alright, so when I'm implementing ISA on microchips from scratch with transistors and it works, we can say that I more or less know what I'm doing. I have faith in my knowledge there. But then, when it comes to "proof by contradiction" in mathematics I do know that it's a valid way to prove things (within its scope). Yet, I have to admit that I have no idea why/how it works more than from an abstract point of view. I put that in contrast to what
I know about microchips where I even know the stuff down to the qunatum mechanics behind them. How do you get such "faith" in the craft in mathematics?
I suppose its built upon the formal system, but I can't just trust it blindly