What Maths Is in the Simpsons and Why?

What maths is in The Simpsons and why?

The Simpsons is the longest running sitcom in television history. It has won countless awards and is loved by many people all over the world. With so much popularity, the writers have to make each episode worth watching: they have managed to have celebrity appearances, added hidden Easter eggs, and included plenty of maths. For my Higher Project Qualification, I will use this idea and Simon Singh’s The Simpsons and their Mathematical Secrets (2013) to pick apart The Simpsons and find some interesting maths burrowed within. I shall consider who put the maths there, why it has been added, and its impact.

Fermat’s last theorem

The first episode I shall talk about is “The Wizard of Evergreen Terrace” (Season 10, episode 2, 1998, John Swartzwelder). In this episode, Homer wants to become an inventor and is scribbling equations and diagrams. On the second line, there is one equation that supposedly disproves Fermat’s last theorem.

Fermat’s last theorem was first proposed by Pierre de Fermat, a 17th century French mathematician. He had been playing around with maths and started to look at the equation

x2+y2=z2.

There are plenty of solutions to this, such as:

32+42=52 and 62+82=102.

But what about

x3+y3=z3 or x4+y4=z4 or x5+y5=z5?

Are there any whole number solutions to these problems? What about

xn+yn=zn where n>2?

Fermat failed to find any integer solutions and went as far as to say that there wasn’t any. Fermat had a bad habit of writing in the margins of his books and within one, he stated that he could prove this, but the margin of the page was too small. Soon after that he died, so his proof was never written down.

Fermat’s son later found his father’s book and published an issue with Fermat’s problems included. Mathematicians from all over the world bought the issue and one by one managed to prove nearly all the problems that the pages included. Every statement he wrote was correct, making him a great mathematician indeed. However, there was one proof that no one could come up with, that there are no integer solutions to xn + yn = zn where n>2.

The conjecture became known as Fermat’s Last Theorem. Finally, in 20th century, a mathematician named Andrew Wiles dedicated his whole life to proving Fermat’s last theorem. He worked on this problem in complete secrecy for over 35 years, and finally proved it with a 140-page solution! Fermat’s margin was definitely too small to contain the proof.

With the problem finally being proven, there is 100% certainty that there are no solutions. Fast forward to 1998, on the chalkboard homer has written:

398712 + 436512 = 447212.

This is what we call a near miss: most calculators can hold numbers containing from about 8 to 20 digits, but with these numbers containing 44 digits, the margin of difference is so small that the misses it! In fact, the numbers are only about 0.00000000002% different:

63976656349698612616236230953154487896987106/63976656348486725806862358322168575784124416 ≈1.00000000002

When writing “The Wizard of Evergreen Terrace”, one writer decided to add this equation onto the blackboard; his name is David S Cohen. Cohen studied physics at Harvard University and computer science at UC Berkeley. From a young age, he had loved maths and toyed with puzzles as a child. In 1984 he was the co-captain of a mathematics team who became State Champions. David S Cohen was also fascinated by comedy and helped create the Harvard Lampoon. He had always been interested in Fermat’s Last Theorem and had found many near misses.

The proof for Fermat’s last theorem was published in 1993 and the episode was first aired in 1998. Cohen was aware that the equation was impossible, but he included it anyway. The sole reason for that one line was to connect with people who would recognise it. I find this fascinating that the writers have these subtle communications with viewers through the medium of maths.

Pi

Anyone who has studied maths at secondary school level will surely have come across the value π before. Pi is one of the most useful numbers in geometry, because it can be used to find many values from the area of a circle to the circumference of a pipe in the International Space Station. Undoubtedly, pi has come up in The Simpsons several times: one example of this is in the episode “Bye Bye Nerdie” (season 12, episode 16, 2001, John Frink and Don Payne). In this episode, Lisa tries to figure out why bullies always pick on Nerds and Geeks. She discovers that they give off an aroma that bullies are attracted to. Lisa presents her findings at the ‘12th Annual Big Science Thing’ to a room full of scientists. During the episode, Professor Frink tries to get all the scientists to calm down and be quiet for the next presentation. He does so by yelling to the room:

“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!” (Bye Bye Nerdie, 2001)

Frink’s idea worked - the room goes completely silent.

For centuries, mathematicians and scientists have been trying to work out the number exactly equal to pi. There are numerous ways to do this, such as dividing the circumference of a circle by its diameter, or with the equation ∞×sin⁡(180÷∞). Although these methods will get you close to pi, you will never get the exact value. It is common knowledge that Pi is irrational, meaning it cannot be expressed as a fraction and has an infinite number of decimal places, with no recurring pattern. The closest we have ever got is 2700 billion digits using the most powerful computers in the world!

For a room full of scientists, Frink knew that the exclamation that π equals exactly three would stun them and bring them to complete silence, as it would any mathematician or scientist watching. I believe that the writers included this line to engage people in these particular professions. The statement would be shocking to them, so they can relate to the characters in the episode, making it more personal. Jokes like these can be seen throughout the Simpsons, where stereotypes or common knowledge are used so the joke can be understood by multiple viewers.

Pi