This may sound like a strange question given that most M.D./Ph.D. students pursue science Ph.D.s, but is it possible to apply to an M.D./Ph.D. program for a Ph.D. in mathematics?
--Why medical school? It will not affect your research at all since they are completely different.
or biophysics...
do they just like to see that the candidate is qualified for each respective program?
Not necessarily true. You could be interested in mathematically modeling disease development, for example.
aka genetics, public health, or bioinformatics???
I doubt that is what he is looking for. Although, I might be wrong
Yes, those are areas in which you could also model disease. But that doesn't mean you can't do that (or want to do that) with a math degree 🙂.
I highly advise against it. I was considering doing a physics PhD in a non-medical field (e.g. particles). What's the point? You can't do both medicine and mathematics well. The days of the polymath are practically over. Focus on one or two things - one of them time-intensive, such as a medicine OR mathematics as a career, and perhaps a hobby like painting, foreign languages, etc.
You'd have to be independently wealthy or have a wealthy benefactor and have abundant free time to pursue multiple subjects seriously, and usually they are related. Even the famous polymaths usually did math or science along with philosophy, theology, art, or some other intellectual subject. Medicine is too hands-on and time-consuming to pursue something parallel like that.
As for the PhD, it would be a nightmare. They wouldn't recognize ANY of your medschool classes, you'd have to complete ALL of their requirements, including likely massive TAing, and it would just be a complete waste of time and downright stupid.
If you want to mathematically model biology, do biophysics, although - and I'm going to get attacked for this - I think even biophysics has a lot less to do with medicine than the more cookbook fields. The one exception are things like radiology and radiation/oncology, where biophysics or medical physics can be of great use in developing new modalities - but, again, that's just a very few fields.
Can I still make it up and are labs usually open for such students?
the hurdles the math department will put on your PhD will tend to lengthen your training with little to no long-term gain. When there is a path of less resistance you should take it in this game.