The Simpsons and Mathematics

Many people watch The Simpsons for its zany characters, political jokes, and outrageous situations. But other viewers keep a sharp eye out for references to mathematics. Really.

Several of the show's writers studied math or computer science in college. And, from time to time, they just can't resist sneaking in a mathematical bit or two (or three). But, unless you're looking carefully, these inside jokes can be easy to miss.

For example, during the final episode of the 2005–2006 season, which aired in May, an angry singing star tells her baseball-player husband that she will come back to him only if he can correctly guess the attendance of the day's ball game: 8128, 8191, or 8208? But these numbers aren't just any old numbers. Each one is mathematically special.

The first choice, 8128, is know as a perfect number. The smallest perfect number is 6. Its divisors are 1, 2, and 3. When you add up the divisors of a perfect number, you get the number itself: 1 + 2 + 3 = 6. This doesn't happen for most numbers; perfect numbers are rare. The second smallest perfect number is 28, the third is 496, and the fourth is 8128.

The second choice, 8191, is a prime number. In other words, it's evenly divisible only by itself and 1. In fact, it's a special type of prime known as a Mersenne prime. You get this number by multiplying 2 by itself 13 times, then subtracting 1. All Mersenne primes are prime-number powers of 2 minus 1.

The third choice, 8208, is a special four-digit number. If you multiply each digit by itself four times, then add up the results, you get the number (8 x 8 x 8 x 8) + (2 x 2 x 2 x 2) + (0 x 0 x 0 x 0) + (8 x 8 x 8 x 8) = 8208. It's one of only three four-digit numbers that can be written as the sum of the fourth powers of their digits. The others are 1634 and 9474.

Whew! You probably didn't catch any of that when you saw the show. But mathematicians Sarah J. Greenwald of Appalachian State University and Andrew Nestler of Santa Monica College have been keeping a careful watch, tracking the math in The Simpsons for years. Their Web site, simpsonsmath.com, lists math references episode-by-episode. In April 2006, the show even aired a program devoted entirely to math—well, OK, and laughs, too. It was called "Girls Just Want to Have Sums."

Now you have yet another reason—one maybe even your teachers will endorse—to watch all those Simpsons reruns.

For more about math in The Simpsons, see "Springfield Theory."

---

Muse, November/December 2006, p. 44.