The Louisville Courier-Journal reports:

Rand Paul, who practices in Bowling Green, says he is certified by the National Board of Ophthalmology, a group that he incorporated in 1999 and that he heads.
But that entity is not recognized by the American Board of Medical Specialties, which works with the American Medical Association to approve such specialty boards.

Substance aside, I kind of liked Paul's answer:

"I'm not going to go through all that right now," Paul said while at the Great Eastern National Gun Day Show and JAG Military Show, in Louisville.
Asked when he would talk, Paul said: "Uh, you know, never."

At least he's honest. It also gives me a chance to post the classic New Yorker cartoon: