When should I use italics in scientific writing?

Question

I noticed that proper nouns, such as names of theorems or techniques are often set in italics in scientific writing but not always. Are there rules about it, for example each proper noun should be set in italic the first time it occurs?

A contrived example

There are many different methods for adding two numbers:

Very Simple Addition (VSA) works by calculating a+b.

Unnecessary Complicated Addition (UCA) works by calculating -(-a-b).

VSA is the method used by everyone but the British who use UCA because of tradition along with their foot-inch based measurement system.

Answer 1

The Style Manual of the American Psychological Association (APA, 2009, pp. 104-106) is very clear on the use of italics. Note especially the bold section (bold emphasis mine):

Use italics for

• titles of books, periodicals, films
  exception: italic words in the title (reverse italicization)
• genera, species, and varietes
• introduction of a new technical term
  (after a term has been used once, do not italicize it)
• a letter, word, or phrase cited as a linguistic example
  ("words such as big and little")
• words that could be misread
  ("the small group", meaning a designation, not group size)
• letters used as statistical symbols or algebraic variables
• some test scores and scales
• periodical volume numbers in reference lists
• anchors of scale
  ("health ratings ranged from 1 (poor) to 5 (excellent)")

Do not use italics for

• foreign phrases and abbreviations common in English
• chemical terms
• trigonometric terms
• nonstatistial subscripts to statistical symbols or mathematical expressions
• Greek letters
• mere emphasis. (Italics are acceptable if emphasis might otherwise be lost; in general, however, use syntax to provide emphasis.)
  Incorrect:
  it is important to bear in mind that this process is not proposed as a stage theory of developments.
• letters used as abbreviations

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I've been writing both in APA and MLA style, and I have never needed to emphasize words. Scientific discourse is encouraged to be neutral and self-constrained, and there are other, semantic, means to direct the reader's attention.

Answer 2

Italics are a common way to emphasize words. As such, it's best to use italics sparingly. A text where every proper noun is italicized gets very annoying to read; it'd be like listening to a commercial.
If you're writing for a specific publication, check their style guide.

Answer 3

Italics are used to emphasize words in general writing, but in technical writing you may have to use them for other forms of distinctive treatment. For that reason, I do not use italics (or bold) for emphasis. Generally, I use bold to highlight terms that I think the reader won't know. I only use italics when my style guide calls for them. I generally ignore Chicago, MLA, and so forth for rules regarding distinctive treatment, unless my own style guide doesn't say anything. Even then, I discuss the style rules I use with the other people on my team before I put them into force.

Remember that concise, clear, and consistent documentation is our goal. Correct style is subservient to that goal. Other technical writers may question your choice, but readers won't be conscious of it.