For maths, there is an idea that if you stop using your skills for a year they become rusty, similar to the way you might become rusty if you were to stop speaking a language for a year or stopped playing a musical instrument.
For this reason, gap years and deferrals are discouraged more than in other subjects and often will reduce the chances of being offered a place.
If someone asks to defer, top departments will often require or strongly suggest a series of activities for maths students to do during a gap year. These might include things like doing additional courses or qualifications, completing work set by the college / department, undertaking specifically relevant employment and so on. Obviously your DS is not deferring, but looking at their suggestions would give him an idea of what he would need to be doing to demonstrate that he is keeping his skills up, so he is disadvantaged as little as possible.
This is a couple of years' old, but if you look here: www.maths.cam.ac.uk/undergrad/admissions/files/admissionsguide.pdf you can see on page 14 each Cambridge college's attitude towards gap years for maths. They are specifically referring to deferrals, but it gives you a broad overview of how different colleges view gaps in studying maths.
- 11 colleges regard a gap year negatively and discourage it unless to do something extremely relevant. It would probably be pointless applying to these colleges as he is not asking to defer due to having some kind of special pre-planned maths-related activity that it is especially valuable for him to take part in.
- 12 say they are neutral on it (although obviously there is a question of theory vs practice).
- Just 2 colleges would regard it in any way positively, and again, one would only see it as a positive if it was spent doing something particularly worthwhile.
So if he was to take a year out and apply to Cambridge, he would need to research and choose his college carefully and also accept that he would have a smaller chance than other applicants of being picked up from the pool because almost half the colleges won't be interested.
I imagine it would be much the same for reapplying to Oxford.