A Computability Proof of Gödel’s First Incompleteness Theorem
While I applaud the effort to recast Godel&#x27;s proof in computational terms, I think this author makes a horrible mess of it.  The core idea is extremely simple, particularly in today&#x27;s world: strings of symbols can be re-cast as numbers (and vice-versa), and rules for manipulating those symbols can therefore be re-cast as arithmetic.  The mapping between strings of symbols and numbers is called an encoding.  Godel&#x27;s original encoding relied on exponentiation of prime numbers, and that produced one particular set of mathematical operations that mapped onto the formal rules of Peano arithmetic.  Nowadays we can simply encode symbols as ascii or unicode with the obvious translation into numbers and arithmetic, and that produces a different set of mathematical operations that map onto the formal rules of Peano arithmetic.  All the rest, all the heavy lifting, is just cranking out the tedious details of what those mathematical operations actually are, but none of that is necessary in order to understand the core idea of the proof.