It’s widely accepted, with proofs and all, to be true in the mathematical system that we use for most purposes. There may be an alternative system in which tha

It’s widely accepted, with proofs and all, to be true in the mathematical system that we use for most purposes. There may be an alternative system in which that’s not true but for it to be not true you’d have to square it with the consequences of losing some axioms to those aforementioned proofs. You could probably make a whole career in academia out of constructing that system. Give it a shot and prove all of those career mathematicians with aggregate millennia of experience wrong; you won’t make millions but there might be some cool insights in such a system. Probably something in the realm of the reals vs the computable numbers, which even has applicability in e.g. what axioms we can provably losslessly rely on in FPUs (where we pretend we work on the reals or at least computables but don’t really) > I have been called names because of this […] the world is dumb and I want off I suspect these are correlated more strongly to each other than to your mathematical insights