Learn English – Comma or semicolon before “see [reference]”

My main publishing client these days has a strict style guideline for dealing with cross references that do not require footnotes: put the cross reference in parentheses as a complete sentence starting with the word See. Under that rule, the text that the poster asks about here would be rendered as

This can be proved via the method of Gauss. (See [1].)

Other publishers that I have worked for required including the reference in parentheses within the sentence leading up to it:

This can be proved via the method of Gauss (see [1]).

Still others took the reference out of parentheses and treated it either as a freestanding sentence:

This can be proved via the method of Gauss. See [1].

or as an independent clause set off by a semicolon (the method used in the OP's example):

This can be proved via the method of Gauss; see [1].

What is right and what is wrong are determined by who pays for the article and its editing. As a copy editor, I would not recommend setting off "see [1]" with a comma in a sentence such as

This can be proved via the method of Gauss, see [1].

because in that construction a comma seems to me to be rather weak for its intended purpose. However, I would enforce a house style that required doing it that way, whether I liked it or not.

The Chicago Manual of Style, sixteenth edition (2010), doesn't discuss in-main-text reference style at all. I imagine that this reflects the extreme variability in preferred style from one publishing house to the next. Nevertheless, CMOS itself uses the "(see xxxxx)" style, as is evident from this excerpt from guideline 13.65:

...it may be advisable to devise an abbreviation for each [title] and to include a list of abbreviations at the beginning or end of the work (see 14.54, 14.55).

Likewise, Words into Type, third edition (1974) doesn't endorse a standard style for such references but in practice it uses the same style as CMOS:

A clause beginning with so, then, or yet should usually be separated from a preceding clause, and a comma is often sufficient for this purpose (see p. 183).

And the MLA Style Manual, second edition (1998), in this typical sentence, shows that it favors the same style:

Of course, whenever the infringement and the registration occurred, the owner of a work infringed is always entitled to actual damages, such as lost income, as well as to the infringer's profits attributable to the infringement, so long as they do not duplicate the award of actual damages (see 2.1.15).

So multiple guides show a preference for the "(see xxxxx)" style, but they seem not at all eager to raise their preference to the level of a guideline. And in the absence of an explicit guideline from an authoritative source, most publishing houses will go their separate ways on issues such as this one.