Computer Science at Cambridge- Project Ideas

For anyone that finds this thread: Cambridge CS really don't need you to have done any programming. Your PS is fairly irrelevant, and is used mostly just to find out what to talk about at interview (and because CS is so mathematical, my PS wasn't even mentioned at all). The most relevant things would probably be things you've done in Maths such as Maths challenges etc.
The best way of standing out from the crowd is excellent UMS scores in maths/further maths (and if taken, physics). I personally spoke about optimising a very simple prime number generator and discussed how it related to CS. I don't think it helped much/at all. Any interviews, tests and of course UMS (to an extent GCSEs as well) are the most important things, so don't worry about spending loads of time doing projects, just get excellent grades.
Source: Current CS offer holder at Cambridge.

I was told the same by my teacher as well, could you explain why math is the only thing they care about please? I don't see how math has so much thing to do with computing?
Plus their course list doesn't seem to have much thing to do with math?