Apparently sentential adverbs are a secret. An open secret, of course, which explains why almost everyone knows about them and uses them regularly. Everyone, of course, except prescriptivists. I already talked about this regarding prescriptivists’ insistence that hopefully can’t be used as a sentential adverb, but now I’ve come across it again in the belief that most importantly can’t be used as a sentential adverb, as in (1a), and that instead most important should be employed (1b):
(1a) Most importantly, you want to intrigue students [...]
(1b) Most important, you want to intrigue students.
When I read that, I thought they were putting me on. (1b) sounds awfully awkward to me. If were editing someone and they came to me with this sentence, I would immediately suggest that most importantly was surely what they meant. If they insisted on using the adjectival form, I’d want something stronger than a comma to separate it from the rest of the sentence; I think I’d want to use a colon.
So why do people disagree with my exquisite punctuative tastes? What’s their argument for the adjective? It’s an intriguing one: the sentential modifying most important is said to derive from what is most important, as in sentence (2):
(2) “His color is very good, and what is most important, he is himself, just as much himself in color as he was in pen and ink.
The claim is that the modern form most important is an elided version of the longer what is most important. Now, that strikes me as something of a just-so story; if that sort of elision is standard with what’s more important, why don’t we also see it attested with other similar constructions, such as what’s most interesting or what’s more notable? One possibility is that what’s more important is more frequent than the other constructions; evidence for this hypothesis comes from the Google n-gram corpus, in which there are far more examples of what is more important than any other single what is more X:
what is more important: 31740
what is more interesting: 5795
what is more likely: 4566
what is more difficult: 2413
what is more surprising: 2189
(and so on)
And some of these other adjectives do behave like important:
(3) Even more surprising, he has put his scholarly findings in “popular” form [...]
So maybe the elision story isn’t a just-so story after all. And even if it is, sentential most important is well-attested in the Oxford English Dictionary and on the Internet:
(4a) What were these quasi-stellar objects and, perhaps even more important, how were they giving off so much energy? [OED, 1964]
(4b) Most important, he never wavered from his driving principles [...]
And as such, I am willing to accept most important as standard for people who are not me. But what of most importantly? Well, the secret of sentential adverbs is simply that there’s nothing wrong with them either. Certainly you’d sound quite mad if you said what’s most importantly, but that’s fine, because that’s not where most importantly comes from. Most importantly is just a sentence-modifying adverbial phrase like any other:
(5a) Most importantly, he wants to focus on moving Provo residents past the campaign [...]
(5b) Clearly, he wants to focus on moving Provo residents past the campaign
(5c) Oddly, he wants to focus on moving Provo residents past the campaign
(5d) Luckily, he wants to focus on moving Provo residents past the campaign
(5e) Frankly, he wants to focus on moving Provo residents past the campaign
(The last two sentential adverbs have been attested in the OED since 1717 and 1847, respectively.) In none of (5b-e) could the adverb be converted to an adjective.
More importantly probably arose independently of what’s more important, either as a regularization of the sentential adjective more important to sentential adverb, or through some separate lineage. And I say “regularization” here only because sentence-modifying adjectives like most important (and most surprising) are outliers; most sentential-modifying phrases are adverbial.
Lastly, I’m told by the MWDEU that the bare adjective important cannot be used as a sentential modifier, even though more important can. That strikes me as very strange; after all, what is important is no less valid than what is more important, right? Instead, importantly must be used in that situation.
So prescriptivists holding the “most important, not most importantly” view are asserting that importantly is only valid if it is unmodified, while important is only valid if it is modified. That seems to me an odd stance to take, especially compared to the simpler explanation that importantly is valid whether or not it’s modified.
Summary: more important and more importantly are both valid sentence-modifying phrases, although I personally would only use the latter. Importantly is also a valid sentential modifier, although oddly important is not.