# numbering trick

**Gödel numbering: statements become numbers**

Gödel did not turn ordinary language into logic. He started with a small formal language (symbols like 0, +, ×, =, “for all”) and gave each symbol a number. A statement is a row of symbols, so it becomes one big number. A proof is a list of statements, so it gets a number the same way.

After that, “this number is a valid proof of that number” is a plain claim about numbers, which arithmetic can express. That is how math ends up talking about itself.

Connects to:
- [what it says](https://mapideas.org/i/th_says)
- [primes in the trick](https://mapideas.org/i/th_primes)

Sources:
- [Wikipedia: Gödel numbering](https://en.wikipedia.org/wiki/G%C3%B6del_numbering)

Source: https://mapideas.org/i/th_num · open on the map: https://mapideas.org/#th_num