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.
> There really isn't anything weird or suspect about renormalization
This is the first time I've heard anyone say that. To me, renormalization is extremely weird, if anything because it's so unrigorous and ad-hoc that I find it hard to believe it even works. Sure, it does the job it's supposed to, and I understand how it does that (for the most part anyway), but that doesn't make it any less weird.
Like, ok, we get testable answers and they match experiments but also this is _so_ hacky and I can't shake the feeling that one day someone will come along and show that there's some reason why these bad assumptions work out fine. You know, like how "to find the Schwarzschild radius for a black hole of known mass, calculate the radius at which the escape velocity is equal to the speed of light" gives the correct answer even though the theory implied by this method is naive and wrong.
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.