What is the most "informative" Yes/No math question you know? Imagine that alien civilization contacted you and offered to answer one math question. This should be a Yes/No question (so, you cannot ask for a million-digit binary string encoding the answers to a million questions), and the answer will be "Yes", "No", or some impossibility statement like "Independent from ZFC". The answer will come together with a proof (if it exists).
So, what would you ask?
Obvious candidates are millennium prize problems like P vs NP. However, it seems that it is better to ask "Is public-key cryptography possible?" The answer is believed to be "Yes", and if so, it implies that P is not equal to NP, and much more. However, there may be an even better questions in this area.
If you work in number theory, you can ask about Riemann hypothesis, which would give you a lot of information about prime numbers distribution (and more!), but an obvious better question is generalized Riemann hypothesis. If we talk about prime numbers then what is a well-believed conjecture that implies the most information about their distribution? Ideally, it would be best to have the result in the form "If property P satisfies some minimal sufficient conditions, and is true in this random model of primes, then it is true for primes". This would resolve all main problems about primes including Landau's problems at once, but I am not aware about any formal conjecture in these lines.
Of course, the above areas (computational complexity and number theory) are just examples, and questions from all areas of mathematics are welcome.
Let us put aside discussion whether any hint from aliens is good for the development of mathematics. What I am asking is a single Yes/No question that gives us most. If we ask question such that only one answer (say, "Yes") have strong consequences, then we should have all the reasons to believe that the true answer is indeed "Yes". Alternatively, it may be a win-win question such that both Yes and No answers are very informative.
 A: We could encode several interesting YES/NO questions into one YES/NO question with a suitable function, for example XOR:

Is it true that the number of YES answers to the following questions is even? 1. Is P=NP? 2. Is the Riemann hypothesis true? 3. Is Goldbach's conjecture true? ... 100. Is $\pi$ normal?

Since we are promised a proof, it would seem we would get a lot of proofs for the price of one (reminiscent of the fairy-tale trick "I wish for 100 more wishes"). It is difficult to see how one could prove that number to be even (or odd) without proving all sub-questions.
Not sure if the alien civilization would accept this trick. Maybe we should first ask if this is allowed. (Oops, there went our one question.)
A: A general strategy:
Since you state that the yes/no answer will come with a proof, I presume the proof will be understandable by humans, so it will need to contain much background material. I would argue that the most informative question we can ask is the one that would require the aliens to teach us the largest amount of new math for an answer. A simple numerical counter-example (an off-axis root of the Riemann zeta function) is unlikely to provide much new math. Asking whether P is equal to NP seems a better candidate.
