Phys and Maths: How Much Physics for Professional Mathematics?

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The discussion explores the relationship between physics and mathematics, particularly how knowledge of physics can enhance understanding of mathematical concepts. It highlights that while physicists often rely on complex mathematics, mathematicians can benefit from understanding physics to grasp certain mathematical ideas, especially in applied mathematics and theoretical physics. Participants note that concepts from physics, such as Newtonian mechanics and Lagrangian mechanics, can clarify mathematical topics like calculus and calculus of variations. The conversation emphasizes that the necessity of physics knowledge depends on one's specialization; pure mathematicians may not need physics, while those in applied mathematics or theoretical physics should have a solid foundation in relevant physical concepts. The dialogue also raises the question of how much physics is beneficial for mathematicians working alongside physicists, suggesting that even in fields like modern analysis, some understanding of physics, such as relativity, could be advantageous.
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I think everyone would agree that physicists often need to use very difficult mathematics to understand physical idea.

how about the converse? How much physics do we, (mathematicians), need to know in order to understand Mathematics?

Personally, I think Newtonian Mechanic helps me to understand Calculus, Lagrangian Mechanic helps me to understand Calculus of Variation, and etc. Many difficult ideas in Vector and Tensor Calculus were explained with physical aspect.

I want to know how much Phys I should study further for a career in professional mathematician! Your personal experience is very appriciated.

Thx You
 
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obviously if your'e heading to pure mathematics then none.
but if you want applied maths or theoretical physics, most of your courses will be in physics.
 
I'd say that applied maths is more to do with general concepts, eg. methods for solving particular problems.

`Physics' is a specific application - and as you go deeper into a particular area of physics, that specialisation increases.
 
yes, correct.
but those who take applied maths, don't they need some course in physics.
for example calculus of variations as far as i know is an applied maths field and most of the questions include physics concepts such as concepts from mechanics like velocity.

so i would agree it depends on your specialisation.
 
Math is a language for physicists, not the other way around. Physicists depend on math, the mathematicians have to supply it.
 
Poop-Loops said:
Math is a language for physicists, not the other way around. Physicists depend on math, the mathematicians have to supply it.

I agree on that totally, this is why I want to know how much Phys I should know to work with Physicists.
 
What if my specialisation is in Modern Analysis. Should I spend sometime on relativity?
 

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