This year I started at the University of Cambridge to study Maths. I was very unfortunate to contract a serious infection early on in the term, and as a reult it has been mutually decided between myself and my tutors that I should defer entry and return next year. Essentially I have taken a forced gap year.
It is preferred, at least in the UK, not to take gap years in Mathematics so as not to 'go stale' - that is, to lose one's ability through inactivity. With this in mind, I'm trying to explore what I can possibly do with the time.
I have a dilemma: I don't want to go over the material in my course because I'll certainly be covering it next year, and so I'll be wasting my time in the future (and risking getting lazy then!). I'm struggling to find internships or jobs involving mathematics which don't require more advanced knowledge than I have. Sure, I could get an unrelated job (or none at all; I'm not desperate for the money) and just look at problems that interest me, but that seems like a waste of the opportunity - it doesn't really count for anything to anyone else.
So essentially my question is this: Is there anything I can do, as a Junior Undergraduate, relating to Mathematics, which will be recognised by others?