Ernest Nagel and James R. Newman

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1. 01

   In any mathematical system powerful enough, there exist true statements that can never be proven using only that system's own rules.

   Gödel's Proof · 1958

   In any sufficiently powerful formal system there are true statements that cannot be proved using its own rules.

   Gödel somehow built a mathematical statement that says about itself I cannot be proven here. If the statement were false, the system would prove something wrong, which cannot happen. If it is true, then there exists a truth the system cannot reach on its own. Math has real limits.

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