Importance of the College GPA

You don't become a good doctor by merely working in a hospital.

This is off-topic since the OP is interested in what he can do with purely a BS in math and chemistry. But it is impressive to become a doctor, much less become a good doctor. What makes a "good" doctor is relevant to the field that they choose as a profession. Yes, being smart or having experience isn't enough to be good at a skills related profession. Being a skillful person makes you good at a skills related profession, however what those skills entails involves things outside of purely skills. Take for instance surgery, you should definitely have some sort of asceptic technique down as well as dexterity to work around organs during the operation. However, you also need stamina to stand for possibly six to eight hours straight during performing the surgery. You also need to have tough skin that is not sensitive to continual alcohol dousing and you have to be flexible and willing to work double shifts leading to possibly sixteen or twenty four hours of operating straight. Residents sometimes work for 36 hours straight in a hospital due to meeting hospital demands. It is an unwritten rule that if you can work, you should work in lieu of whatever legalities there are to working overtime. There is no doubt that just working in a hospital makes you a "good" doctor. Don't be insulting. Being a good doctor requires you to be a superhuman for certain specialties and that's not defined by experience or grades, some people just have it in them to perform and others weren't met to be certain-doctors or doctors in the first place. At the same time, I encourage anyone who wants to work as a doctor to work in a hospital. A hospital can be a very claustrophobic environment because you are dealing in a sterile environment with little room for personal creativity or dimensions of growth outside from stalwart responsibility and professionalism. You make a mistake and a patient suffers, you are getting fired because the hospital would rather see you out the door then to incur any liability for malpractice. If you are unionized, then that may be a different story entirely ie nurses. However in a serious case of malpractice, I find it hard to believe that the hospital won't be riding on any practitioner's ass.