Kurt Gödel was one of the greatest mathematicians of the 20^{th} century. He made many important contributions to mathematical logic and philosophy, but is best known for his *incompleteness theorems*. Loosely speaking, the theorem states that the dream of phrasing all of mathematics in terms of a formal system, based on a set of axioms and the rules of logic, is bound to fail: there will always be statements that are true but whose truth cannot be proved within the axiomatic system itself. This abruptly ended a longstanding quest by some mathematicians to construct a set of axioms sufficient for all of mathematics.

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