This is one of the complicated steps in physics (I have a PhD in physics (and forgot everything since)).

First you have some math that goes along discovering physics. You split vectors, multiply mass by something and it's fine.

Then you have math that helps you with physics. Simple differentials equations that uncover while laws of nature (cooling down speed for instance). This is the golden time for many because you're at this sweet spot where it is exciting but not too hard.

Then comes the travel in desert of abstract things you have no idea about and winner why someone hates you by shoving Abel groups down your throat for no reason.

Finally comes that sight of relief when you can binding do some maths to end up with a real life solution without too much thinking because you have solid tools.

The last part is a bit morally complicated because you have the feeling that you are cheating. Renormalization, I am looking at you.

But then I forgot everything because I left academia and my memories may be faulty.