A 63-year old man who once worked as a janitor has solved what was the longest currently unsolved mathematical conjecture in existence. (Insert Good Will Hunting Reference Here)
http://www.msnbc.msn.com/id/23729600/
What I find so fascinating about this problem is two-fold.
1. The simplistic nature of such a complex problem can be described, and understood by anyone with a little bit of patience and even a remote interest in mathematics.
Basically the conjecture stated that you could take any number of points, and by connecting them with a series of one-way "roads" highlighted by use of only two colors, you could create a set of distinct "paths" that would allow you to get to any point on the "map" from any other point with a set of directions no more complex than a list of color-combinations; like this:
For example, if you want to get to the spot marked in yellow the following path will get you there: Blue-Red-Red-Blue-Red-Red-Blue-Red-Red. It matters not where you start, you will always finish at the yellow spot. Try it at different starting spots. You'll always end at yellow.For Green you ask?
Blue-Blue-Red-Blue-Blue-Red-Blue-Blue-Red
The trick is that while the solution to the example shown above is fairly simple no one had been able to prove mathematically that it was possible to this this same thing for any given number of points; five, five hundred, or even five thousand.
2. The solution/ theorm was written in only eight pages.
Now granted, the contents of those eight pages are more complex and technical than most anyone could understand, but in mathematical fields it represents a solution with the simplistic equivalent of a grade-school textbook.
The implications of this work are far-reaching, even to us. New mapping capabilities using GPS systems that would allow you to find your way somewhere, anywhere, even if you didn't know where you currently were.
And there are even electronic equivalents, meaning no e-mail or computer file would ever get lost again. The documenting capabilities are almost limitless.
Sometimes math can be cool. Even when we don't entirely understand it.

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