The plumber knows how many inches per foot the pipe has to drop in order for the poop to flow away and not get stuck in the pipe. It's easy enough to either not drop it enough and everything gets stuck or for it to drop too much and the water flows away but the poop stays in place. And they're the ones that actually make it happen and their clients really do care about that in the end. Without knowing this the plumber is nothing. They don't necessarily need to know they why and especially don't need to calculate it out!

Some mathematician can probably calculate that properly. Some mathematician probably first did calculate that out to prove it. I'm not entirely certain that a mathematician was the reason that we know what drop we need. A lot of things in "real life" were "empirically discovered" and used and done for centuries before a mathematician proved it.

Exceptions prove the rule, like when we calculate(d) things out for space travel before ever attempting it ;)