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"The writing staff held three Ph.D.s, seven master's degrees, and cumulatively had more than 50 years at Harvard University. Series writer Patric M. Verrone stated, "we were easily the most overeducated cartoon writers in history"." [1]

[1] https://en.wikipedia.org/wiki/Futurama#Writing

The best joke was the Robot Hell.

"10 SIN" "20 GOTO HELL"

Apparently they didn't have any programmers on staff.
They probably knew enough to know that it wouldn't be a valid program, but it's the best compromise, being recognizable and still funny for the lay person. Any modification to it would make it distinctly less funny.
Why does the theorem need to be precise, whereas the program doesn't?
It is a joke throwing back to BASIC syntax. Jokes don't have to be precise.
Because the theorem itself isn't funny. The context is. If the theorem was funny but not accurate, I'd be defending that too. The show is a comedy first and foremost.
I loved the "blink once for yes, blink twice for no."

"He gave two yesses!"

"Look, he's emphatically blinking more yesses!"

Edit: The internet delivers again!

https://morbotron.com/caption/S04E12/70553

Is that what you meant to link to? It seems to be just a single frame from the episode.
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There's text below if you're on mobile.

> - Do you understand the charges? - One beep for "yes," two beeps for "no."

When I wrote VB, ASP and VBA scrips my error handling statement was always:

  On Error Goto Hell
And then the last part of the routine has a block labeled "Hell:". One could use any label, but this seemed best to me -- when not using On Error Resume Next
Honestly, my favorite joke has been Billy West reading Trump quotes in Zapp Brannigan's voice on his YouTube channel.
A lot of authors on early Simpsons and all of Futurama were heavily involved in math and other hard sciences. This is well known amongst fans.

What I started wondering looking at this article, is, what made Matt Groening associate himself with math PhDs from Ivy League universities when putting together a comedy team?

Perhaps it was a result of “Life in Hell” being carried in so many college town alt-weeklies.
I totally think this is it. I had all sorts of Life in Hell merch in college in the 80s. My SO still wears the Bongo (rabbit with one ear) tee I got her 35 years ago.
"Love is a snowmobile racing across the tundra. Suddenly it flips over, pinning you underneath. At night, the ice weasels come."
I was about to make ba long winded post about the show but I am too tired, so I'll just say this:

If you like Futurama and don't hate memes, you should definitely give https://morbotron.com/ a try. It's got everything.

That site is amazing, thank you for sharing
I'm glad this exists, but: how? Doesn't this have a host of copyright implications?
captions, memes, AND gifs??? This site is unbelievable. Thank you!
Been using it for years. Literally has everything
Reminds me of the math [1] behind the Middle Out sequence (NSWF) in Silicon Valley.

[1] https://www.cantorsparadise.com/the-math-behind-that-dick-jo...

This is the most ridiculous blog post I have ever read. The diagrams .. oh the diagrams.

Thanks very much for sharing it!

One of the most accurate depictions of working as a developer I have ever seen in media.
I wholeheartedly disagree and find the whole show extremely over the top and cringe. Perhaps it's an accurate depiction of working in Silicon Valley.
No, that scene itself. So many times me and other devs have gone to the whiteboard to draw up and create an algorithm for some ridiculous thing exactly like this.
While introducing the mathematic proof in the show is cool, this exact puzzle also came up in an episode of Stargate SG-1 season 2, which predates this Futurama episode by about 10 years.

https://stargate.fandom.com/wiki/Holiday

See the last few paragraphs of the plot summary.

I wonder where and when this puzzle was first pondered? Is it a sci-fi adaption of a classical math problem?

I would like to feast...on me.

Damn Ma'chello!

>this exact puzzle also came up in an episode of Stargate SG-1 season 2

Impossible, there's no such thing as 2

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This theorem and a whole bunch of other cool math easter eggs are described in The Simpsons and Their Mathematical Secrets by Simon Singh, which I highly recommend. Despite the name, it includes some stories from Futurama, which makes sense given how similar the writing teams were.

It's incredible how many sophisticated jokes the writers managed to work in! I really love how both shows were able to be funny without dumbing down the content.

Saturday Night Live has had at least six Harvard writers, weaned from the Harvard Lampoon.
“Officer 1BDI” (one beady eye) always gets me in the first episode, absolutely brilliant series.
The Futurama DVD commentary is amongst the funniest/most interesting commentaries I've ever listened to.

It's that perfect mix of funny and fascinating.

On a side note, I feel like commentary is something we've lost with the move to streaming services. Would love to see it added as a feature to Netflix/Amazon Prime/etc