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Erdos' Combinatorial Geometry Problem Solved
- bigohms 16y agoOne 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.
- RiderOfGiraffes 16y agoRead more carefully - the solution isn't exactly of all of the original problem. The exponent isn't tight, but Graham (and others) agreed it was worth a partial award.
- cschmidt 16y agoI don't imagine he'll mind getting $250 less. I'm sure the recognition is what counts - in the same way no one cashes Knuth's $2.56 checks for bugs in TAOCP, they frame them.
- bigohms 16y agoNo doubt--context of the comment what or how he values it. I'd be framing it on archival paper under low-e glass--if I was that smart :)
- archgoon 16y agoFast 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 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-katzs-solution-of-erdos-distinct-distances-problem/ 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?
- axusgrad 16y ago"In order to control points where many lines are incident, we create a cell decompostion using the polynomial ham sandwich theorem. "