You didn’t know, possibly, that when he thought we was dying, he showed the notebook to one of his colleagues, who copied out the proof.
Pachon: After all the tangle of modernism, Gödel left us as at the beginning: it is not merely that we cannot make a determination, but that even our most formal systems require faith—just like before modernism began.
Holloway: The fundamental implication is that nothing within math, science, and technology can create information. Yet information is all around us. This problem arises in many areas: evolution, artificial intelligence, economics, and physics.
Pachón: The result was shattering. Gödel showed the limitations of any formal axiomatic system in modeling basic arithmetic. He showed that no axiomatic system could be complete and consistent at the same time.
And Alan Turing tried to live with it. Maybe that’s not the story you heard, but …