I'm an undergraduate student majoring in mathematics; I totally love it and I want to get Ph.D in pure mathematics.
I'm also interested in physics, especially the theoretical field; my favorite areas are relativity and quantum theory. Of course, I'm more into mathematics than physics, that is why I majored in math; plus I don't get as high grades in physics as I do in math.
Now here is my question, if I became a mathematician, can I switch to physics easily if I wanted to? I heard a lot about mathematicians contributing to string theory and other areas. I guess what I'm looking for is not a total switch to another field; rather it's more like the ability to learn more about physics easily and being able to contribute to the theories.
What I meant was that I want my Ph.D to be in pure math; in essence my focus would be on math. But also I want to study the stuff that interests me in physics, e.g. GR, String theory, etc. I'm asking if it's possible for a professional mathematician to
- study these subjects in depth without much difficulties; and I'm referring to difficulties in getting enrolled in classes and being able to handle them, and
- be able to contribute to these fields
I'm sorry English isn't my first language, I hope I made my question clear.