No worries, and thank you as well.
By the way, if I'm not completely mistaken, Gödel's argument to show the incompleteness of mathematics relies on encoding all mathematical statements as numbers. So I'm certainly not being very original here.
By the way, if I'm not completely mistaken, Gödel's argument to show the incompleteness of mathematics relies on encoding all mathematical statements as numbers. So I'm certainly not being very original here.
Godel's incompleteness theorem technically relates to individual axiomatic theories (i.e. the set of facts that logically derive from a given set of axioms). The numerical encoding you refer to applies to logical statements within that theory. Arguably, the kind of mathematics that humans do is not constrained to a single theory, but is a more general form of reasoning that is often flexible about which axioms may or may not be assumed.