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I'm a Master Math Student And I'm very interested in Some fields in Physics Like Cosmology. I even Considered Changing my field and Apply for physics(Cosmology) but wasn't really possible (my professors told me it will be risky to apply for Physics PhD), then I thought I could continue my Math studding, and Have my own Math approach to this problems in physics like studding Geometry or Stochastic ... but recently I've heard a lot that these advance field of mathematics aren't really very useful for physics and most of physicians don't believe in using these kind of math. is it possible to do something interdisciplinary in PhD ? or I really should try to change my field 'cause I love math but it was the desire to knowing the world which lead me to studding math .

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There are definitely huge overlaps between math and physics, and the tools you learn in math can be incredibly useful in physics. If you have a heavy math background, then you are uniquely prepared to tackle many theoretical problems in physics that require mathematical sophistication. Relativity is built on differential geometry, high energy physics uses a lot of modern algebra, and representation theory abounds in all sorts of fields. There are many people who do mathematical physics, and a few professors that are even dual appointments in math and physics departments, so there are certainly options available to you. There will likely be insights that people with a more traditional physics background will have that may not be immediate for you, but in the long run you will understand the theory much better and be able to make better contributions to it if you truly understand and appreciate its mathematical underpinnings. Good luck!

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Physical cosmology today is dominated by statistics on the $\Lambda$CDM model. The astronomers involved are very keen on looking for anisotropies in the cosmic microwave background and searching for other clues of large-structure formation. What this means to you, a mathematician, is that people are mostly interested in looking at cross-correlations on two-point statistics.

It is not exactly true that advanced mathematics is not appreciated by physicists, but the truth is that it is harder to convince experimentalists over theorists of the utility of a new mathematical technique. That being said, the best work in physics comes from theorists that are highly aware of experimental limitations and from experimentalists that want to refine the formalism of theoretical models.

I highly suggest you pursue general relativity for your Ph.D. It's the best of all worlds, and if you're somewhat philosophically minded, it can bring you profound joy.

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