I'm in year 12 now and I want to study maths in university, especially in Cambridge's Trinity College.
I do not have any Olympiad awards, mainly because I do not like the combination of mathematics and Olympiads. (I can do most of the Olympiad problems quickly and accurately, but I just do not accept treating mathematics as an Olympics sport, or something alike, in my values.)
What I have now: I wrote and published an article on a SCI journal (JCR section 1) last year about automatic theorem deduction and category theory. (I also created a prototype software as an implementation of the methods I presented in my paper.)
I found the STEP II & III papers pretty easy for me and the specimen test papers from Trinity's website can also be solved without difficulty. i.e. I could solve all 10 problems in less than 1 hour.
Recently I found that most applicants have at least one award in Olympiad contesets, and the Trinity College's application is very competitive (and very hard, I think?) so will my application has a huge disadvantage compared with others?
PS: I read Wolfram's A New Kind of Science in my 10th grade and created a cellular automata simulation which can evolve itself via genetic algorithm to do various tasks. Should I mention this in my P.S. as this may be more of computer science than of mathematics?