While you might be seeking a rewarding career, I think it's important to consider going into a field you're passionate about. Maths is very understanding based, while there is a lot of rote-learning involved in biomed (so pretty different). Biomedical science offers pathways into medicine or research predominantly, but it's important to have a backup that you are actually interested in. In your case, seeing as maths is a passion, perhaps consider science as an alternative as it will offer a few more years for you to pursue mathematics (alongside science subjects) and then you can choose if you want to pursue medicine or not in third year (note: this pathway for monash only will offer 25 spots not the normal 75 in biomed). Also, consider that while working in a hospital can change a few lives a day, you can be helping more people if you discover something upstream (so research is crucial too and its contribution to society shouldn't be underestimated). Best of luck though!