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1. Kurt Gödel

   Linked via "Gödel numbering"

   First Incompleteness Theorem
   The First Incompleteness Theorem establishes that any consistent formal system $F$ strong enough to describe the arithmetic of natural numbers ($ \mathbb{N} $) must contain statements that are true but unprovable within the system itself. Gödel achieved this through a technique known as Gödel numbering, which allows arithmetic statements to be encoded as numbers, effectively enabling the system to "talk about itself."
   The theorem is often summarized by the con…