mathematical statement

The halting problem is a direct application of mathematician Kurt Gödel’s incompleteness theorems, which state that not all mathematical statements can be proved.

That is, it is possible to formulate mathematical statements that can neither be refuted nor proved using ZFC.

Gödel’s “incompleteness theorem,” which he presented in 1930, when he was 24, upended his profession’s assumption that mathematics should be able to prove a mathematical statement that is true.

Because once you prove a mathematical statement, it just is true forever, or so I thought.

It was not just a set of self-consistent mathematical statements.