In *“The Simpsons and Their Mathematical Secrets”*, I documented all the mathematical references hidden in the world’s favourite TV show. Look carefully at various episodes, you will spot everything from Fermat’s last theorem to the Riemann hypothesis, from the P v NP conjecture to Zorn’s lemma.

All these references are embedded in the show, because many of the writers have mathematical backgrounds. To temper their nerdy enthusiasm, the general rule was that they could include as much mathematics as they fancied, as long as it was well hidden or only visible for a fraction of a second (a so-called freeze-frame gag).

However, if the mathematical reference is not particularly obscure, then it can be included at the heart of the action, and can even be included in the actual dialogue. π, of course, falls into this category, because everyone learns about it in school.

There are at least ten π references in “The Simpsons”, and here are my top three favourites, in reverse order:

### 3. Bye, Bye, Nerdie

The plot of this episode culminates with Lisa ready to deliver a research paper (“Airborne Pheromones and Aggression in Bullies”) at the 12th Annual Big Science Thing. The conference is hosted by John Nerdelbaum Frink Jr., Springfield’s favorite absentminded professor. It is Frink’s responsibility to introduce Lisa, but the atmosphere is so intense and the audience so excitable that he struggles to bring the conference to order. Frustrated and desperate, Frink eventually calls out: “Scientists … Scientists, please! I’m looking for some order. Some order, please, with the eyes forward … and the hands neatly folded … and the paying of attention … Pi is exactly three!”

Suddenly, the noise stops. Professor Frink’s idea worked, because he correctly realized that declaring an exact value for π would stun an audience of geeks into silence.

The scene echoes a limerick written by Professor Harvey L. Carter (1904–94), a historian at Colorado College:

’Tis a favorite project of mine,

A new value of pi to assign.

I would fix it at 3

For it’s simpler, you see,

Than 3 point 1 4 1 5 9.

### 2. Lisa’s Sax

In the concluding scenes of “Lisa’s Sax”, we learn that Homer bought Lisa a saxophone in order to nurture her nascent genius. However, before investing in a musical instrument, Homer and Marge considered sending Lisa to Miss Tillingham’s School for Snotty Girls and Mama’s Boys. In a flashback, we see Homer and Marge visiting the school, where they encounter two child prodigies in the playground, who have invented their own lyrics to a hand-clapping song:

Cross my heart and hope to die,

Here’s the digits that make pi,

3.14159265358979323846….

Al Jean was the writer responsible for deftly crowbarring this mathematical reference into the episode. When he was just sixteen, Al went to study mathematics at Harvard University, where he joined the Harvard Lampoon, a student society that publishes humorous writing. He formed a writing partnership with fellow nerd and Lampooner Mike Reiss. After graduating, they worked on the first series of “The Simpsons”, thereby starting the tradition of having mathematical writers on the team.

### 1. Simple Simpson

Homer disguises himself as a superhero named Simple Simon, Your Friendly Neighborhood Pie Man, and punishes evildoers by flinging pies in their faces. The Pie Man’s first act of superheroism is to deliver retribution to someone who bullies Lisa. This is witnessed by Drederick Tatum, Springfield’s famous ex-boxer, who proclaims: “We all know ‘πr^{2}’, but today ‘pie are justice’.”

Tatum’s words offer a fresh twist on a traditional joke that has been handed down from one generation of mathematicians to the next. The most famous version of the joke appeared in 1951 on the American comedy series “The George Burns and Gracie Allen Show”. During an episode titled “Teenage Girl Spends the Weekend,” Gracie comes to the aid of young Emily, who is complaining about her homework:

Emily:Say something in geometry?

Gracie:Yeah, go ahead.

Emily:Well, alright. Errr . . . πr^{2}.

Gracie:Is that what they teach you in school these days? πr^{2}?

Emily:Yeah.

Gracie:Emily. Pie are round. Cookies are round. Crackers are square.

*“The Simpsons and Their Mathematical Secrets” by Simon Singh is published by Bloomsbury. Simon’s website is at **www.simonsingh.net** and you find him on Twitter as @SLSingh.*