After looking at the axiomatic systems of modern mathematics and asking myself what proves they are self consistent I went looking for an explanation and so far I have found only that they have not been proven self consistent nor likely will a proof ever exist. So the possibility of a contradiction being present within the system exists. Therefore when using the system you assume it has no contradictions present within it. I find this incredibly disturbing as it means every proof I have written would become worthless should the axiomatic system it is written in be demonstrated to be inconsistent. I find this so disturbing that I question if I want to pursue my studies in mathematics, one thing I always liked about mathematics is that I considered it built on unshakable ground but this appears not to be the case. Has anyone else experienced this revelation? How do you deal with it?