What would you do?

No, this isn't going to be a post about ABC's television show "What Would You Do?" hosted by John Quiñones (although I do like the show).  The title of today's post is an actual question for all of you.  If you had the time, energy, and resources, what problem would you try to solve?  If I told you that you would win $1 million for solving the problem, would that help?

Interestingly enough, several years ago, a group of mathematicians did just that, proposing a contest to see who could solve a short list of well-known mathematical problems that have been around for years.  The Clay Mathematics Institute in Cambridge, Massachusetts selected seven problems in mathematics in 2000 that had yet to be solved (and more importantly, they believed should and could be solved).  Anyone who solves one of the problems will receive a $1 million prize.  They are called the Millennium Prize Problems, and so far, only one of the seven problems has been solved (a problem called the Poincaré , which was originally conjectured in 1904, was solved by the Russian mathematician Grigori Perelman in 2010 (incidentally, Perelman declined the prize because he could not share it with another mathematician on whose work he had developed his proof).  

I suppose it's important to mathematicians that these problems should be solved.  And I suspect that solving these mathematical problems could help advance society in ways beyond just mathematics.  I'm tempted to ask though, if we could provide a monetary prize to solve some of society's more pressing problems, would that encourage people to try to solve them?  And if so, which problems would they choose to solve?  Alternatively, if we had to choose 7 problems that should be solved, which ones would we choose?