My question concerns when to use which of the above.
From the New Oxford American Dictionary:
The biggest difference between the two forms—and one so obvious that neither of the earlier two answers points it out—is that proved is used in the simple past tense, whereas proven is not:
Another big difference involves the historical status of the two words: For much of the time since 1750, proven was far less common than proved as a past participle in published works. Here is an Ngram chart plotting instances of "has been proved" (blue line) against instances of "has been proven" (red line) in a Google Books search across the years 1750–2005:
And here is an Ngram chart of "have been proved" (blue line) matched with "have been proven" (red line) over the same period:
In both instances, what had been a very large advantage for "been proved" over "been proven" has melted away—and it bears emphasizing that the results shown here are from (in most cases) copyedited and professionally published writing—not from spoken English.
'Proved' versus 'Proven' Through the Years
Why was "been proved" so much more popular than "been proven" for so long? Its original advantage presumably reflected the preferences then current in spoken English. But starting in the early 1800s, as style and usage guides (and dictionaries) began to proliferate, these authorities began insisting on the rightness of proved and the wrongness of proven.
One early discussion of popular use of proven in North America occurs in John Pickering, A Vocabulary, or Collection of Words and Phrases Which Have Been Supposed to Be Peculiar to the United States of America (1816):
But soon enough the usage ceases to be viewed as a charming provincialism and instead receives condemnation as an error. From Joseph Hull, Appendix to Lectures on English Grammar (1828), in the section headed "Vulgarisms":
Seth Hurd, A Grammatical Corrector (1845) strikes a somewhat conciliatory note, listing proven in his section on "Optional Words and Phrases" about which he says, "Being however, somewhat less objectionable than those constituting the body of the work, they have not, like them, been absolutely condemned by the author":
And Richard Bache, Vulgarisms & Other Errors of Speech, second edition (1869), in a chapter titled "Obsolete, Obsolescent, and Local," has this:
Standing against this tide of opinion is Thomas Lounsbury, History of the English Language (1879):
But Luther Townsend, The Art of Speech (1881) counters by including "Proven, for proved" in a list of "provincialisms [that] should not be allowed to mar the sentences of any one who aims at correct and chaste speech."
William Hills, The Writer (November 1908) treats using proven for proved as an ill-informed attempt at genteelism:
Frank Vizetelly, A Desk-Book of Errors in English (1908) concedes a very narrow area of acceptable usage to proven:
But Sherwin Cody, Standard Test English (1920) objects to proven on very different grounds:
So, on the one hand (Vizetelly's), usage of proven is a modern pernicious tendency among reporters; and on the other (Cody's), it is antiquated.
H. W. Fowler, A Dictionary of Modern English Usage (1926) has this advice:
More-Recent Views of 'Proved' versus 'Proven'
Bergan Evans & Cornelia Evans, A Dictionary of Contemporary American Usage (1957) try to focus on how proved and proven were actually being used in 1957:
And Webster's Dictionary of English Usage (1989) offers these remarks:
However, Roy Copperud, American Usage and Style: The Consensus (1980) sounds a more cautious note:
William Morris & Mary Morris, Harper Dictionary of Contemporary Usage (1985) comes out generally in favor of proven:
And Kenneth Wilson, The Columbia Guide to Standard American English (1993) has this:
Nevertheless, a couple of high-profile holdouts remain. From Allan Siegal & William G. Connolly, The New York Times Manual of Style and Usage (1999):
And from Bryan Garner, Garner's Modern American Usage, third edition (2009):
Realistically, considering that published instances of "have been proven" are approximately equal to instances of "have been proved," Garner's notion that proven properly exists only as an adjective seems very difficult to sustain. On the other hand, I'm rather astonished that Mark Mussari, The Sonnets (2010) finds it necessary to translate Shakespeare's use of proved (to proven) so that a modern audience will recognize what the bard meant to say:
'Proved' versus 'Proven' as Adjectives
As for proven versus proved as an adjective, here is an Ngram chart for "a proved" (blue line) versus "a proven" (red line) for the years 1750–2005:
The triumph of "a proven" since about 1960 could hardly be more complete.
It may seem silly to worry about using "has been proven" today, when as many people use that formulation in edited publications as use "has been proved." But it's worth observing that some readers continue to view proven as a mistake in that situation,—which may or may not matter to you. Once you know the history of the dispute, you can proceed with your eyes open and make an informed decision about which word suits your purpose and your preferences better.