politics - nice, could be involved in a political society
theatre - shows signs of participation in university wide drama
debate - excellent, can join the cambridge union (debating)
sci-fi - nice, bound to be a soc for him and shows he likes reading
the fact he read a lot about maths, quoted a book he's fond of, done the UKMT - gaining golds and silvers for it shows he's fond of maths, so yeah, you're right. you just have to get the right balance. tbh, this is just part of the ps, if this is the standard of part of it, it must be very good. that's why he got the offer.
the one thing is that he didn't mentioned what type of politics, like conservative politics, because politics is such a broad term, but that's just me. and also "I'm passionate about maths" is very over-used, and could use a better sentence.
but overall, v. good!
I would most definitely make him an offer.