GR does use a lot of mathematics. For example, the subject also mentioned that if you want to learn GR and even study GR and cosmology in the future, you need at least differential geometry, Riemannian geometry, tensor analysis, group theory and so on. In mathematics, and you can basically understand GR, if the basic knowledge of mathematics in the subject is good, my suggestion is to start learning Guangxiang while watching mathematics. For example, if you just want to have something you can't understand in mathematics, you can turn over the mathematics again, so that the learning efficiency will be higher, you won't spend too much time on pure mathematics, and you can enter the study of GR core theory as soon as possible. Of course, if there is plenty of time in the subject, it is also a good choice to do a good job in mathematics before starting physics study. For example, modern algebra, involving simple related theories of groups, rings and fields, is still of learning significance and helpful for later systematic study of group theory. As for real analysis and complex analysis, I think these should be the basic courses of mathematics for physics majors, so if you are not very proficient, you should at least understand them. Linear algebra and calculus are mentioned in other answers, so I won't say more. This is the most basic mathematics. Finally, it is a great decision to engage in mathematical physics. Although there are not many people engaged in mathematical physics now, there must be many, especially if you go abroad to study for a doctorate like this, the academic environment will be better. Say a digression. These days, the five-day International Conference on 20 16 String Theory was held in Tsinghua University. I also participated in some Daniel's lectures, such as world-famous mathematical physicists Witten, Gross, Nima and Qiu Chengtong. String theory is a branch of mathematical physics and I like it very much. Although I haven't dabbled in it, I just have a suggestion that GR is naturally good, but string theory has been an active and hot research field in mathematical physics for decades, and I can consider doing string theory research if I want.