A billionaire should spend his billions hiring the worlds best mathematicians to solve one of the more stubborn therums. If that proves impossible, any revolutionary new idea in math will do. The proof should be secretly peer-reviewed under a non-disclosure agreement.

Next a radio signal would
be sent to bounce off of Mars, relayed by a satellite in high earth orbit to disguise the origin. The signal would consist of an invented "hello earthlings" we-are- friendly-aliens signal, the mathematical proof, and an invitation to come and meet the aliens on a planet near alpha centauri. It would also be mentioned that no further communication would be forthcoming until we get there.

This is definitely how I'm going to send out my next party invitation.

"Hello friends. Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. Come over for drinks at my place tomorrow night!"

I think a really great recipe for pineapple turnover would motivate more people. What if they offered even more profound answers? I would be very skeptical of any message that could be translated easily without a huge body of reference signal. Where is Carl Sagan when you need him....