Science is about building and refining models (theories) in order to make them match observable reality as close as possible, in order to use those models to predict what happens in the future - both by itself, and in consequence of us poking stuff. That's what it means to know "how something works".

Engineering takes these models and adds a "what's the best way to poke things to achieve a desired outcome?" aspect.

Formal proofs are for mathematicians. Mathematics is a purely abstract invention and operates in its own universe, where absolute formal proofs are possible.