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1. I am puzzled about which to be : theoretical physicist or pure mathematician !! what should i do ?

2. If i decided to be a theoretical physicist : should i study some pure maths to make new theory in physics ?

Like general relativity : the maths used on it was before it a pure maths that is useless .

3. Is learning or reading the proofs of maths theorems useful for theoretical physicist ?

Note : if i decided to be a theoretical physicist i would specialize in quantum gravity .