Mathematical Physics vs Theoretical Physics

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Discussion Overview

The discussion centers on the distinctions between Mathematical Physics and Theoretical Physics, particularly in the context of academic and research interests. Participants explore the nature of work in both fields and the suitability of each for individuals with varying interests in mathematics and problem-solving.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses a desire to understand the differences between Theoretical and Mathematical Physics, mentioning interests in Quantum Gravity, Cosmology, QFT, and Quantum Optics.
  • Another participant notes that some universities have Mathematical Physics programs within the Mathematics department, suggesting a distinction in focus between the two fields.
  • A different viewpoint introduces fluid dynamics and kinetic theory as areas of Mathematical Physics, highlighting the role of differential equations inspired by physics.
  • One participant suggests that Mathematical Physicists are more focused on the mathematical tools and beauty behind problems, while Theoretical Physicists prioritize solving problems and formulating theories.
  • A later reply indicates that Theoretical Physics may be more suitable for those who view mathematics as a means to an end rather than an end in itself.
  • Another participant emphasizes the collaboration between the two fields and suggests seeking a strong undergraduate program for further exploration.

Areas of Agreement / Disagreement

Participants express varying perspectives on the distinctions and overlaps between Mathematical and Theoretical Physics, indicating that there is no consensus on a definitive difference. The discussion remains open-ended with multiple viewpoints presented.

Contextual Notes

Some assumptions about the nature of work in each field and the motivations of individuals pursuing them are not fully explored, leaving room for further clarification.

Niflheim
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Hello PF, pardon me if this isn't the wrong place but I just had a quick question. So I have always wanted to do Theoretical Physics (particular interests are Quantum Gravity, Cosmology, QFT and Quantum Optics, but those are subject to change), but recently I have started to look into Mathematical Physics. Apart from finding out that Mathematical Physicists work on String Theory and Cosmology, which are my primary interests, I really don't know whether I would be more suited to Mathematical or Theoretical Physics.

So can someone please describe the work that that Theoretical and Mathematical Physicists do, and what is the difference between them?

Thanks for any and all replies!
 
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Some universities have a "mathematical physics" research program in the MATH department as as opposed to the physics department. That, I'm guessing, would be the difference. Mathematical physicists are concerned with the mathematical tools needed to do physics, I believe.
 
Another area that could be considered "mathematical physics" might be fluid dynamics and kinetic theory...there is much work being done in math departments on differential equations that are inspired by these fields of physics. See Cédric Villani, Fields Medalist.
 
"Mathematical" anything tends to be academics that are more concerned and intrigued by the actual mathematics behind novel problems, not the problems themselves. Theoretical physicists tend to be more concerned with the actual solving of the problem or the formulation of a theory to suggest rather than the beauty of the mathematics which are being used.
 
I see. So Theoretical would be better for someone who cares about the math more as a means to an end, like if I cared more about the answer than the math behind it?
 
On a very basic level, yes. Truthfully, there is a lot of collaboration between the fields.

My best answer is, go the best undergrad program you can get into and ask more educated questions when you are contemplating postgrad options.
 
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Okay, thanks a lot! That helped a bunch.
 

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