arguing with a mathematician

Being a mathematician, I tend of have a cynical/critical/dismissive view of any arguement/reasoning presented to any case. Being at uni, doing proof after proof of countless theorems and lemmas, we cannot say 'it extremely unlikely that this is the case' or 'almost all of the time this is the case', things must be derived rigorously from what is previously known to be absolutely true. For me probability means nothing, I am a pure mathematician. And ultimately, no one can convince me of anything about the physical world because the only possible thing that can be known for sure is what descartes said, cogito ergo sum. Wether the world is as simple as what we see or something much more complex, I know I am thinking, from which I can derive that I must exist. But why? why do I exist? or more accurately why am i existing at this moment? does existing imply that i was created? born? my mother? i can't be sure she exists. Also how do i exist? What am I? Must i exist 'somewhere'? Must 'somewhere' exist? Must 'somewhere' have been created too? its hard to derive stuff from just the fact that you exist. all these question have seemingly obvious answers, but none of those answers follow logically.