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I plan on getting my PhD in physics soon.

I've been told several times that all you need to become a physicist is Calculus I-III, differential equations, linear algebra, and maybe vector analysis and advanced differential equations, and the rest of the math you need, you will be taught in your physics courses.

While that has held true, recently I have heard two things that have made me think. The first was the quote, "physics is too hard for physicists." which I'm most of you've heard.

The second was something about Einstein intensely studying differential geometry before developing general relativity.

This made me think that I, as a theoretical physicist, wanting to reach the ranks of Einstein, must endeavor deep into the mathematical realm.

Therefore I ask what fields of mathematics should I study to be more than successful as a physicist?