How to stay academically active during a Mathematics Gap Year? 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?
 A: It turned out my answer was too long to be a comment
tbh, I'd try to cover the material in the first year during your year off. Unless you got an IMO medal and go to Trinity, I very much doubt you will find first year a breeze. This comes from a ex-Cambridge student. I think it is very hard to do any meaningful research without good foundations, unless it is something which does not need a lot of undergraduate knowledge like combinatorics or graph theory.
I am not sure how many weeks you spent in Cambridge, but like try to learn 1 course from a textbook and see how many questions you would be able to do on your example sheets or past exam papers. They are not easy....
A: It might be a good idea to go ahead and learn the material you would have covered had you been in school. It's possible that if you obtain a very good understanding beforehand, administrators and professors would let you test out of those courses, and let you take the next course in the degree sequence. If not, then you'll at least be very well prepared for the subject for when you return.
A: you can always do some type of independent research! and also you can keep reviewing the previous course work you've taken, and make sure you have a good thorough understanding of it, before you continue your studies. I'm sure you can find certain professors you can work with, and help them with research!
