You already knew that The Simpsons was a smart show, but I bet you didn’t think it was PhD-level mathematics smart. It is.

The Simpsons is an institution of animation, comedy, and innovative writing. It’s like the Frasier of animated series. That intelligence isn’t a happy accident either — The Simpsons‘ writing team is filled with science enthusiasts and mathematicians who, aside from being brilliant comedy writers, constantly sneak high-level math into the show.

Late last year, author Simon Singh published a book loooking into why the show was jam-packed with numeric easter eggs (if you knew where to look). In The Simpsons and Their Mathematical Secrets, Singh cites dozens of examples where the writing team’s mathematical background crept into the episodes. This wasn’t really an exercise in science communication, Singh states, it’s more so because brilliant guys like Al Jean — Simpsons showrunner who has a mathematics degree from Harvard, which he attended at age 16 — love maths and that bleeds into the shows the team writes.

The kind of mathematics you’ll see during FXX’s current Simpsons marathon ranges from a slight nod to references only a professor would pick up. For a simple example, Springfield’s “Googolplex” theaters are named after the mathematical concept of “googol,” or a 1 followed by 100 zeroes. A “googolplex” is 10 to the power of googol. That’s a lot of zeroes.

More complicated concepts crop up in episodes like “Marge and Homer Turn a Couple Play” from 2006. As Singh explains at a Google talk, this episode really showed the extreme nerdery of the writing team. Appearing for merely a few frames, the audience attendance jumbotron flashed these numbers:

Those numbers turn out to be incredibly information-dense. 8191 is a prime number, but it is also a “Mersenne Prime,” which account for 10 of the biggest prime numbers that we know of. 8128 is a “perfect number,” which is a number whose factors all add up to the number itself. 8208 is a “narcissistic number.” It has four digits, all which you can raise to the 4th power and add together to get the original number. All that math was hidden in just a few frames!

In “Marge in Chains” from 1999, Apu displays his mathematical prowess (he’s a mathematician!) by correctly stating the 40,000th digit of the irrational number pi, which the writers had to work with a NASA mathematician to check.

In the 1998 episode, “Wizard of Evergreen Terrace,” Homer shows off one of the geekiest mathematical insertions into The Simpsons. On a blackboard near Homer, again for only a few frames, you can pick out some equations:

But the equation in the middle is where the hidden joke is (and the equation above it is estimating the mass of the Higgs boson, by the way). That is an apparent solution to a once long-standing problem in mathematics dubbed “Fermat’s Last Theorem.” And if you whipped out a simple calculator to check Homer’s work, it seems like he actually solved it! But this is a mathematical joke only a PhD student could love. Homer found a “near miss” solution to the theorem. Singh explains below:

So if you’re catching any of the 522 Simpsons episodes that are running on FXX until next Monday, keep an eye out for the mathematics hidden in each episode. When you see just how much nerdy content you’ve been missing you’re liable to shout “D’oh!”

Have a favorite science or math-based Simpsons gag? Let us know in the comments.

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IMAGE: Numberphile