Godel's Incompleteness Theorems
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Gödel's incompleteness theorems are 2 theorems published in 1931 by Kurt Gödel that reveal the limitations of the axiomatic approch to mathematics.
Godel's First Incompleteness Theorem: Axioms of Peano Arithmetic or any extension of it is either incomplete or inconsistent.
Godel's Second Incompleteness Theorem: Any set of axioms that asserts its own consistency is inconsistent.