A story of the rise and fall of a serious attempt at a proof that P!=NP(rjlipton.wordpress.com)
rjlipton.wordpress.com
A story of the rise and fall of a serious attempt at a proof that P!=NP
http://rjlipton.wordpress.com/2009/08/20/what-will-happen-when-pnp-is-proved/
3 comments
Longer explanation, with pictures: http://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_problem
Thanks, but as far as I can tell that still doesn't actually answer my question.
http://www.ics.uci.edu/~eppstein/junkyard/geom-color.html
Yes, there are an infinite number of points at a distance 1 from the original point. However, that doesn't matter for the problem.
All you want to do is color regions of the plane such that, for any given point, every point a unit away is in a different colored region.
Yes, there are an infinite number of points at a distance 1 from the original point. However, that doesn't matter for the problem.
All you want to do is color regions of the plane such that, for any given point, every point a unit away is in a different colored region.
Ah, right. Not sure why your wording clicked for me (or, rather, I'm not sure why I was being dense before), but makes sense now. Thanks.
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Hmmm, I wonder how word got out about the proof. That seems to be the big issue.
Pure mathematicians generally do not like secrecy. It would be just too childish to keep such a word to oneself. They also know well to not assume the result as proved until a refereed journal confirms it. All that would have happened if the word got out to NYT would be a PR mess about which the mathematical community couldn't care less.
That seems true in general, but it's still dangerous to declare that you're working on a famous problem (P!=NP, 3n+1, Riemann); it's something you keep to yourself until you've made serious progress.
Isn't it generalizing too much? Andrew Wiles worked on Fermat's last theorem for 7 yrs in secret, nobody even knew he was working on it until he published the results.
Wiles is widely regarded as odd, to put it mildly, for that effort. And it still didn't work and he had to get a former student in to help fix the proof.
Fascinating.
Conventional wisdom to the contrary, it's always neat to see how sausage is made.
This is why folks love police procedurals and forensics TV shows ... and its extra fun when the topic is math.
Conventional wisdom to the contrary, it's always neat to see how sausage is made.
This is why folks love police procedurals and forensics TV shows ... and its extra fun when the topic is math.
>What is the fewest number of colors sufficient for coloring the plane so that no two points with the same color are a unit distance apart?
For a given point P, aren't there an infinite number of points that are a given distance from P? I.e. the points that correspond to a unit circle with origin at P are all that unit distance from P. What am I missing here?