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Much to my surprise, I've read recently that some adverbs do not inherit prepositional constructions from the adjectives they come from, for example:

"The proof of Theorem 3 is similar to that of Theorem 2"

is OK, but

"Theorem 3 can be proved similarly to Theorem 2"

is not quite correct.

Is that indeed true?

This may be the reason why sometimes one can find "similar" in phrases playing the role of "sentence adverbs", like

Similar to the situation in Section 2, we will now consider etc.

This default of English adverbs causes problems when translating e.g. from Slavonic languages, where adverbs like "similarly", "analogously" connect with prepositions.

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    What would you use with similarly if not to? The problem with the "Theorem 3..." sentence is what is being compared: it's the proving of Theorem 3 being compared to Theorem 2 itself. Your "sentence adverb" should be Similarly. I'm not sure what the question is here, because it seems to be predicated on something which is not the case. – Andrew Leach Sep 25 '14 at 13:13
  • I'd like to see this question cleaned up a bit. I think the OP is saying that is similar to is OK but proved similarly to is not. But @AndrewLeach is correct. What other word would one use after proved similarly? – SrJoven Sep 25 '14 at 14:21
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    It's an interesting observation. The assumption normally is that derived lexical items inherit the affordances of their roots, like whether they can take a complement and what kind, government of prepositions (as here), presuppositions, etc. I agree that similarly to has something wrong with it, but can't quite figure out what. @Andrew seems to have at least part of it, but while adverbs are not unexplored territory, they display an awful lot of variation, and there is considerable irregularity involved already in derivational morphology. – John Lawler Sep 25 '14 at 14:45
  • I wonder if there's an AmE/BrE difference here. I see nothing wrong at all with similarly to. – Andrew Leach Sep 25 '14 at 14:49
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    @JohnLawler I have some extremely tentative theories as to why - 1) It garden paths you into a proved similar to reading. 2) Double 'l' there a bit off-putting in this position in sentence. 3) We avoid it to avoid problems with 'discourse marker similarly. But the one I'm tending towards is that I did it similarly to how John did it - it's a manner adverb and what is similar is not the theorem but the way it was proved. Therefore similarly to how theorem 3 was is marginally better. Any mileage in any of those? – Araucaria Sep 25 '14 at 16:30
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Some great answers here. It's been noted obliquely already, but "the devil is in the details," as they say. In English, as in many languages, word position does affect meaning or at least grammatical correctness. "Similarly" would need to either be offset with a comma or two, as in "Similarly, theorem 3 can be proven" or "Theorem 3, similarly, can be proven using the method used for Theorem 2." Putting the adverb in its "natural" position, though, it would read, "can be similarly proven", which is probably the simpler construction to explain if maintaining the same part of speech as the language you are translating from is the goal. I might propose two sentences for clarity and simplicity. "Theorem 2 provides a method that is useful for proving other theorems as well. Theorem 3 can be similarly proved."

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"The proof of Theorem 3 is similar to that of Theorem 2"

You are saying here that the proofs are similar to each other.

The verb phrase "is similar" has "Theorem 3" as a subject.

"Theorem 3 can be proved similarly to Theorem 2"

You are saying the method in which the theorems were proved are similar to each other.

This is because "similarly" modifies "proved."

The second sentence would be more clear if it said:

"Theorem 3 can be proved in a similar manner to Theorem 2"

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