Studying Focus on in-depth understanding of the Maths behind Physics

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Understanding the mathematics behind physics is crucial for a comprehensive grasp of the subject, especially for junior physics undergraduates. While it may feel overwhelming at times, particularly in calculus, delving into the mathematical principles enhances overall comprehension. Physics often requires a solid foundation in various mathematical concepts, as they serve as the language through which physical theories are expressed. The discussion emphasizes that while a deep understanding of math is beneficial, it is not necessary to master every aspect immediately. Over time, students will naturally find a balance between physics and its mathematical underpinnings. Engaging with specific examples, such as the Frenet-Serret equations, can provide clarity and context for applying mathematical concepts in physics. Ultimately, investing time in understanding the math is seen as worthwhile for long-term success in the field.
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As a Junior year physics undergrad, how much should i focus on understanding the maths behind the physics i use. One one hand i believe that understanding maths behind the physics i use is necessary but sometimes specially in calc i feel that i am going in too much.
Simply speaking from your experience is it worth to go deep into the maths?

P.S. this is my first writing on physics forum, actually first time writing on a forum so i am sorry if the title seems off.

P.P.S. I have forgotten to give an example, For example Frenet-Serret Eqn, they haven't been taught in my class, though the principal normal is used heavily in my electrodynamics class.
 
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Carolus_Rex said:
As a Junior year physics undergrad, how much should i focus on understanding the maths behind the physics i use. One one hand i believe that understanding maths behind the physics i use is necessary but sometimes specially in calc i feel that i am going in too much.
Simply speaking from your experience is it worth to go deep into the maths?

P.S. this is my first writing on physics forum, actually first time writing on a forum so i am sorry if the title seems off.

P.P.S. I have forgotten to give an example, For example Frenet-Serret Eqn, they haven't been taught in my class, though the principal normal is used heavily in my electrodynamics class.
Hello and :welcome: !

I am sure that good physicists also have a good understanding of mathematics. But there are differences. The most different and least obvious thing is, that studying - probably any field, but here, too - is far more learning a new language than it is learning theorems. The same things can be expressed very differently, hence your question could be rephrased as: Will I have to learn both new languages?

Well, yes, in a way, but certainly not at the beginning. E.g., physics is all about frames. You need a coordinate system to measure something! Hence there will be coordinates of all kinds all over the place. Mathematicians normally hate coordinates. They distract from looking at the essentials.

You mentioned calculus. A subject which wouldn't come to mind first. It is pretty much the same in both fields; at least if it isn't taught the most possible abstract way in mathematics, which it usually isn't. I.e. knowing the mathematical principles in calculus is equally essential for physics and mathematics. Things change if we talk about abstract algebra or topology. Maybe it is better to ask this question on specific examples rather than in general. PF is a good place to do so.

You will automatically develop a balance between the two over the years.
 
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I consider a mathematical method understood once I've followed the proof for it step by step, noting the techniques involved. I find it helpful in holding the method in mind or, failing that, deriving it from more basic principles when needed.
 
"Physics is to math what sex is to masturbation"

-RF
 
fresh_42 said:
Hello and :welcome: !

I am sure that good physicists also have a good understanding of mathematics. But there are differences. The most different and least obvious thing is, that studying - probably any field, but here, too - is far more learning a new language than it is learning theorems. The same things can be expressed very differently, hence your question could be rephrased as: Will I have to learn both new languages?

Well, yes, in a way, but certainly not at the beginning. E.g., physics is all about frames. You need a coordinate system to measure something! Hence there will be coordinates of all kinds all over the place. Mathematicians normally hate coordinates. They distract from looking at the essentials.

You mentioned calculus. A subject which wouldn't come to mind first. It is pretty much the same in both fields; at least if it isn't taught the most possible abstract way in mathematics, which it usually isn't. I.e. knowing the mathematical principles in calculus is equally essential for physics and mathematics. Things change if we talk about abstract algebra or topology. Maybe it is better to ask this question on specific examples rather than in general. PF is a good place to do so.

You will automatically develop a balance between the two over the years.
Thank you. I will try to develop better understanding of the maths behind the physics. Though it will be both hard and time consuming. I hope in the end,it will be all worth it.
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...
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