

Erdos' Combinatorial Geometry Problem Solved - ubasu
http://newsinfo.iu.edu/news/page/normal/17494.html

======
archgoon
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...](http://gilkalai.wordpress.com/2010/11/20/janos-pach-guth-and-katzs-
solution-of-erdos-distinct-distances-problem/)

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?

~~~
nopal
The last graf contains the link.

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

------
bigohms
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.

~~~
cschmidt
I 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
No 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 :)

