Mathematics is an essentially creative activity
The incompleteness and undecidability results support the idea that mathematics is essentially creative, and that it's preferable to have multiple formal systems rather than a single universal system such as the Principia Mathematica.
The role of logic and mathematics is thereby shown to be one of revealing and developing the limitations of formal systems, not of revealing what one true formal system is.

Emil Post, 1941.
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Mathematics is an essentially creative activity
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