Mathematical proofs, physics and time management

[Dante Augusto]

How important is for a physics undergraduate to know the mathematical proofs for every theorem learnd on the math courses? Is it better to trust the math, learn the intuitive notions, and then learn the methods and operations in a more mechanical way, memorizing formulas and steps through repetition, using math more as a tool? Or go through detailed mathematical proofs consequently spending less time grasping the physics concepts?

 

[ZapperZ]

How important is for a physics undergraduate to know the mathematical proofs for every theorem learnd on the math courses? Is it better to trust the math, learn the intuitive notions, and then learn the methods and operations in a more mechanical way, memorizing formulas and steps through repetition, using math more as a tool? Or go through detailed mathematical proofs consequently spending less time grasping the physics concepts?

How important is it for you to intimately know how your car engine work, or how they assemble the airplane that you are about to fly on?

Zz.

 

[PeroK]

How important is for a physics undergraduate to know the mathematical proofs for every theorem learnd on the math courses? Is it better to trust the math, learn the intuitive notions, and then learn the methods and operations in a more mechanical way, memorizing formulas and steps through repetition, using math more as a tool? Or go through detailed mathematical proofs consequently spending less time grasping the physics concepts?

I think you have to be pragmatic. You don't need to know the technical details, like the precise class of functions for which a theorem holds. But, working though a proof of Green's theorem or the Divergence theorem can give you a useful physical insight.

I would use my judgement about whether a better understanding of the maths is truly useful to you as a physicist. Linear algebra is another good example where you will have to decide where to draw the line between knowledge and a deeper understanding.