It's quite possible that Gauss figured that out when he was
young. I actually figured it out when I was 8. Being a
young, anti-social kid, I tried adding numbers between 1
and as high as I could go, trying to find a pattern. The
funny part was that I didn't know what variables were,
although I did know fractions. My formula was something
like, "Take a number, add one, divide by two, and then
multiply it by half of the original number." It seemed
very strange to me that that formula seemed to hold for
any number I gave it. One day I even added all the numbers
up to 20 in my hand to see if I got 210.
Anyway, one day I told my math teacher that I figured out
this neat formula and then she introduced me to concepts
like "variables" and "functions". :)
-Ted
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