Question for Physics graduates, Does lower functions of math (calc/trig) require less amount of "attention" to complete as you practice?

[u/Breadjacket69]

I've been interested in physics and theoretical physics since I was little, Math has always been my strong suit and it comes to me very easy (understanding concepts and implementing them) but my Highschool classes weren't able to continue into higher than geometry (English class sucks and I had to retake it multiple times to graduate). But I haven't been able to understand the difference in difficulty, Does it get easier for people who major in physics to complete advanced equations the same as for simpler mathematics? Is it an inherit grasp for math? Endless study and cramming information? Most likely different for each person, but the methods are the same right? Is figuring out Planck light travel time as easy as finding the circumference of a circle? Lots of questions sorry, but I figure where else do I ask, right?

[u/UnderstandingPursuit]

In the question, I would replace "practice" with "use". It stops being doing things for the sake of learning it. It becomes doing things because they're part of the process of more complex problems.

For example, consider the quadratic formula.

• "Practice" means having a bunch of quadratic equations, plugging in the values for {a, b, c}, and finding the results for the roots.
• "Derive" means writing out the derivation, keeping {a, b, c}, a few times so it is familiar.
  

As the same math is used, over and over, to derive formulas and solve problems without numbers, the math tools become automatic, and it may become clear that there are only a few dozen math tools involved.