Every writer has also to be a proofreader, whether it be of his or her own drafts or of proofs sent by a publisher. In this post I will give some real-life examples of corrections to proofs. The problems to be corrected are not all errors: some are subtle aspects of the typesetting that need improvement. These examples should give you some ideas on what to look out for the next time you have a set of proofs to inspect.
Example 1
The first example is from proofs of one of my recent papers:
The article had been submitted as LaTeX source and it was reasonable to assume that the only differences between the proofs and what we submitted would be in places where a copy editor had imposed the journal style or had spotted a grammatical error. Fortunately, I know from experience not to make that assumption. These two sentences contain two errors introduced during copy editing: the term “Anderson acceleration” has been deleted after “To apply”, and “We denote by unvec” has been changed to “We denote by vec” (making the sentence nonsensical). The moral is never to assume that egregious errors have not been introduced: check everything in journal proofs.
In a similar vein, consider this extract from another set of proofs:
There is nothing wrong with the words or equations. The problem is that an unwanted paragraph break has been inserted after equation (2.6), and indeed also before “Only”. This set of proofs contained numerous unwanted added new paragraphs.
Example 2
Here is an extract from the proofs of my recent SIAM Review paper (with Natasa Strabic and Vedran Sego) Restoring Definiteness via Shrinking, with an Application to Correlation Matrices with a Fixed Block:
We noticed that the word “how” appears at the end of a line four times within seven lines—an unfortunate coincidence. We suggested that the production editor insert a hard space in the LaTeX source between one or more of the hows and the following word in order to force different line breaks. Here is the result as published:
Example 3
What’s wrong with this example, from a paper in the 1980s?
The phrase “best unknown” should be “best known”!
Example 4
The next example is from a book:
At first sight there is nothing wrong. But the 
When you realize that the left parenthesis and the digit
Example 5
The final example (from a 2013 issue of Private Eye) is completely different and illustrates a rare phenomenon:
If you cannot see anything wrong after a minute or so, click here. This phenomenon, whereby white spaces in successive lines join up to make a snake, is known as rivers of white. The fix, as in Example 2, is to force different line breaks.
Nick Higham 
