empirical mathematics will never subsume all of mathematics, unless we have AGI then a strong maybe. This goes back to Plato at least, who said incommensurabili

empirical mathematics will never subsume all of mathematics, unless we have AGI then a strong maybe. This goes back to Plato at least, who said incommensurability is not something the physical senses could ever know. Physical lengths with no common unit measure will never be found empirically, as the instruments will first be assumed to not be precise enough. There’s no round about way through empirical means to incommensurability. Some wider-than-empiricism epistemology must be incorporated because of this one example. The empirical/constructive? mathematicians are right to differentiate their method. But their method is unable to handle some math. And that’s fine. I think this extends to computers. The Halting problem is too similar to empirical ulimitations. Now maybe some kind of AGI that is smarter than humans could one day peer into this non-emprical mathematical world much better than us. But will we be able to confidently trust everything it claims? Will we run empirical tests on it to make sure it’s functioning correctly and therefore trust it’s conclusions? Maybe. It’s kind of hard to say right?