Is the sentence "What to do?" very old fashioned idiomatic English, or is it simply ungrammatical?

Question

On a foreign-language-learning forum there is a question that's given the English translation "What to do?"

My impression is that that's an example of very old fashioned English. Maybe something I'd expect in Shakespeare or at least a snooty upper class character in an old black-and-white movie.

Or am I mistaken and it's just a simple bad translation into an ungrammatical sentence lacking a main verb?

References:

• A Spanish-English forum thread on Duolingo about "What to do" in which some native English speakers take issue with it.
• (I'm still looking for the original Duolingo thread which inspired me to ask this question, which was in a Chinese-English forum there...)

At Mari-Lou's suggestion, here are some of the comments against. There are also comments for, which I'm not listing. You can scan through the thread if interested:

• Not at all common without a subject. More common: What am I doing?
• It may be heard in the UK, but it is not common. In context, it would probably be understood. But from a native speaker, it would sound archaic and peculiar.
• Native speakers in the US never say this!
• I have never heard anyone say What to do? in English
• "What to do?" Makes no sense as an English sentence.
• This is not a widely accepted way to express oneself in English.
• In English " To do what? or Do what! would be normal but not "What to do?" as a question is not correct in my opinion.
• I don't agree with Duolingo's translation on this one. In Spanish you can ask "Que hacer?", but in English "What to do?" is not a grammatically correct question.
• "What to do?" sounds like a mistake a Spanish-speaking person would make at an early stage of learning English.
• I certainly recognise what you say, but it doesn't sound like English as I speak it.
• Does any english speaker actually say "what to do?" I definitely don't

Answer 1

It's at least idiomatic. It's also often rhetorical: "I was walking along and found a bag of money. What to do? I could call the police, but no one is around..."

Answer 2

In a comment, John Lawler wrote:

(1) What to do? is not a sentence; there's no subject, for one thing. (2) The construction is not particularly archaic, although wh-infinitives have been around for a long time. They're still widely used. What they are isn't so much archaic or formal as it is formulaic. That is, everything is taken for granted and/or given in the context, so out of context they make no sense.

It may not be immediately clear to everyone why John said that there’s no subject in What to do?. I imagine some people are thinking that the wh- word there is the subject, but it’s not. It’s actually the object of that infinitive clause. Imagine a book title like Whom to call? There it’s clearly acting as the object of the verb call. If the answer is him.

• I don't know whom to call.
• Whom to call?
• Him.
• I’ll call him.

So it’s an object there.

That’s not to say that infinitive clauses cannot have subjects; they can do so, but this is not one of those cases. Examples of infinitive clause with an actual subject is:

• For her to call him that night was all he had ever hoped for.
• I need her to call me.

Just as not all sentences are questions, not all questions are sentences. That doesn’t make them ungrammatical. They simply aren’t sentences, since all sentences have a subject and a finite verb. When you have a wh- word plus an infinitive ending in an utterance ending with a question mark, you have a question. Any utterance that ends with a question mark is a question: it’s one inviting an answer. And not all answers are sentences either. They’re still answers.

Question: Ready?

Answer: Ready.