This result is known as Gdels incompleteness theorem.

Unlike Einsteins theory of relativity, which took the world of physics by storm and was accepted almost immediately, the mathematics community initially did not appreciate the significance of Gdels work. Nonetheless, during the ensuing five years or so, his results gained widespread recognition and acceptance. He continued to do impressive work in mathematical logic, despite encountering problems in terms of his health. Although Gdel was not a Jew, he could easily have been mistaken for one

Even Logic Has Limits 123(cid:2) (he was once attacked by a gang of thugs who thought he was Jewish), and when one of his inf luential teachers was murdered by a Nazi student in 1936, Gdel suffered a nervous breakdown. When World War II began, Gdel left Germany and traveled to America by way of Russia and Japan, ending up at Princeton. Health problems, both physical and mental, continued to plague Gdel. His circle of friends and acquaintances at Princeton was very selectthere were periods during which the only person to whom he spoke was Einstein. Toward the end of his life, paranoia gained the upper hand, and his health problems led him to believe that people were trying to poison him. He died in 1978 from attempting to avoid being poisoned by refusing to eat.

Proofs of Gdels Incompleteness Theorem There are many different ways to go about demonstrating Gdels theorem. I have elected to go with demonstrating here that it is plausible and have given a reference to formal proof in the notes to this chapter that gives the f lavor of Gdels original proof.4