I'm in my last year of school and starting a mathematics degree at a British university this Autumn. I've always liked mathematics, especially 'pure' side of mathematics. I love poofs and always enjoyed solving puzzles and brainteasers for fun. Some of my favourite topics of maths are geometry (especially plane Euclidean geometry), sets/logic and probability/combinatorics. I've also always liked physics. I'm doing Physics A-Level and I especially loved electric & magnetic fields chapter and special relativity chapter (which doesn't go into much detail unfortunately). However, mechanics has not grabbed my attention so far. Maybe it will get more interesting at university? This seems a bit strange because many people who like both maths and physics seem to like mechanics. My friends assume that I like mechanics because they know how much I like maths, which is funny because for me, it's the least interesting topic in physics A-Level. My question is, how much is pure mathematics and (theoretical) physics related? I love elegant proofs and pure mathematics. But I always had trouble memorising integrals at school, which is one of many reasons why I chose to study maths over physics at university. People told me physics was more of using maths techniques. Is this true for very advanced level physics such as in PhD course? Also, what are some branches of theoretical physics that rely heavily on using ideas from pure mathematics? Do you think it's possible to do a PhD on theoretical physics with mathematics background? Thanks.