Catapults Invented Before Theory Explained Them

I suspect that many engineering developments occur in this way. If you look back into the theories behind chemical reactions, etc. you will find that only after a significant amount of trial and error were we able to arrive at today's somewhat accurate analyses.

The discovery of stainless steel is a good example. Numerous different combinations of elements were added to steel to see if they could make a metal for gun barrels that didn't rust. They gave up in the end and threw all the samples in the dump. Year(s) later someone noticed one of the samples was pristine (a pity they also threw out all of the lab notes and did not know which combination the sample was, and so redid the tests over again).

Let that be a lesson to always create and file good lab work.