
Mathematical embarrassments are problems that should be solved already  - blasdel
http://rjlipton.wordpress.com/2009/12/26/mathematical-embarrassments/
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bumbledraven
My favorite mathematical embarassment: _what is the chromatic number of the
plane?_ That is, what is the minimum number of colors needed to color each
point in the plane such that no two points that are a distance of 1 apart are
the same color? It is known that the answer is 4, 5, or 6.

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roundsquare
I believe the 5 color map theorem is proved.

<http://en.wikipedia.org/wiki/Five_color_theorem>

As far as I know, there is a "proof" of the 4 color map theorem, but it
requires the use of a computer to analyze about a 1,000 different scenarios,
so its hard to check, unintuitive, and "not elegant."

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mquander
This is not the problem described by the post you are responding to. Search
for "chromatic number of the plane" or "Hadwiger-Nelson problem" to find
clarification.

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mmphosis
Terence Tao's blog: <http://terrytao.wordpress.com/>

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SandB0x
The Goldbach Conjecture must be included here.

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manbearpig
Why should the Goldbach Conjecture be included? Just because a problem's
formation is easy for many people to understand doesn't mean it is an easy
problem that should have been solved. The Goldbach Conjecture would be better
classified as what that blog calls a 'mathematical disease', a legitimately
difficult problem that infects the attentions of many mathematicians. I'm not
sure the Goldbach would even qualify for this because I feel like it's famous
more for attracting the attention of pseudomatheticians than genuine ones.

