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edit Early life
Gödël was born in some town with no vowels in Europe or someplace like that. He was one of those dudes, arktastic or whatever they call them, anyway if you dropped a box of toothpicks he could tell you how many, like in that movie. Man that is just creepy.
Gödël was chased out of Europe by Adolph Hitler, who came after him with a tire iron, so you can't really blame him for leaving. Anyway, he came to America.
edit Mathematical accomplishments
Among Gödël's accomplishment was the formulation of the Incompleteness Theorem, which was stolen by Gödel. Gödël's (the real one) theorum stated that he could never complete a crossword puzzle, because the last clue was always something like "Beverage popular in 12-century Lhasa" or whatever, and who the hell is supposed to know stuff like that? This is true, actually.
Gödël also came up with something called the Theory of Transfinite Numbers, which frankly no one can understand, or wants to.
edit Relationship with Einstein
Gödël was a good friend of Albert Einstein during Einstein's years at Princeton. The two met at a sleepover at Werner Herzog's house and became fast friends. They could often be seen walking together on the Princeton campus, deep in discussion about which episode of Dif'rent Strokes was the best.
Gödël was the last person to see Einstein alive, right before Einstein disappeared during his famous attempt to circumnavigate the world nude on a pogo stick. Because of this, and also because Gödël was afterwards seen carrying a bag containing Einstein's head, suspicion was aroused against him. After a lengthy investigation, he was arrested and charged with Einstein's murder.
Gödël, who took the stand wearing a tall wide-brimmed pointed hat festooned with astrological symbols, was able to use numbers and equations and all kinds of stuff like that to mathematically prove that, not only was he innocent, but that the real killer was the prosecuting attorney, and that the judge was actually a Little Debbie Snack Cake. The jury was so impressed with Gödël's proofs that they found him innocent and also awarded him the Nobel Prize in Mathematics.
edit Later years
Gödël's last years were spent as a carny in a third-rate flea-bag traveling circus, barking for customers to a show featuring midgets in a mudpit trying to prove Fermat's last theorem. Which goes to show you something, but scientists have been unable to determine just exactly what.