Proof Reading

“Writing is hard work. A clear sentence is no accident.
Very few sentences come out right the first time, or even the third time.
Remember this in moments of despair.
If you find that writing is hard, it’s because it is hard.”
-- William Zinsser. On Writing Well

I use proof-reading and re-writing synonymously. I hope that in time, this document will become something of a useful framework for proof reading. Right now, these are just tips I find useful.

• Print the paper with line numbers.
• Start by checking the theorems, lemmas and proposition statements, try to make them as self contained as you can, even at the cost of repeating yourself. This is the most important proof-reading step, typos in formal statements (specially in mathematical expressions) can easily make them formally wrong. I have learnt this the hard way, after getting a paper rejected because I wrote $A(x)$ instead of $A(x,y)$.
• Spellings I struggle with: it's vs its, being, their vs there, principal vs principle $\dots$
• Punctuations: Can change everything. Check them !
• Start proof reading in reverse order. Firstly, it will allow you to see the errors more clearly. But more importantly, you will make much safer choices of notation changes. It is very easy to fall in trap of changing the notation in the introductory section, when everything looks neat and elegant. And then you reach the appendix, realizing that you renamed a matrix to $S$, but $S$ was also another constant that is littered across your appendix in tens of hidden places.
• Adverbs: Use sparingly !
• Audience: You cannot write keeping the reader in mind, academia is just too vast to keep everyone in mind. Maybe introduction and related work can be made more accessible. But for technical stuff, just write for the version of you who would be reading the paper after a year long sabbatical.
• Indeed: it introduces a brief informal proof of the preceding statement
• Examples: The best aid for the general reader could be examples, if space is no limit, just go for many examples.