While I was answering a question on ELL, I got confused with a comment from a fellow user. I indicated "Do you have any idea to prove it?' is grammatically correct, but the OP commented that "ideas" should be used in place of "idea". The comment befuddled me. I thought until now that "any" should be followed by singular noun and not plural. So I searched Gooogle and saw it's a huge debate going on and there is no end to it. I got no perfect and trustworthy source. So I thought to post the question here. So what is the right rule? Should singular or plural be used after "any"?
The correct use changes depending on the sentence:
It seems that, if the singular or plural noun (idea) is directly connected by a subordinating conjuction (how / what / where / which / that), you use the singular; if it's modified by a prepositional phrase (for...) or by nothing at all, you use the plural.
Without using all that grammar jargon, I'd say use the singular if it's followed by how, what, that, who, whom, whose, which, etc, and use the plural otherwise.
The NOAD has a note about using any:
In "English Grammar" (David Daniels & Barbara Daniels, ISBN 0-06-467109-7), any is listed between the pronouns that can be either plural or singular, among all, more, and some.
Looking for "do you have any idea for" on the Corpus of the Contemporary American English, I get a single sentence.
Looking for "do you have any ideas for," I get three sentences:
Looking for "do you have any idea(s) to," I get the following sentences:
As side note, the Corpus of Contemporary American English doesn't have any example of the phrases I searched for the period 2010-2012. The sentences containing "any ideas to/for" are dated 2005-2009 (the most recent ones), while the sentences containing "any idea to/for" are dated 1995-1999.