I know a senior Oxford mathematics tutor and he told me he generally doesn’t even read personal statements. I’d imagine they hold more weight with other tutors and interviewers, but they generally don’t hold much weight. Your interview, courseload and LoR hold more weight. As mentioned above, you shouldn’t mess it up but you shouldn’t worry too much about it.
For applicants applying to other subjects- especially humanities- don’t extrapolate from one subject or example.
The PS may not hold much weight in Mathematics, and/or it may vary considerably between subjects and tutors- but you don’t know for which subject and which tutor it will make a difference. It is also a potential asset- an opportunity for you to make your case.
i might give some good insight on this; i got an offer from oxford for ppe, st andrews for international relations, and king’s college london for international relations (still waiting on lse and ucl). my personal statement was almost completely geared around ir; i didn’t mention philosophy at all. my ps was only brought up once during interviews at oxford (during my economics one), and although i wouldn’t say they don’t care about the ps, they certainly seem to care less than the other british universities who don’t have interviews. for ppe in particular, the most important factors for getting an offer, in my opinion, are the tsa (admissions test) and the interviews.
The personal statement is important to focus on, despite fears that some universities may not look at it. You are applying to five universities, and each may give different weighting to it than the other. In order to be sure to keep them all happy, you have to work incredibly hard on it. It’s the only method through with a university can see that you are committed to the chosen degree subject over and above your school subjects. For example, if you are applying to read law at university, you are unlikely to have studied it at school, so you need to be able to show commitment beyond your grades. This would be via reading of books, journals and magazines, as well as things like public lectures, relevant podcasts, documentaries and essay competitions, for example. There is no other way of showing this in the UCAS form. There are, of course, anecdotal stories of tutors who don’t look at it and prefer to give precedence to the teacher reference, but I would never advise an applicant to rely on that. If you love the subject, show off about it and evidence that love with academic engagement. It is what the majority of admissions teams want to see.
They only see three things before any potential interview. Test scores, reference, PS.
All of those should be a excellent as possible. I don’t even know why this is in question.
It’s true that the PS won’t matter if you don’t have the required grades, they probably won’t even read it. However, once you pass that threshold, the PS is important. I have an offer to read medicine at cambridge next fall and in my experience, what was really important were my grades, ps and interview. The admissions test can be important, but personally, I did very badly in it and still got in thanks to the other things. For me, they did ask me a few questions about my ps during my interviews, but they hadn’t read it beforehand. Oh, and the limit is 4000 characters and 47 lines, not 500 words!