I competed and was highly successful in a number of maths competitions.

A few points:

1. Regarding the applicability of maths to programming, from experience I know it to be a major advantage in algorithm design; but admittedly not so much in building an iPhone app.
2. My degree is Science (Advanced Maths), so that is probably enough proof for most employers - mentioning competitions might just be overkill
3. I now have two years of programming experience, so maybe even something as significant as top of Australia might seem to irrelevant to many employers
4. If I remove this completely from my resume, then I don't really have anything to make my resume stand out at all. Lots of others would have similar work experience or have achieved reasonably good marks in university
5. This might be more relevant for companies such as Google that have been known to hire a large number of competitors in the International Olympiads. In fact, they are now a major sponsor of the [International Maths Olympiad](http://news.softpedia.com/news/Google-Donates-1-million-to-the-International-Mathematical-Olympiad-179882.shtml).

Should I mention my maths competition results and if so, how should I include them?