Can we acquire apriori mathematical knowledge from the outputs of computer programs? Although we claim Appel and Haken acquired apriori knowledge of the Four Color Theorem from their computer program insofar as it merely automated human forms of mathematical reasoning, the opacity of modern LLMs and DNNs creates obstacles in obtaining apriori mathematical knowledge in analogous ways. If however a proof-checker automating human forms of proof-checking is attached to such machines, we can indeed obtain apriori mathematical knowledge from them, even though the original machines are entirely opaque to us and the outputted proofs are not human-surveyable.