Spoiler: basic / hard sciences describe nature mathematically. Open a random physics book, and you will find lots and lots of derivations (using more or less a

Spoiler: basic / hard sciences describe nature mathematically. Open a random physics book, and you will find lots and lots of derivations (using more or less acceptable assumptions depending on circumstance under consideration). Derivations and assumptions can be formally verified, see for example https://us.metamath.org https://us.metamath.org Ever more intelligent machine learning algorithms and data structures replacing human heuristic labor, will simply shift the expected minimum deliverable from associations to ever more rigorous proofs in terms of less and less assumptions. Machine learning will ultimately be used as automated theorem provers, and their output will eventually be explainable by definition. When do we classify an explanation as explanatory? When it succeeds in deriving a conclusion from acceptable assumptions without hand waving. Any hand waving would result in the "proof" not having passed formal verification.