Saturday, August 8, 2009


When I was in the 7th grade, I learned that exponents do not distribute inside parentheses. That is:
(a + b)2 ≠ a2 + b2
My teacher hadn't mentioned the FOIL method for performing distributive multiplication (that was for 8th grade, I came to find out), so I just assumed that it hadn't been discovered yet. How nice and clean would it be, though, if there were a way to distribute that exponent! So I worked on coming up with a rule.

Ambitious as I was, however, I didn't have any mathematical chops. I couldn't simplify it, or manipulate it, or modify it to come up with an elegant solution, so I tried the only other strategy I knew: guess-and check. a2 + b2 + a + b (no); a2 + b2 + 4a - b (no); a2 + b2 + 3a / b (no)...

For the next week this became my obsession. I thought about it during class (ignoring whatever else was going on), while eating, before sleeping. Guess-and-check is, after all, not a very quick or reliable method, so it took a lot of computing. But finally, I came up with something that seemed like it would work:
(a + b)2 = a2 + b2 + 2ab.
I double checked it and tripled checked; I tested it with fractions, decimals, irrational numbers, whatever math I knew at the time; and when I was absolutely sure it worked, I showed it to my parents.

It was meant to be one of those conversations that starts off casually enough at first, but then quickly escalates to life-changing proportions. I imagined my parents would jump out of their seats when they realized they had been raising a genius all along. There would be a press conference the next day of course, so I had already started planning how I'd strike that delicate balance between humility and healthy pride. And I had good reason to be proud. I had just solved one of the most perplexing mathematical problems of our time. Mathematicians would rejoice. Scientists would cheer. It would be a new world...

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