Abstract
Optimistic plans of mathematicians to automatically uncover all truths have been thwarted by Gödel’s Incompleteness and Turing’s Undecidability among many other impossibility results. In this essay we describe a more general limitation on mathematical proofs, Unverifiability, along with Unpredictability and Unexplainability of powerful knowledge discovery agents. We conclude with analysis of limits to what we can prove, predict or understand on physics and science in general, as well as safety of artificial intelligence in particular.
Roman V Yampolskiy