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diff --git a/posts/2013-06-01-q-robinson-schensted-paper.md b/posts/2013-06-01-q-robinson-schensted-paper.md
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--- /dev/null
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+---
+template: oldpost
+title: A \(q\)-weighted Robinson-Schensted algorithm
+date: 2013-06-01
+comments: true
+tags: RS, \(q\)-Whittaker_functions, Macdonald_polynomials
+archive: false
+---
+In [this paper](https://projecteuclid.org/euclid.ejp/1465064320) with [Neil](http://www.bristol.ac.uk/maths/people/neil-m-oconnell/) we construct a \\(q\\)-version of the Robinson-Schensted
+algorithm with column insertion. Like the [usual RS
+correspondence](http://en.wikipedia.org/wiki/Robinson–Schensted_correspondence)
+with column insertion, this algorithm could take words as input. Unlike
+the usual RS algorithm, the output is a set of weighted pairs of
+semistandard and standard Young tableaux \\((P,Q)\\) with the same
+shape. The weights are rational functions of indeterminant \\(q\\).
+
+If \\(q\\in\[0,1\]\\), the algorithm can be considered as a randomised
+RS algorithm, with 0 and 1 being two interesting cases. When
+\\(q\\to0\\), it is reduced to the latter usual RS algorithm; while
+when \\(q\\to1\\) with proper scaling it should scale to directed random
+polymer model in [(O'Connell 2012)](http://arxiv.org/abs/0910.0069).
+When the input word \\(w\\) is a random walk:
+
+\\begin{align\*}\\mathbb
+P(w=v)=\\prod\_{i=1}^na\_{v\_i},\\qquad\\sum\_ja\_j=1\\end{align\*}
+
+the shape of output evolves as a Markov chain with kernel related to
+\\(q\\)-Whittaker functions, which are Macdonald functions when
+\\(t=0\\) with a factor.
+
+
diff --git a/posts/2014-04-01-q-robinson-schensted-symmetry-paper.md b/posts/2014-04-01-q-robinson-schensted-symmetry-paper.md
new file mode 100644
index 0000000..38874bb
--- /dev/null
+++ b/posts/2014-04-01-q-robinson-schensted-symmetry-paper.md
@@ -0,0 +1,19 @@
+---
+template: oldpost
+title: Symmetry property of \(q\)-weighted Robinson-Schensted algorithms and branching algorithms
+date: 2014-04-01
+comments: true
+archive: false
+tags: RS, growth_diagrams
+---
+In [this paper](http://link.springer.com/article/10.1007/s10801-014-0505-x) a symmetry property analogous to the well known symmetry
+property of the normal Robinson-Schensted algorithm has been shown for
+the \\(q\\)-weighted Robinson-Schensted algorithm. The proof uses a
+generalisation of the growth diagram approach introduced by Fomin. This
+approach, which uses "growth graphs", can also be applied to a wider
+class of insertion algorithms which have a branching structure.
+
+![Growth graph of q-RS for 1423](../assets/resources/1423graph.jpg)
+
+Above is the growth graph of the \\(q\\)-weighted Robinson-Schensted
+algorithm for the permutation \\({1 2 3 4\\choose1 4 2 3}\\).
diff --git a/posts/2015-01-20-weighted-interpretation-super-catalan-numbers.md b/posts/2015-01-20-weighted-interpretation-super-catalan-numbers.md
new file mode 100644
index 0000000..6d9e75e
--- /dev/null
+++ b/posts/2015-01-20-weighted-interpretation-super-catalan-numbers.md
@@ -0,0 +1,40 @@
+---
+template: oldpost
+title: AMS review of 'A weighted interpretation for the super Catalan numbers' by Allen and Gheorghiciuc
+date: 2015-01-20
+comments: true
+archive: false
+---
+The super Catalan numbers are defined as 
+\$\$ T(m,n) = {(2 m)! (2 n)! \over 2 m! n! (m + n)!}. \$\$
+
+   This paper has two main results. First a combinatorial interpretation
+of the super Catalan numbers is given: 
+\$\$ T(m,n) = P(m,n) - N(m,n) \$\$
+where \\(P(m,n)\\)
+enumerates the number of 2-Motzkin paths whose \\(m\\) -th step begins at an even level (called \\(m\\)-positive paths) and \\(N(m,n)\\)
+those with \\(m\\)-th step beginning at an odd level (\\(m\\)-negative paths). The proof uses a recursive argument on the number of
+\\(m\\)-positive and -negative paths, based on a recursion of the super Catalan
+numbers appearing in \[I. M. Gessel, J. Symbolic Comput. **14** (1992), no. 2-3, 179–194;
+[MR1187230](http://www.ams.org/mathscinet/search/publdoc.html?r=1&pg1=MR&s1=1187230&loc=fromrevtext)\]:
+\$\$ 4T(m,n) = T(m+1, n) + T(m, n+1). \$\$
+This result gives an expression for the super Catalan numbers in terms
+of numbers counting the so-called ballot paths. The latter sometimes are
+also referred to as the generalised Catalan numbers forming the entries
+of the Catalan triangle.
+
+   Based on the first result, the second result is a combinatorial
+interpretation of the super Catalan numbers \\(T(2,n)\\)
+in terms of counting certain Dyck paths. This is equivalent to a
+theorem, which represents \\(T(2,n)\\)
+as counting of certain pairs of Dyck paths, in \[I. M. Gessel and G.
+Xin, J. Integer Seq. **8** (2005), no. 2, Article
+05.2.3, 13 pp.;
+[MR2134162](http://www.ams.org/mathscinet/search/publdoc.html?r=1&pg1=MR&s1=2134162&loc=fromrevtext)\],
+and the equivalence is explained at the end of the paper by a bijection
+between the Dyck paths and the pairs of Dyck paths. The proof of the
+theorem itself is also done by constructing two bijections between Dyck
+paths satisfying certain conditions. All the three bijections are
+formulated by locating, removing and adding steps.
+
+Copyright notice: This review is published at http://www.ams.org/mathscinet-getitem?mr=3275875, its copyright owned by the AMS.
diff --git a/posts/2015-04-01-unitary-double-products.md b/posts/2015-04-01-unitary-double-products.md
new file mode 100644
index 0000000..a2f8ccb
--- /dev/null
+++ b/posts/2015-04-01-unitary-double-products.md
@@ -0,0 +1,10 @@
+---
+title: Unitary causal quantum stochastic double products as universal interactions I
+date: 2015-04-01
+template: oldpost
+comments: true
+archive: false
+---
+In [this paper](http://www.actaphys.uj.edu.pl/findarticle?series=Reg&vol=46&page=1851) with [Robin](http://homepages.lboro.ac.uk/~marh3/) we show the explicit formulae for a family of unitary
+triangular and rectangular double product integrals which can be
+described as second quantisations.
diff --git a/posts/2015-04-02-juggling-skill-tree.md b/posts/2015-04-02-juggling-skill-tree.md
new file mode 100644
index 0000000..be39822
--- /dev/null
+++ b/posts/2015-04-02-juggling-skill-tree.md
@@ -0,0 +1,33 @@
+---
+template: oldpost
+title: jst
+date: 2015-04-02
+comments: true
+archive: false
+---
+jst = juggling skill tree
+
+If you have ever played a computer role playing game, you may have
+noticed the protagonist sometimes has a skill "tree" (most of the time
+it is actually a directed acyclic graph), where certain skills leads to
+others. For example,
+[here](http://hydra-media.cursecdn.com/diablo.gamepedia.com/3/37/Sorceress_Skill_Trees_%28Diablo_II%29.png?version=b74b3d4097ef7ad4e26ebee0dcf33d01)
+is the skill tree of sorceress in [Diablo
+II](https://en.wikipedia.org/wiki/Diablo_II).
+
+Now suppose our hero embarks on a quest for learning all the possible
+juggling patterns. Everyone would agree she should start with cascade,
+the simplest nontrivial 3-ball pattern, but what afterwards? A few other
+accessible patterns for beginners are juggler's tennis, two in one and
+even reverse cascade, but what to learn after that? The encyclopeadic
+[Library of Juggling](http://libraryofjuggling.com/) serves as a good
+guide, as it records more than 160 patterns, some of which very
+aesthetically appealing. On this website almost all the patterns have a
+"prerequisite" section, indicating what one should learn beforehand. I
+have therefore written a script using [Python](http://python.org),
+[BeautifulSoup](http://www.crummy.com/software/BeautifulSoup/) and
+[pygraphviz](http://pygraphviz.github.io/) to generate a jst (graded by
+difficulties, which is the leftmost column) from the Library of Juggling
+(click the image for the full size): 
+
+[![The juggling skill tree](../assets/resources/juggling.png){width="38em"}](../assets/resources/juggling.png)
diff --git a/posts/2015-05-30-infinite-binary-words-containing-repetitions-odd-periods.md b/posts/2015-05-30-infinite-binary-words-containing-repetitions-odd-periods.md
new file mode 100644
index 0000000..8f2ff8e
--- /dev/null
+++ b/posts/2015-05-30-infinite-binary-words-containing-repetitions-odd-periods.md
@@ -0,0 +1,94 @@
+---
+template: oldpost
+title: AMS review of 'Infinite binary words containing repetitions of odd period' by Badkobeh and Crochemore
+date: 2015-05-30
+comments: true
+archive: false
+---
+This paper is about the existence of pattern-avoiding infinite binary
+words, where the patterns are squares, cubes and \\(3^+\\)-powers.
+   There are mainly two kinds of results, positive (existence of an
+infinite binary word avoiding a certain pattern) and negative
+(non-existence of such a word). Each positive result is proved by the
+construction of a word with finitely many squares and cubes which are
+listed explicitly. First a synchronising (also known as comma-free)
+uniform morphism \\(g\\: \\Sigma_3^\* \\to
+\\Sigma_2^\*\\)
+
+is constructed. Then an argument is given to show that the length of
+squares in the code \\(g(w)\\) 
+for a squarefree \\(w\\) is bounded, hence all the squares can be obtained by examining all \\(g(s)\\) for \\(s\\)
+of bounded lengths. The argument resembles that of the proof of, e.g.,
+Theorem 1, Lemma 2, Theorem 3 and Lemma 4 in \[N. Rampersad, J. O.
+Shallit and M. Wang, Theoret. Comput. Sci. **339**
+(2005), no. 1, 19–34;
+[MR2142071](http://www.ams.org/mathscinet/search/publdoc.html?r=1&pg1=MR&s1=2142071&loc=fromrevtext)\].
+The negative results are proved by traversing all possible finite words
+satisfying the conditions.
+
+   Let \\(L(n_2, n_3, S)\\) be the maximum length of a word with \\(n_2\\) distinct squares, \\(n_3\\) 
+distinct cubes and that the periods of the squares can take values only
+in \\(S\\) 
+, where \\(n_2, n_3 \\in \\Bbb N \\cup
+\\{\\infty, \\omega\\}\\) 
+and \\(S \\subset \\Bbb N_+\\) 
+.
+   \\(n_k = 0\\) 
+corresponds to \\(k\\)-free, \\(n_k = \\infty\\) 
+means no restriction on the number of distinct \\(k\\)-powers, and \\(n_k = \\omega\\) 
+means \\(k^+\\)-free.
+
+   Below is the summary of the positive and negative results:
+
+(1) (Negative) \\(L(\\infty, \\omega, 2 \\Bbb N)
+    < \\infty\\)
+    : \\(\\nexists\\)
+    an infinite \\(3^+\\)
+    -free binary word avoiding all squares of odd periods.
+    (Proposition 1)
+
+(2) (Negative) \\(L(\\infty, 0, 2 \\Bbb N + 1) \\le
+    23\\)
+    : \\(\\nexists\\)
+    an infinite 3-free binary word, avoiding squares of even periods.
+    The longest one has length \\(\\le 23\\)
+    (Proposition 2).
+
+(3) (Positive) \\(L(\\infty, \\omega, 2 \\Bbb N +
+    1) = \\infty\\)
+    : \\(\\exists\\)
+    an infinite \\(3^+\\)
+    -free binary word avoiding squares of even periods (Theorem 1).
+
+(4) (Positive) \\(L(\\infty, \\omega, \\{1, 3\\}) =
+    \\infty\\)
+    : \\(\\exists\\)
+    an infinite \\(3^+\\)
+    -free binary word containing only squares of period 1 or 3
+    (Theorem 2).
+
+(5) (Negative) \\(L(6, 1, 2 \\Bbb N + 1) =
+    57\\)
+    : \\(\\nexists\\)
+    an infinite binary word avoiding squares of even period containing
+    \\(< 7\\)
+    squares and \\(< 2\\)
+    cubes. The longest one containing 6 squares and 1 cube has length 57
+    (Proposition 6).
+
+(6) (Positive) \\(L(7, 1, 2 \\Bbb N + 1) =
+    \\infty\\)
+    : \\(\\exists\\)
+    an infinite \\(3^+\\)
+    -free binary word avoiding squares of even period with 1 cube and 7
+    squares (Theorem 3).
+
+(7) (Positive) \\(L(4, 2, 2 \\Bbb N + 1) =
+    \\infty\\)
+    : \\(\\exists\\)
+    an infinite \\(3^+\\)
+    -free binary words avoiding squares of even period and containing 2
+    cubes and 4 squares (Theorem 4).
+
+
+Copyright notice: This review is published at http://www.ams.org/mathscinet-getitem?mr=3313467, its copyright owned by the AMS.
diff --git a/posts/2015-07-01-causal-quantum-product-levy-area.md b/posts/2015-07-01-causal-quantum-product-levy-area.md
new file mode 100644
index 0000000..cbf2fcf
--- /dev/null
+++ b/posts/2015-07-01-causal-quantum-product-levy-area.md
@@ -0,0 +1,13 @@
+---
+template: oldpost
+title: On a causal quantum double product integral related to Lévy stochastic area.
+date: 2015-07-01
+archive: false
+comments: true
+---
+In [this paper](https://arxiv.org/abs/1506.04294) with [Robin](http://homepages.lboro.ac.uk/~marh3/) we study the family of causal double product integrals 
+\\[ 
+\\prod_{a < x < y < b}\\left(1 + i{\\lambda \\over 2}(dP_x dQ_y - dQ_x dP_y) + i {\\mu \\over 2}(dP_x dP_y + dQ_x dQ_y)\\right) 
+\\]
+
+where $P$ and $Q$ are the mutually noncommuting momentum and position Brownian motions of quantum stochastic calculus. The evaluation is motivated heuristically by approximating the continuous double product by a discrete product in which infinitesimals are replaced by finite increments. The latter is in turn approximated by the second quantisation of a discrete double product of rotation-like operators in different planes due to a result in [(Hudson-Pei2015)](http://www.actaphys.uj.edu.pl/findarticle?series=Reg&vol=46&page=1851). The main problem solved in this paper is the explicit evaluation of the continuum limit $W$ of the latter, and showing that $W$ is a unitary operator. The kernel of $W$ is written in terms of Bessel functions, and the evaluation is achieved by working on a lattice path model and enumerating linear extensions of related partial orderings, where the enumeration turns out to be heavily related to Dyck paths and generalisations of Catalan numbers.
diff --git a/posts/2015-07-15-double-macdonald-polynomials-macdonald-superpolynomials.md b/posts/2015-07-15-double-macdonald-polynomials-macdonald-superpolynomials.md
new file mode 100644
index 0000000..efdd416
--- /dev/null
+++ b/posts/2015-07-15-double-macdonald-polynomials-macdonald-superpolynomials.md
@@ -0,0 +1,73 @@
+---
+template: oldpost
+title: AMS review of 'Double Macdonald polynomials as the stable limit of Macdonald superpolynomials' by Blondeau-Fournier, Lapointe and Mathieu
+date: 2015-07-15
+comments: true
+archive: false
+---
+A Macdonald superpolynomial (introduced in \[O. Blondeau-Fournier et
+al., Lett. Math. Phys. <span class="bf">101</span> (2012), no. 1, 27–47;
+[MR2935476](http://www.ams.org/mathscinet/search/publdoc.html?pg1=MR&s1=2935476&loc=fromrevtext);
+J. Comb. <span class="bf">3</span> (2012), no. 3, 495–561;
+[MR3029444](http://www.ams.org/mathscinet/search/publdoc.html?pg1=MR&s1=3029444&loc=fromrevtext)\])
+in \\(N\\) 
+Grassmannian variables indexed by a superpartition \\(\\Lambda\\) 
+is said to be stable if \\({m (m + 1) \\over 2}
+\\ge |\\Lambda|\\) 
+and \\(N \\ge |\\Lambda| - {m (m - 3) \\over
+2}\\) 
+, where \\(m\\) 
+is the fermionic degree. A stable Macdonald superpolynomial
+(corresponding to a bisymmetric polynomial) is also called a double
+Macdonald polynomial (dMp). The main result of this paper is the
+factorisation of a dMp into plethysms of two classical Macdonald
+polynomials (Theorem 5). Based on this result, this paper
+
+(1) shows that the dMp has a unique decomposition into bisymmetric
+    monomials;
+
+(2) calculates the norm of the dMp;
+
+(3) calculates the kernel of the Cauchy-Littlewood-type identity of the
+    dMp;
+
+(4) shows the specialisation of the aforementioned factorisation to the
+    Jack, Hall-Littlewood and Schur cases. One of the three Schur
+    specialisations, denoted as \\(s_{\\lambda, \\mu}\\), also appears in (7) and (9) below;
+
+(5) defines the \\(\\omega\\)
+    -automorphism in this setting, which was used to prove an identity
+    involving products of four Littlewood-Richardson coefficients;
+
+(6) shows an explicit evaluation of the dMp motivated by the most
+    general evaluation of the usual Macdonald polynomials;
+
+(7) relates dMps with the representation theory of the hyperoctahedral
+    group \\(B_n\\)
+    via the double Kostka coefficients (which are defined as the entries
+    of the transition matrix from the bisymmetric Schur functions \\(s_{\\lambda, \\mu}\\)
+    to the modified dMps);
+
+(8) shows that the double Kostka coefficients have the positivity and
+    the symmetry property, and can be written as sums of products of the
+    usual Kostka coefficients;
+
+(9) defines an operator \\(\\nabla^B\\)
+    as an analogue of the nabla operator \\(\\nabla\\)
+    introduced in \[F. Bergeron and A. M. Garsia, in *Algebraic methods and \\(q\\)-special functions* (Montréal, QC, 1996), 1–52, CRM Proc. Lecture
+    Notes, 22, Amer. Math. Soc., Providence, RI, 1999;
+    [MR1726826](http://www.ams.org/mathscinet/search/publdoc.html?r=1&pg1=MR&s1=1726826&loc=fromrevtext)\].
+    The action of \\(\\nabla^B\\)
+    on the bisymmetric Schur function \\(s_{\\lambda, \\mu}\\)
+    yields the dimension formula \\((h + 1)^r\\)
+    for the corresponding representation of \\(B_n\\)
+    , where \\(h\\)
+    and \\(r\\)
+    are the Coxeter number and the rank of \\(B_n\\)
+    , in the same way that the action of \\(\\nabla\\)
+    on the \\(n\\)
+    th elementary symmetric function leads to the same formula for the
+    group of type \\(A_n\\)
+    .
+
+Copyright notice: This review is published at http://www.ams.org/mathscinet-getitem?mr=3306078, its copyright owned by the AMS.
diff --git a/posts/2016-10-13-q-robinson-schensted-knuth-polymer.md b/posts/2016-10-13-q-robinson-schensted-knuth-polymer.md
new file mode 100644
index 0000000..4d31e37
--- /dev/null
+++ b/posts/2016-10-13-q-robinson-schensted-knuth-polymer.md
@@ -0,0 +1,23 @@
+---
+template: oldpost
+title: A \(q\)-Robinson-Schensted-Knuth algorithm and a \(q\)-polymer
+date: 2016-10-13
+comments: true
+archive: false
+---
+(Latest update: 2017-01-12)
+In [Matveev-Petrov 2016](http://arxiv.org/abs/1504.00666) a  \\(q\\)-deformed Robinson-Schensted-Knuth algorithm (\\(q\\)RSK) was introduced. In this article we give reformulations of this algorithm in terms of Noumi-Yamada description, growth diagrams and local moves. We show that the algorithm is symmetric, namely the output tableaux pair are swapped in a sense of distribution when the input matrix is transposed. We also formulate a  \\(q\\)-polymer model based on the \\(q\\)RSK and prove the corresponding Burke property, which we use to show a strong law of large numbers for the partition function given stationary boundary conditions and  \\(q\\)-geometric weights. We use the  \\(q\\)-local moves to define a generalisation of the \\(q\\)RSK taking a Young diagram-shape of array as the input. We write down the joint distribution of partition functions in the space-like direction of the  \\(q\\)-polymer in  \\(q\\)-geometric environment, formulate a  \\(q\\)-version of the multilayer polynuclear growth model (\\(q\\)PNG) and write down the joint distribution of the  \\(q\\)-polymer partition functions at a fixed time. 
+
+This article is available at [arXiv](https://arxiv.org/abs/1610.03692).
+It seems to me that one difference between arXiv and Github is that on arXiv each preprint has a few versions only.
+In Github many projects have a "dev" branch hosting continuous updates, whereas the master branch is where the stable releases live.
+
+[Here]({{ site.url }}/assets/resources/qrsklatest.pdf) is a "dev" version of the article, which I shall push to arXiv when it stablises. Below is the changelog.
+
+* 2017-01-12: Typos and grammar, arXiv v2.
+* 2016-12-20: Added remarks on the geometric \\(q\\)-pushTASEP. Added remarks on the converse of the Burke property. Added natural language description of the \\(q\\)RSK. Fixed typos.
+* 2016-11-13: Fixed some typos in the proof of Theorem 3.
+* 2016-11-07: Fixed some typos. The \\(q\\)-Burke property is now stated in a more symmetric way, so is the law of large numbers Theorem 2.
+* 2016-10-20: Fixed a few typos. Updated some references. Added a reference: [a set of notes titled "RSK via local transformations"](http://web.mit.edu/~shopkins/docs/rsk.pdf).
+It is written by [Sam Hopkins](http://web.mit.edu/~shopkins/) in 2014 as an expository article based on MIT combinatorics preseminar presentations of Alex Postnikov.
+It contains some idea (applying local moves to a general Young-diagram shaped array in the order that matches any growth sequence of the underlying Young diagram) which I thought I was the first one to write down.
diff --git a/posts/2017-04-25-open_research_toywiki.md b/posts/2017-04-25-open_research_toywiki.md
new file mode 100644
index 0000000..1b9b45a
--- /dev/null
+++ b/posts/2017-04-25-open_research_toywiki.md
@@ -0,0 +1,19 @@
+---
+template: oldpost
+title: Open mathematical research and launching toywiki
+date: 2017-04-25
+comments: true
+archive: false
+---
+As an experimental project, I am launching toywiki.
+
+It hosts a collection of my research notes.
+
+It takes some ideas from the open source culture and apply them to mathematical research:
+1. It uses a very permissive license (CC-BY-SA). For example anyone can fork the project and make their own version if they have a different vision and want to build upon the project.
+2. All edits will done with maximum transparency, and discussions of any of notes should also be as public as possible (e.g. Github issues)
+3. Anyone can suggest changes by opening issues and submitting pull requests
+
+Here are the links: [toywiki](http://toywiki.xyz) and [github repo](https://github.com/ycpei/toywiki).
+
+Feedbacks are welcome by email.
diff --git a/posts/2017-08-07-mathematical_bazaar.md b/posts/2017-08-07-mathematical_bazaar.md
new file mode 100644
index 0000000..00a8724
--- /dev/null
+++ b/posts/2017-08-07-mathematical_bazaar.md
@@ -0,0 +1,208 @@
+---
+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.