I've always loved physics but I don't think it loves me back.
That is, I've always found it fascinating since high school but once you need calculus to understand some of the more advanced stuff I feel that I get lost in the math (which, admittedly, I suck at) and lose the intuition for what's really going on. Then it just becomes a giant math problem that prevents me from seeing the bigger picture.
It's just this problem I've had that I always sweat the small things and sometimes miss the bigger picture or the main concept when I get frustrated that I can't understand the details.
There is a point early in your education as a physicist (Quantum Mechanics) where it becomes impossible to have an intuitive understanding. For Quantum Mechanics you can just do the calculation, there is no way you can get an intuitive understanding, other than by becoming comfortable with the mathematics.
I used the feel the same as you, but then I gave up. One day I was like "screw it, I'm just going to take it for granted". I stopped caring about getting a feel for why things happen, just that they do and I know how to calculate them. When that changed I was suddenly free, I didn't have to worry about why things made sense or not anymore.
You still should understand what the problem is though. Physics isn't just about understanding the mathematics, it's also about understanding the physical arguments that goes along with it. Like how can we come up with the problem to solve in the first place?
One problem I have often had is that in a long derivation my brain will be so fried on the mathematics that I eventually forget what the terms in the equations actually represent. I'm like "what is q again? oh yeah it's a generalised coordinate".
It's cliche but the important part is not giving up. My favourite lecturer, who is a theorist, says that the main issue that students have is fluency. They can do the mathematics, but they aren't fluent at it. They aren't quick, they're slow, it takes them time to work it out, etc. That is what makes you forget, but eventually after seeing the mathematics so many times it will becomes ingrained in your brain, and it will just feel obvious, and you don't have to think about it. Eventually you will become fluent in the mathematics and it will disintegrate as a boundary, and all you'll have to think about is the physics. It's just practise.
> I used the feel the same as you, but then I gave up. One day I was like "screw it, I'm just going to take it for granted". I stopped caring about getting a feel for why things happen, just that they do and I know how to calculate them. When that changed I was suddenly free, I didn't have to worry about why things made sense or not anymore.
A very important development in my understanding of mathematics was developing an intuition of when something is worth visualizing. Sometimes visualization is extremely helpful. Sometimes it just makes understanding the problem more difficult (looking at you quaternions).
> One problem I have often had is that in a long derivation my brain will be so fried on the mathematics that I eventually forget what the terms in the equations actually represent. I'm like "what is q again? oh yeah it's a generalised coordinate".
I had a professor who said something along the lines of "a good notation liberates the mind while a poor one clutters it." I suspect he was quoting a famous mathematician (as he was wont to do), but I cannot remember who (Whitehead?).
Thanks for the last paragraph. I'm currently studying convex optimization and feeling pretty dumb despite having done well in some reasonably challenging math classes before. Gotta remember that it will get easier as these new topics trickle into the realm of intuition.
This is something that everyone who studies physics has to work hard to get past.
Understanding the math as a description of the physics rather than just a bunch of symbols takes time and hard work.
Someplace to start: find a differential equation you are trying to understand and walk through what it means. Look at each term and try to suss out the physics that is going on by thinking about the differentials as descriptive. It takes time, but it is very powerful (even when thinking about non-physics related equations)
You're not alone. I was lucky enough to go to undergrad with Nima Arkani-Hamed [1]. I later had lunch with him while he was at Harvard, and he mentioned that a lot of what he did in the intervening years was to get away from the very formal mathematical, proof-based thinking of our math courses back then.
That is, I've always found it fascinating since high school but once you need calculus to understand some of the more advanced stuff I feel that I get lost in the math (which, admittedly, I suck at) and lose the intuition for what's really going on. Then it just becomes a giant math problem that prevents me from seeing the bigger picture.
It's just this problem I've had that I always sweat the small things and sometimes miss the bigger picture or the main concept when I get frustrated that I can't understand the details.