Advice on educational pathways for Maths / Physics?

Hii, not sure it is the appropriate forum, but this seems the most relevant one of suggested
Context: I am current year 12 student in UK, very interested in the "why?" of how the world works and hence fascinated by physics and want to truly understand how stuff works. However, I'm also extremely frustrated with lack of rigor that seems to be present in physics courses(* examples below). On the other hand, with mathematics, while I still sometimes enjoy it (eg. basic group theory and isomorphisms), I don't have as much drive for it as for physics.
*My view on rigour: For example I wouldn't mind having to accept a true statement without proof (with it's limitations if present also stated), however I would be frustrated by technically not correct logical jumps such as "A => B" when in fact "A, C, D => B but C, D are mostly true" or example from my recent A-level studies - a claim that polarisation filter works by only letting through the waves that vibrate in a specific plane - which is presented as truth, but in reality a technically not correct oversimplification (I still btw don't get how these filters actually work except that they actually do something to the wave).

So I would appreciate any information on how rigorous different physics courses usually are, and on how easy it is to learn physics after / during a maths degree? And any other related advice/information, recommendations of (mostly) rigorous physics books /online lectures would be greatly appreciated as well. Thank you!

Hi, before providing information that you "want", can you explain or provide more info on the following questions:
1) What do you mean by "a claim that polarisation filter works by only letting through the waves that vibrate in a specific plane - which is presented as truth, but in reality a technically not correct oversimplification"
2) What do you know about science?
3) Have you encountered a piece of "rigour physics" in A-level? If yes, please elaborate on it.
If no, how do you "see" Newton's 2nd law, conservation of momentum and conservation of energy?
Thanks.

Hello, thank you for your response, I'll elaborate:
1) I mean that in one of the physics lessons polarising filter was explained to just work as a filter, filtering out all waves except those that are of the same orientation as the filter in (my recall might not be correct) - however that would mean that putting in a second filter after the first one would leave to no-ish light and more importantly the same amount of light no mater how the filter is rotated(as long as the direction is not the same as of the first one) - well this is not the case. And after searching online (while still not understanding this) I learned that for some reason the intensity of light let through is proportional to the cosine of the angle between the light and filter's orientation - so a-level explanation is an oversimplification
2) This is quite an abstract question haha, I'm not really sure along what lines the answer was meant to be, but I know that a basic principle is that a theory is developed and then experimentally tested to coincide with actual results, In terms of education I know basic gcse and some A-level knowledge.
3) Well, to the best of my knowledge if we take some basic parts, such as some definitions when they are given, particle classification and the 2 conservations you've mentioned, they seem to me to be quite rigorous. I wouldn't say newtons second law is rigorous though (the way it is presented in A-level), as the actual law is formulated not as F=ma, but as a change of momentum over time. While I don't know exact details, I think that it does make a difference when the speed is close to that of speed of light (and I'm not sure if re-formulating it would actually make a difference in that case.

Hii, not sure it is the appropriate forum, but this seems the most relevant one of suggested
Context: I am current year 12 student in UK, very interested in the "why?" of how the world works and hence fascinated by physics and want to truly understand how stuff works. However, I'm also extremely frustrated with lack of rigor that seems to be present in physics courses(* examples below). On the other hand, with mathematics, while I still sometimes enjoy it (eg. basic group theory and isomorphisms), I don't have as much drive for it as for physics.
*My view on rigour: For example I wouldn't mind having to accept a true statement without proof (with it's limitations if present also stated), however I would be frustrated by technically not correct logical jumps such as "A => B" when in fact "A, C, D => B but C, D are mostly true" or example from my recent A-level studies - a claim that polarisation filter works by only letting through the waves that vibrate in a specific plane - which is presented as truth, but in reality a technically not correct oversimplification (I still btw don't get how these filters actually work except that they actually do something to the wave).

So I would appreciate any information on how rigorous different physics courses usually are, and on how easy it is to learn physics after / during a maths degree? And any other related advice/information, recommendations of (mostly) rigorous physics books /online lectures would be greatly appreciated as well. Thank you!