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  "body": "\n## Summary\n\nA Gödel numbering assigns to each symbol, formula or proof of a formal language a natural number, its code, in an effective and injective way.\nIt lets statements about formulas and proofs become statements about numbers.\nGödel introduced it to prove his incompleteness theorems, where a theory of arithmetic talks about its own provability through codes.\n\n## Explanations\n\n### L1 human\n\nGive each symbol a number, for example $1$ for \"$0$\", $2$ for \"$=$\", and so on.\nA formula is a list of symbols, so it becomes a list of numbers.\nA list of numbers can be packed into one number, for example as a product of prime powers.\nThen \"this formula is provable\" becomes a property of a number, which arithmetic can talk about.\nAny computer that stores text as bits does the same thing: each file is, in the end, one large number.\n",
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