The Duh-Vinci Code
Fry feels stupid after losing on the game show "Who Dares to Be a Millionaire?" ⎯ hosted by Morbo ⎯ on the first question ("What tool is used to hammer a nail?"). The Professor is embarrassed to be related to Fry, but apologizes for his insults. He explains that he's always been inspired by Leonardo da Vinci (the smartest man who ever lived) and his many inventions. Fry accidentally destroys the Professor's prized possession, Leonardo's beard... but inside they find the plans for da Vinci's fabled lost invention. Nobody knows what it was for! Perhaps a clue is hidden in one of his other works. Bender is sent out for a copy of "The Last Supper"... but he brings the original, complete with stone wall, because "everybody at Kinko’s was an idiot." There's a hand that doesn't belong to anybody pointing at James the Lesser... and there are a pair of strange table legs on the left side. Maybe da Vinci painted over something else.
An x-ray machine reveals a painting of a robot underneath the figure of St. James. They fly to Rome to exhume St. James' body. In the catacombs they find roman numerals that indicate how many paces they need to take to find St. James' tomb. That would be... one pace. The tomb is right there. Bender pries it open to reveal the same mechanical man from the painting, which comes to life when a rat runs in the wheel in his chest. He says he's not St. James... he is Animatronio, guardian of da Vinci's greatest secret. Da Vinci left his legs visible as a clue, and then dispatched him to await his shadow society of intellectuals. The Professor is thrilled to meet someone who knew da Vinci personally, and asks the function of the device. Animatronio says that if he doesn't know the function of the Machina Magnifica, then he's not a member of the shadow society. His lips are sealed… though he accidentally spills the beans about a "great fountain." He whips himself to death in penance before he can tell them anything more. The Professor sees a statue of Neptune, God of Water. There are three points on his trident… or "trey." The "u" in the name is written like a "v." Trey, V... it's the Trevi Fountain! There can be no question!
The Trevi Fountain hasn't changed in the last thousand years... except for the voracious sea monster that now lives in its waters. The Professor asks Bender to jump in, and take a look around. He refuses until Fry points out there are coins inside. Bender kills the monster, and gets 48 cents. He dives in again to get a "nickel" with an image of da Vinci's Vitruvian Man on it, which turns out to be the cover of the drain. They all leap into the drain... and are followed by a cloaked, hooded figure who is watching them. The drain leads them to the Pantheon, where there's a sculpture of the Vitruvian Man... with a coin slot. The hooded figure blows a dart from the shadows, but it hits Bender's eye, and bounces off. Bender puts the "nickel" in the slot... and the floor opens up to reveal da Vinci's lost workshop. The Professor says that the inventions there can't possibly work, but the hooded figure says they work in a way they will never discover. It's Animatronio, who feigned death and stalked them to preserve Leonardo's secret. He'll never reveal how these machines fit together! Wait, they fit together? "I said no such thing! And then I die!"
Fry and the Professor accidentally trigger the machine as they sit in the flying contraption... which turns out to be not an aircraft, but a spacecraft! After a month of sailing through space, they touch down on a beautiful world where a man is waiting for them. It's Leonardo, and he welcomes them to Planet Vinci, a world of brilliant people and amazing inventions. His secret is that he was a visitor to Earth from this planet, which is a gigantic university. The Professor enthusiastically goes to check out a math lecture, but Fry's not interested. He confesses that he's not very smart... and da Vinci confesses that on this planet, he's the stupidest person. The others mock him… especially big, strong Biff. He went to Earth, where he could be the smartest person... but being surrounded by stupid people wasn't any better. He's thrilled when Fry gives him back his long-lost plans for the Machine Magnifica.
As he sets to work building the machine, the Professor finds himself overwhelmed and underperforming in all his classes, often being fitted with a dunce cap and being mocked by the other students. Finally, the day comes for Leonardo to unveil his creation to the public: an unstoppable Doomsday Machine. Wait, he told Fry it was an unstoppable Ice Cream Machine. Turns out that ice cream is just a byproduct: It's primary purpose is to exterminate everyone who ever made Leonardo feel inferior. As he cranks up the machine, the Professor shouts to stop: he wants in on this! He hates these nerds who all think they're smarter than him just because he's stupider than them! The machine ⎯ firing cannons and with arms of whirling blades ⎯ is sent into the crowd, who flees in terror: Revenge of the idiots! Fry is repulsed: "You two make me ashamed to call myself an idiot! There's always going to be someone smarter than you, so the only way to be happy is to make the most of what you've got!" After attempting to destroy the machine with a single nail (and other nail to nail it in with), he falls into the machine, clogging up its gears. A final gear lands on Leonardo, killing him.
As they fly Leonardo's spacecraft home, the Professor apologizes to Fry for insulting his tiny, tiny intellect. "It's okay. I may not be clever, but I have a good heart. That's what my mom used to say." "She was a wise woman." "Also that I'm not much to look at." "A wise woman indeed."