A phrase used to describe someone who is sexually attractive because of their high IQ or because the way they think is unique or seems very similar to the attractee's own ideals.
"He has a PhD in psychiatry & neuroscience and works for Doctors Without Borders. He doesn't look like much, but damn, he's got a sexy brain."
"I love her sexy brain! It's like she knows what I'm thinking before I do."
Some examples of famous sexy brains: Pierre Elliot Trudeau, Dr. Ruth Westheimer, John Stewart, Jodie Foster, Barrack Obama, Oprah Winfrey, Steve Jobs, Ayn Rand