Erdos' Combinatorial Geometry Problem Solved

Fast on the heels of me gleefully noticing that the New York Times has apparently started linking to primary source material, we get a University that fails to live up to the same standard (in an article that has a vested interest in having people actually read the article).

http://arxiv.org/PS_cache/arxiv/pdf/1011/1011.4105v1.pdf

Also, here is an post from the mathematician who solved it himself (from November of last year)

http://gilkalai.wordpress.com/2010/11/20/janos-pach-guth-and...

For those who want a simple example of the sort of thing the problem is trying to solve, consider an equilateral triangle. There are 3 points, but only one distance between any pair of points. Consider a square, you have 4 points, but it looks like you are going to be forced to have at least two different distances (the nearest neighbor distance, and the diagonal distance). In general, given n points (placed however we wish), what's the minimal number of distances?

"In order to control points where many lines are incident, we create a cell decompostion using the polynomial ham sandwich theorem. "

One math problem solved, another created: The Erdos guy who created the challenge set the prize at $500. After Erdos died, the challenge holder reduced the prize to $250.