This is what happened behind the scene.
In the first draft, I was very pedantic. The resulted draft is notation-heavy and has no introductory section. It was then totally discarded. However, the structure of the proof was reused in the later drafts. My advisor suggested a useful dictionary by Trzeciak for mathematicians like me who write in English as a second language.
The second draft was finished after 3 months. This time, I started with the history of the problem. The entire process of tracking down the history is like this.
![](https://blog.zilin.one/wp-content/uploads/2014/05/string_notes_on_wall-1024x435.jpg)
The picture is exaggerated. The reality is that for the first time I was handling 10+ references at the same time and that I had to figure out how and in what order I should introduce them in my article. The introductory took 1/3 of the time. Another 1/3 of the time, I was struggling how I could turn the notation-heavy proof in my first draft into English words and sentences which are more friendly to readers. The rest 1/3 of the time, I was drawing pictures and figures. I had never used Tikz (a standard LaTeX graphics package) before. After I learnt how to draw points, lines, how to fill in shape with color and how to put labels, I started my ambitious project to draw a 3D triangulation of a sphere. The result was a super slow Ruby script that outputs Tikz code, which was later complied to generate pictures.
![](https://blog.zilin.one/wp-content/uploads/2014/05/first-paper-figure.png)
The hope was to have the top notch graphics in my paper to compensate the weak mathematics result I got.
Advisor was pretty happy with the second draft and provided several suggestions. Takeaways:
- In LaTex,
:
is a binary operator. The correct unary operator is\colon
. Use\smallskip
,\midskip or
\bigskip
to manually adjust spacing. - Citation information on MathSciNet is generally better than Google Scholar in terms of accuracy of information.
- Starting with the introduction section might be a better way to start a paper. By looking at others’ writings, one can familiarize himself/herself with the language and writing style of the field.
Advisor also drew me the following picture on my second draft.
![](https://blog.zilin.one/wp-content/uploads/2014/05/readership-1024x768.png)
The third draft was a revision of the second draft with two new figures. One of the major pictures is enhance by the Phong shading algorithm. A more refined fourth draft followed with more than 70 places of modifications.
The outcome of this creative process can be found on arXiv:1405.2503.
Wow~