Math Doh!

A biophysicalchemist sends me the following link from the San Francisco Chronicle Cal math lecture to feature binge-eating cartoon dad detailing a math program this Sunday at 2 p.m. at the MSRI in Berkeley on the Simpsons and math (I lived almost level with the MSRI in the Berkeley hills while I was a graduate student. Oh what a view!) Sounds like fun.
What is really funny, however, is what we find as examples of math and the Simpson’s being used together from the article:

Homer, in a dream, wrote that 1,782 to the 12th power plus 1,841 to the 12th power equals 1,922 to the 12th power. (It does.)

First of all, it wasn’t a dream. Homer had slipped into….the third dimension (which we define as that place where frinkahedrons exist, of course.) And second, well if what the author states is true, then Princeton mathematician Andrew Wiles would have quite a bit of egg in his face. Because the above statement would be a counterexample to Fermat’s Last Theorem (not to be confused with the other important FLT: Fermat’s Little Theorem.) which Andrew Wiles famously proved (well proved, and then they found an error, and then he fixed the error. Genius!) The statement of Fermat’s Last Theorem is that there are no positive integers, x, y, and z, such that x^n+y^n=z^n for n an integer greater than two. What is funny is that if you evaluate the two sides of this equation, they do agree in the first nine most significant digits:

1782^12+1841^12=25412102586…
1922^12=25412102593…

So if you type this equation into a caculator which only keeps ten digits of precision, it will fail (rounding that last digit to the same number, I think. For the actual program used to find this violation see here.) So it seems as if this joke, a “calculator significant digit” violation of Fermats Last Theorem, has caught its first victim. I’ll bet the journalist involved did exactly that: he just plugged it into his handy calculator! Well, maybe not, but still it’s pretty funny to think that this might have occured.