you to resolve these conflicts.

It takes a little getting used to, but I now find it so essential to how I work that I use it for everything. I wouldn't dream of writing a paper without using git to help me manage versions, especially if I am working on it with another person.

Github provides a free method for people to host their papers, and allow others to collaboratively edit them, comment on them, make "bug reports", and so on, which I feel would be of great value to the mathematical community.

I think that Git really does solve all of the problems raised by the OP.

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    $\begingroup$ If mathematicians were programmers, and if their output were source code, I might find some merit in this answer. It so happens that there are other issues resulting from the fact that the basic material being handled is not source code. I suspect some features of git would be useful, but the system being proposed has a social and economic context that I believe will not be well served by adopting your suggestion. Gerhard "Not A Professional Programmer Either" Paseman, 2013.02.17 $\endgroup$ Feb 18, 2013 at 2:59
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    $\begingroup$ The basic material being handled is source code - .tex files to be specific. If you have an idea for how to improve a paper, just start a new branch and modify it. $\endgroup$
    – Steve
    Feb 18, 2013 at 3:51
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    $\begingroup$ What I mean is that this system already exists, and is perfectly suited to the task. I cannot imagine writing papers without git anymore. This is a general skill which we should really be teaching in middle school - editing your work by saving over old copies is just horrible compared to the elegance and ease of using git. This is only more apparent for any kind of collaborative effort. $\endgroup$
    – Steve
    Feb 18, 2013 at 6:33
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    $\begingroup$ Dear Steve, many of us in the mathematics community are familiar with Git, for various reasons. For example, the Stacks project has used it for years. I suspect some of the negative reactions to your answer are not from the core message, but because it is easy to interpret your tone as aggressive and dismissive. If you are willing to invest a couple more minutes of your time into spreading your wisdom effectively, please click on the "edit" button below the answer text, and change your message to one that sounds more diplomatic. $\endgroup$
    – S. Carnahan
    Feb 18, 2013 at 7:01
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    $\begingroup$ "This very nicely solves attribution issues". Not really. There is a difference between who found the proof and who wrote the proof. $\endgroup$ Feb 18, 2013 at 8:55

Internet group according to "Art of Agreement"


  1. Axioms
  2. Implementation: bees & hives
  3. Practical considerations
  4. Philosophy


  1. Freedom of Speech (of posting)
  2. Freedom of not listening (of not seeing, of not reading)
  3. Responsibility (for posts)
    • Axioms 1-2 imply that everybody and nobody is a moderator, i.e. every participant $X$ is a moderator for $X$, and for nobody else.
    • Responsibility means that no post gets ever erased (it may be declared obsolete though, while it is still available to the public)--think of wiki's history.

Implementation: bees $\&$ hives

It's a highly decentralized system (tightly glued together by links, see below).

Some mathematicians may start hive Art of Thinking. Some other people may start hive Mathematics 2013++. There is no need for more than one hive devoted to mathematics but if that's what they want, nobody will stop them.

Hives form a partially ordered set. You may start a Geometry hive, and declare it to be under Art of Thinking, but above Euclidean Geometry hive. More about the organization of the world of Bees and Hives later.

You start a hive by yourself or with others by simply agreeing on its name, and by creating bee sites, which declare that they are, say, a bee site of Art of Thinking or of Mathematics 2013++, etc. Each participant, a bee, has their own Internet place under their own exclusive control. Typically, a bee (a participant) is just one person (Internaut).

The goal of a hive is to create a dynamically growing data base of posts (texts) and tables of contents, i.e. tables of links to other tables and to posts.

As a bee, you write mainly texts (research, comments about posts by other bees, teaching materials, etc.), but also tables which organize your bee site, which allow readers to navigate your bee site. Your tables may go beyond your own site, they may include links to any posts and tables within your hive. Of course you may also promote any materials, and you may have links to any Internet pages--but that would be more like writing an article (for your hive), for instance something like "Internet resources concerned with mathematics of XVIII century"--it would not be a part of hive's partially ordered hierarchical organization.

If you are socially inclined then you may declare yourself an administrator (with no power though), and then you create a hive site, say for Art of Thinking, e.g. Internaut $X$ may create site titled: Hive Art of Thinking by $X$. The difference between a bee site and a hive site is the intent. In the case of a hive site you want to serve the whole hive rather than just your own bee site.

There can be several hive sites (administrative sites) for the same site, just any number of them. Administrators create table by including the links selectively (rather than all of them).

Any bee or administrator may maintain lists of scores which evaluate posts and bees. Finally, bees and administrators may provide tables of posts and bees which should be avoided.

Practical considerations

Realistically speaking, the described system has a chance only if some (relatively simple to code) software will be created, so that maintaining the tables of contents will be easy. For instance, you may like to copy someone else's several tables, and adopt them for your own bee site after some modifications. The software should also protect you from running into material which you declared to be avoided, e.g. when you want to avoid what administrator X suggests to avoid. Care always has to be taken to avoid loops, to follow always a partial order (rather than a tree--the tree organization is often not adequate).


Art of Agreement is based on one commandment only: you shall not impose.

This commandment applies to adults of sound mind. It's not something to discuss. You either accept it or not. You may only discuss whether or not Art of Agreement leads to better economy, to higher quality of life, etc.

The above bees & hives organization is an example. It should work not because an authority (like wikipedia teen editors) is moderating things for you, including the moderation of you. Instead, you yourself choose your authorities which you follow voluntarily (to whatever extent you choose), and whom you may drop at any time, whom you may replace with other authorities, etc. Why, you may be an authority yourself :-)

Good mathematicians easily recognize other good mathematicians. They would read each other, and they would read papers by unknown to them authors, who are recommended by good mathematicians. The recognition spreads around easily and quite fast. This way a high quality body of mathematics is created and collected without being adversely affected by more numerous weaker articles. And all this judgmental notions of "good" (partially subjective, partially objective) are custom taylored to each bee (which is nice, I feel :-)).

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    $\begingroup$ This does not seem to be an attempt to answer the question. Instead, it appears to be a proposal for an alternative publishing system. $\endgroup$
    – S. Carnahan
    Feb 18, 2013 at 23:53
  • $\begingroup$ Already today, in view of the Internet technology avalable, the distinctions between publishing, discussion groups, and perhaps other related notions, are vanishing. I certainly was addressing the issues raised in @Ingrid Daubechies question--sorry if I didn't stress clearly one point after another. BTW, voting on non-mathematical questions amounts more to censorship than to a meritorious reaction. Perhaps there should be no voting on non-mathematical questions which are loaded politically (and there should be very few such questions in the first place :-)). $\endgroup$ Feb 19, 2013 at 0:50
  • $\begingroup$ The question by I.D. is fine,of course--but I knew that this thread is bad news :-) $\endgroup$ Feb 20, 2013 at 6:11

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