On the use of "it is shown"

This usage seems extremely confusing to me. I expect that the authors are trying to avoid any use of "we" in this paper (and so are avoiding the standard phrase in math papers "we now show"), but they are doing so incompetently. I would suggest you recommend that the authors replace all of these instances with a phrase like "it will now be shown" or "it will next be shown".

Like other answerers, I'm not a referee for academic papers either. But I see nothing unusual in the usage. Google Books, for example, claims 1,550,000 results for "thus it is shown". As I would expect, there's a fairly high percentage of "academic-looking" texts in the results.

Obviously the word "thus" normally indicates that the showing/exposition was in some preceding text, but even that needn't be the case. Section 1 of a paper could start by saying, for example,

First, we [will] prove that A = B, then prove that B = C. Thus it is shown that A = C, the implications of which will be considered in detail in Section 2.

Clearly, the exposition hasn't even happened yet. I think one reason the usage works in academic texts better than in common parlance is because the subject matter is more in the nature of "universal, eternal truths", making present tense a more natural/neutral choice. Similar to the way academic writing tends to favor the passive voice, and eschew personal pronouns.

In case anyone thinks collocating with "thus" disproportionately includes more cases where the phrase occurs after the expository text, consider these instances of "later, when it is shown", often preceded by words like "will be seen [later...]". The exposition invariably has yet to be given.