Become a Physicist: PhD in Mathematics or Physics?

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Hello
I want to become a physicist.Can a phD in mathematics lead me to that or a phD in physics?
Or to become a mathematician will a phD in physics help?
My point is that do I have to do phD in the specific field to become one?
 
Adjacent,

Ultimately, what matters is "what career do you see for yourself?". What does your dream job look like? What would make you wake up in the morning eager to go to work?

Once you have answers to these, finding your path will be easier.
 
Generally speaking, in order to become what most people would call a "physicist" you need a PhD in physics. There are people in mathematics who do work in physics. There are physicists who make contributions to the field of mathematics.

That said, it's also important to point out that getting a PhD in physics is not a guarantee that you will have a career as an academic physicist, and similar for mathematics.