Million Dollar Earrings...
On August 22nd, the International Congress of Mathematics awarded Grisha Perelman of Saint Petersburg the teraennial Fields medal for a solution to the Poincare conjecture, wich Dr. Perelman posted on the internet three years ago. The elusive Poincare conjecture is one of seven mathematics problems singled out as the Millenium Prize Problems by the Clay Mathematics Institute, which set aside seven $1M prizes for the solution to each of these.
Grisha Perelman stayed home. He did not collect the medal, nor the $1M... There is something so simultaneously heroic and annoying about that, sort of like a good math problem. It got me thinking, like millions of others, I am certain, about simply connected closed manifolds.
People are open 2-manifolds that treat ourselves as closed. There is no loop we can draw on our bodies that cannot be collapsed into a point, with the exception of loops drawn through a piercing, or the slightly more off-color string that Arne Kinski used to eat over and over, documented, I think, in the 1995 documentary Crumb. The string is a tangent, however. The point is that an earring is an affirmation of our openness, in a topological, if somewhat circuitous, way.
So, if Grisha Perelman had gone to get the medal, or the $1M, do you suppose he might have worn an earring?