How do you cope with the fact that a large portion of science and math is something a human being cannot possibly rationalize in a common sense way?

You are supposed to "make sense of the world", but on some level you just have to put blind faith in what has already been established. You cant just go around questioning everything because that ultimately just leads to madness, but at the same time something might technically work even if the reasoning is wrong.

How the fuck do you deal with this problem? Am I just supposed to shut up and say "It just werks."?