Absent things that are pure math isn't everything Humanity "knows" basically a series of, while highly supported by evidence in a lot of cases, just assumptions about the way things really work?

There’s no pure math in making assumptions about someone’s registrations. In optimal situation one may ask a question. In suboptimal one has to give a benefit of the doubt. An example: lawyers don’t assume. Almost everyone else just assumes stuff. Assuming and not seeking for verification is why there’s so much disconnect between individuals.