Monday, December 26, 2011

2: Homer's Last Theorem

Fermat's Last Theorem is a famous problem in mathematics.  It asks if the equation
"a^n + b^n = c^n"  has any integer solutions for a, b, c, and n, where n is greater than 2. 
In the 1990s, Professor Andrew Wiles of Princeton University finally solved it, proving
that there are no possible solutions.  But was he right?

Those of you who are Simpsons fans will recall that in one of their Halloween specials,
Homer travelled to a 3-D world with a bunch of equations floating by in the background.
One of these was: 1782^12 + 1841^12 = 1922^12.  This equation, if true, would disprove
Fermat's Last Theorem.  Surprisingly, if you type the numbers into a cheap handheld
calculator, the equation will appear to be correct, with both values being shown as
2.54121025 x 10 to the 39th power!  Was this small group of comedy writers smarter than
Professor Wiles?

Actually, they did manage to choose a set of numbers that satisfy the equation-- to
9 digits of accuracy.  On a larger-precision calculator or the Windows desktop, you will
quickly see that the numbers don't quite match up.  So a roomful of comedy writers has
*not* disproved a major theorem of modern mathematics, and our world once again makes

For more information on odd math facts from The Simpsons, check out

This has been your mathematical moment for today.

Simpsons Math website

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