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+---
+template: oldpost
+title: The Mathematical Bazaar
+date: 2017-08-07
+comments: true
+archive: false
+---
+
+In this essay I describe some problems in academia of mathematics and
+propose an open source model, which I call open research in mathematics.
+
+This essay is a work in progress - comments and criticisms are welcome!
+[^feedback]
+
+Before I start I should point out that
+
+1.  Open research is *not* open access. In fact the latter is a
+    prerequisite to the former.
+2.  I am not proposing to replace the current academic model with the
+    open model - I know academia works well for many people and I am
+    happy for them, but I think an open research community is long
+    overdue since the wide adoption of the World Wide Web more than two
+    decades ago. In fact, I fail to see why an open model can not run in
+    tandem with the academia, just like open source and closed source
+    software development coexist today.
+
+problems of academia
+--------------------
+
+Open source projects are characterised by publicly available source
+codes as well as open invitations for public collaborations, whereas closed
+source projects do not make source codes accessible to the public. How
+about mathematical academia then, is it open source or closed source? The
+answer is neither.
+
+Compared to some other scientific disciplines, mathematics does not
+require expensive equipments or resources to replicate results; compared
+to programming in conventional software industry, mathematical findings
+are not meant to be commercial, as credits and reputation rather than
+money are the direct incentives (even though the former are commonly
+used to trade for the latter). It is also a custom and common belief
+that mathematical derivations and theorems shouldn\'t be patented.
+Because of this, mathematical research is an open source activity in the
+sense that proofs to new results are all available in papers, and thanks
+to open access e.g. the arXiv preprint repository most of the new
+mathematical knowledge is accessible for free.
+
+Then why, you may ask, do I claim that maths research is not open
+sourced? Well, this is because 1. mathematical arguments are not easily
+replicable and 2. mathematical research projects are mostly not open for
+public participation.
+
+Compared to computer programs, mathematical arguments are not written in
+an unambiguous language, and they are terse and not written in maximum
+verbosity (this is especially true in research papers as journals
+encourage limiting the length of submissions), so the understanding of a
+proof depends on whether the reader is equipped with the right
+background knowledge, and the completeness of a proof is highly
+subjective. More generally speaking, computer programs are mostly
+portable because all machines with the correct configurations can
+understand and execute a piece of program, whereas humans are subject to
+their environment, upbringings, resources etc. to have a brain ready to
+comprehend a proof that interests them. (these barriers are softer than
+the expensive equipments and resources in other scientific fields
+mentioned before because it is all about having access to the right
+information)
+
+On the other hand, as far as the pursuit of reputation and prestige
+(which can be used to trade for the scarce resource of research
+positions and grant money) goes, there is often little practical
+motivation for career mathematicians to explain their results to the
+public carefully. And so the weird reality of the mathematical academia
+is that it is not an uncommon practice to keep trade secrets in order to
+protect one\'s territory and maintain a monopoly. This is doable because
+as long as a paper passes the opaque and sometimes political peer review
+process and is accepted by a journal, it is considered work done,
+accepted by the whole academic community and adds to the reputation of
+the author(s). Just like in the software industry, trade secrets and
+monopoly hinder the development of research as a whole, as well as
+demoralise outsiders who are interested in participating in related
+research.
+
+Apart from trade secrets and territoriality, another reason to the
+nonexistence of open research community is an elitist tradition in the
+mathematical academia, which goes as follows:
+
+-   Whoever is not good at mathematics or does not possess a degree in
+    maths is not eligible to do research, or else they run high risks of
+    being labelled a crackpot.
+-   Mistakes made by established mathematicians are more tolerable than
+    those less established.
+-   Good mathematical writings should be deep, and expositions of
+    non-original results are viewed as inferior work and do not add to
+    (and in some cases may even damage) one\'s reputation.
+
+All these customs potentially discourage public participations in
+mathematical research, and I do not see them easily go away unless an
+open source community gains momentum.
+
+To solve the above problems, I propose a open source model of
+mathematical research, which has high levels of openness and
+transparency and also has some added benefits listed in the last section
+of this essay. This model tries to achieve two major goals:
+
+-   Open and public discussions and collaborations of mathematical
+    research projects online
+-   Open review to validate results, where author name, reviewer name,
+    comments and responses are all publicly available online.
+
+To this end, a Github model is fitting. Let me first describe how open
+source collaboration works on Github.
+
+open source collaborations on Github
+------------------------------------
+
+On [Github](https://github.com), every project is publicly available in
+a repository (we do not consider private repos). The owner can update
+the project by \"committing\" changes, which include a message of what
+has been changed, the author of the changes and a timestamp. Each
+project has an issue tracker, which is basically a discussion forum
+about the project, where anyone can open an issue (start a discussion),
+and the owner of the project as well as the original poster of the issue
+can close it if it is resolved, e.g. bug fixed, feature added, or out of
+the scope of the project. Closing the issue is like ending the
+discussion, except that the thread is still open to more posts for
+anyone interested. People can react to each issue post, e.g. upvote,
+downvote, celebration, and importantly, all the reactions are public
+too, so you can find out who upvoted or downvoted your post.
+
+When one is interested in contributing code to a project, they fork it,
+i.e. make a copy of the project, and make the changes they like in the
+fork. Once they are happy with the changes, they submit a pull request
+to the original project. The owner of the original project may accept or
+reject the request, and they can comment on the code in the pull
+request, asking for clarification, pointing out problematic part of the
+code etc and the author of the pull request can respond to the comments.
+Anyone, not just the owner can participate in this review process,
+turning it into a public discussion. In fact, a pull request is a
+special issue thread. Once the owner is happy with the pull request,
+they accept it and the changes are merged into the original project. The
+author of the changes will show up in the commit history of the original
+project, so they get the credits.
+
+As an alternative to forking, if one is interested in a project but has
+a different vision, or that the maintainer has stopped working on it,
+they can clone it and make their own version. This is a more independent
+kind of fork because there is no longer intention to contribute back to
+the original project.
+
+Moreover, on Github there is no way to send private messages, which
+forces people to interact publicly. If say you want someone to see and
+reply to your comment in an issue post or pull request, you simply
+mention them by `@someone`.
+
+open research in mathematics
+----------------------------
+
+All this points to a promising direction of open research. A maths
+project may have a wiki / collection of notes, the paper being written,
+computer programs implementing the results etc. The issue tracker can
+serve as a discussion forum about the project as well as a platform for
+open review (bugs are analogous to mistakes, enhancements are possible
+ways of improving the main results etc.), and anyone can make their own
+version of the project, and (optionally) contribute back by making pull
+requests, which will also be openly reviewed. One may want to add an
+extra \"review this project\" functionality, so that people can comment
+on the original project like they do in a pull request. This may or may
+not be necessary, as anyone can make comments or point out mistakes in
+the issue tracker.
+
+One may doubt this model due to concerns of credits because work in
+progress is available to anyone. Well, since all the contributions are
+trackable in project commit history and public discussions in issues and
+pull request reviews, there is in fact *less* room for cheating than the
+current model in academia, where scooping can happen without any
+witnesses. What we need is a platform with a good amount of trust like
+arXiv, so that the open research community honours (and can not ignore)
+the commit history, and the chance of mis-attribution can be reduced to
+minimum.
+
+Compared to the academic model, open research also has the following
+advantages:
+
+-   Anyone in the world with Internet access will have a chance to
+    participate in research, whether they are affiliated to a
+    university, have the financial means to attend conferences, or are
+    colleagues of one of the handful experts in a specific field.
+-   The problem of replicating / understanding maths results will be
+    solved, as people help each other out. This will also remove the
+    burden of answering queries about one\'s research. For example, say
+    one has a project \"Understanding the fancy results in \[paper
+    name\]\", they write up some initial notes but get stuck
+    understanding certain arguments. In this case they can simply post
+    the questions on the issue tracker, and anyone who knows the answer,
+    or just has a speculation can participate in the discussion. In the
+    end the problem may be resolved without the authors of the paper
+    being bothered, who may be too busy to answer.
+-   Similarly, the burden of peer review can also be shifted from a few
+    appointed reviewers to the crowd.
+
+related readings
+----------------
+
+-   [The Cathedral and the Bazaar by Eric Raymond](http://www.catb.org/esr/writings/cathedral-bazaar/)
+-   [Doing sience online by Michael Nielson](http://michaelnielsen.org/blog/doing-science-online/)
+-   [Is massively collaborative mathematics possible? by Timothy Gowers](https://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/)
+
+[^feedback]: Please send your comments to my email address - I am still looking for ways to add a comment functionality to this website.