Rand Paul graduated college and medical school, and passed certification of American Board of Ophthalmology — before running for Senate and winning.
Rand Paul isn't board certified by the American Board of Ophthalmology--at least he hasn't been since 2005. Yes, he passed his board exam in 1995, but rather than recertify (like every other doctor has to), he opted to create his own "National Board of Ophthalmology" with himself as president. (see wikipedia if you don't believe me)
To be fair, it does take a certain amount of intelligence to give the middle finger to your accrediting board and create your own professional board "shell" company. Doesn't say much for his ethics or proficiency at ophthalmology. I guess that's why he went into politics, those traits likely serve him well.