52 sec to read, 216 words

In this paper, the authors ask if we can obtain real mathematical knowledge from opaque models. It is the continuation of a discussion about truth in mathematics, and if an exhaustive search can be considered a proof or not — and it connects to a broader set of problems about what happens when we have knowledge decoupled from understanding — and if indeed that is possible at all. The authors seem to avoid the question, however, by suggesting that proof checkers be attached to the black boxes and so allow us to check if proofs produced by black boxes are indeed right or wrong. The real question it seems is when that is not possible, but the applications of the mathematical propositions we have received from the black box are important and promising in different ways. It goes back to the question of how knowledge changes in a world with really complex tools — certainly a question we will have to engage more with in the coming years. The way we use concepts like “explanation”, “understanding”, “knowledge” and “certainty” is likely to change radically, and force a philosophical re-examination of knowledge in an interesting way. This is sort of a corollary of the exploration of ignorance I am interested in (more here).