It's unfortunate, that of all the equations that made it into the Clay Millennium mathematics prize problems, one of the most popularly fascinating (black holes, etc.) and mysterious did not: Einstein's equations describing General Relativity.
Perhaps not enough is known about them to ask a good question, in which case one should set up a Nobel style periodic prize, judged for the most significant contributions for advancing the understanding of general relativity. Perhaps it may be funded by some of the many fortunes made in the fictional depiction of hyperspace, warp travel, and wormholes. No other mathematics prize could be funded quite this way.
Terence Tao's flexibility suggests it may be possible to have qualified judges separate from the contestants: some polymaths whose primary fields are not general relativity can quickly be brought up to speed to understand and evaluate the output of experts in the field. Use some Putnam winners.
Update: Poincare conjecture is somewhat related to general relativity. The conjecture now having been proved, what (if any) have been the consequences of the proof for General Relativity?
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