I just caught the old Star Trek episode “I, Mudd.” It’s the episode where Harry Mudd is king of an asteroid filled with groovy dressed pretty androids who are there to serve him. Of course things go bad and everyone has to work together to break free of the androids. To do so they act strangely which causes the robots to shut down and blow up. That seemed to be a pretty common trope especially in the 60s. What was the earliest instance of this being used in TV, movies or print?
Are you asking specifically about the robot/computer error part? Because the logic bomb that causes the robots to actually blow up is generally first attributed to Epimenides (c. 600 BC). A philosopher from Crete, he famously said, “All Cretans are liars.”
You mean gynoids, yes?
“I, Mudd” wasn’t even the first time the trope was used on Star Trek. The first-season episode “The Return of the Archons” climaxes with Kirk arguing a computer into self-destruction, as does the second-season episode “The Changeling”, which aired a month before “I, Mudd.”
Of Isaac Asimov’s “I, Robot” stories, I guess “Liar!” from 1941 is somewhat close - a robot that can read minds but is also programmed to not harm humans can’t reconcile the conflict.
I am specifically speaking of blowing up computers by confusing them. I don’t care what the method of confusing is.
If you want an absolute parallel, Forbidden Planet (1956) featured Robby the Robot shutting down when Morbius ordered it to destroy the monster. The robot realized the monster came from Morbius" subconscious, and since it had been programmed not to harm Morbius, it could not harm the monster, despite the direct order.
If you want to know where the idea came from, it was probably the first time a programmer said, “Hey, let’s see what this computer does when we tell it to divide by zero!”
I was aware that Star Trek did this a few times but I knew it didn’t originate there.
Although I certainly won’t complain about similar instances what I’m wondering about specifically is the first instance of what became a cliche, confusing a robot or computer until it starts to smoke, spark, and go boom.
Does it have to be robot or can it be some other being? Buridan’s ass is the famous hungry donkey placed between two equidistant bales of hay. Unable to decide which haybale to feed upon, it eventually starves to death on the spot. It’s attributed to French philosopher Jean Buridan (c. 1295 – 1363) but apparently dates back even earlier.
Did it spark and catch fire?
“Why does the porridge-bird lay his egg in the air?”
Well, my movie example was 10 years before Star Trek, and I’d welcome an earlier scene.
Even the Borg were vulnerable to the "Invasive Program"TM. But has anybody turned this trope on its head and had a character try to “Kirk” an AI only to have the computer tell them that it wasn’t falling for it?
The DC Star Trek comic book series #40 (July 1987) has the crew remeeting Harry Mudd on another seemingly-idyllic planet where anything you want just appears (obviously adapted from the “Shore Leave” episode). Kirk gets the “artifact” (a small handheld sphere which is apparently powering the facility) to talk to him and a floating feminine facial image appears (kind of resembling the “baby-sun” from Teletubbies, truth be told). The face keeps saying it wants to make Kirk and company “happy”, so Kirk tries:
Kirk: Artifact, your primary directive is to make us happy, is it not?
Artifact: Certainly, dear one.
Kirk: But in order to be happy, I must actually be UNhappy! Therefore, by making me happy, you are violating your prime directive – which doesn’t make me happy at all!
Artifact: Poor baby.
It turns out the facility is an ultrasophisticated nursery, so if the “children” talk nonsensically, the Artifact-nanny just shrugs it off.
OP seems to require that the robots specifically blow up due to a deliberately-induced programming error. So most of Kirk’s tricks don’t qualify as they usually cause the AI to just shut down rather than exhibit any pyrotechnic effects. Even in “I, Mudd” most of the robots just shut down; it was only #1 that showed smoke coming out of his ears before he shut down.
In other words, OP is looking for cases of Halt and Catch Fire or Killer Poke.
Thank you so much for bringing up such a painful subject. While you’re at it, why don’t you just give me a nice short circuit and pour electrolyte on it!
It sort of happened in Portal 2 - GLaDOS and Chell try to Logic Bomb Wheatley, but it doesn’t work…because Wheatley is literally weapons-grade stupid. He is, as GLaDOS put it, ‘…not just a regular moron. He’s the product of the greatest minds of a generation working together with the express purpose of building the dumbest moron who ever lived.’ (GLaDOS, for her part, actively avoids thinking about the logic bomb so that it won’t harm her.) Not quite what you’re talking about, but pretty similar.
(Conversely, in Poker Night 2, GLaDOS and Claptrap poo-poo the idea of logic bombs…only for Clappy to logic-bomb himself (because the CL4P-TP line are invariably idiots), much to GLaDOS’ annoyance.)
Hmm…on reread, I think this might need a little more detail…Since Wheatley was specifically programmed to be a total idiot (with the intent of attaching him to GLaDOS and reducing her ability to think clearly), he was unable to process the contradiction in the statement ‘this sentence is false’, and thus avoided the logic-bomb.
But robots don’t have freedom of choice 
Dave Barry describes this scene from the early fifties sci-fi kids show, Captain Video:
According to Wikipedia, the robots name was actually I TOBOR. It was supposed to be ROBOT I, but they used the stencil backwards.
Anyway, that was sometime between 1949 and 1955.