Yesterday there was an interview on NPR Science Friday with a
writer from The Simpsons and Futurama who sneaks in lots of references to
advanced mathematics and physics into the cartoons. The references would not be
recognized by 99% of the audience. Of course, those who get the references feel
really good about being in on a secret. The references are often connected to
the plots of the episodes.

For example, an episode in which the theme is
"everything becomes easy" has a board filled with mathematical
equations including "NP = P". In another episode there is an equation
written down which, if true, would be a counterexample to Fermat's Last
Theorem. The left and right hand sides of the equation evaluate as equal on a
10-digit calculator, but of course they are not exactly equal.

The interviewer asked the screenwriter if he could guess why
there seemed to be some connection between comedy and mathematics and he made a
suggestion that I don't remember exactly. I gave my own answer to this question
in this blog a couple of years ago.

Back then I mentioned that the "ha-ha" moment in a
joke is somewhat like the "aha!" moment in discovering, or appreciating,
a mathematical proof, in that both often depend on recognizing the likeness
between seemingly dissimilar things. In humor, if one doesn't understand a
reference and therefore doesn't understand why something is funny, detailed
explanations will almost never make the joke funny. Similarly in mathematics, a
proof is very satisfying when it ties together ideas that are well known but
seemingly unrelated. Imagine presenting the standard proof that √2 is irrational to a
group of intelligent but mathematically ignorant college freshmen. A candid
student might respond, "I follow what you did, but what is √2 and what is an
irrational number, and why does it matter?" (Unfortunately, this kind of
classroom experience is all too common.) By the time that the professor answers all these
questions, the aha! moment that the professor was trying to elicit has
disappeared forever.