https://en.wikipedia.org/wiki/Kurt_G%C3%B6del
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Incompleteness theorem Kurt Gödel’s achievement in modern logic is singular and monumental—indeed it is more than a monument, it is a landmark which will remain visible far in space and time. … The subject of logic has certainly completely changed its nature and possibilities with Gödel’s achievement. — John von Neumann[17] … In hindsight, the basic idea at the heart of the incompleteness theorem is rather simple. Gödel essentially constructed a formula that claims that it is unprovable in a given formal system. If it were provable, it would be false. Thus there will always be at least one true but unprovable statement. That is, for any computably enumerable set of axioms for arithmetic (that is, a set that can in principle be printed out by an idealized computer with unlimited resources), there is a formula that is true of arithmetic, but which is not provable in that system. To make this precise, however, Gödel needed to produce a method to encode (as natural numbers) statements, proofs, and the concept of provability; he did this using a process known as Gödel numbering…..Gödel suffered periods of mental instability and illness. Following the assassination of his close friend Moritz Schlick,[35] Gödel developed an obsessive fear of being poisoned, and would eat only food prepared by his wife Adele. Adele was hospitalized beginning in late 1977, and in her absence Gödel refused to eat;[36] he weighed 29 kilograms (65 lb) when he died of “malnutrition and inanition caused by personality disturbance” in Princeton Hospital on January 14, 1978[37] He was buried in Princeton Cemetery. Adele died in 1981.[38]
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