TITLE: The ten martini problem - reason for name
QUESTION [6 upvotes]: Why is the problem called the ten martini problem? Sounds like an interesting name for people who drink.

REPLY [8 votes]: The name was coined by Barry Simon in this 1982 article (page 487):

The Ten Martini Problem: The almost Mathieu operator has a Cantor spectrum.
The name comes from the fact that Mark Kac* has offered ten
  martinis to anyone who solves it.  [...] Actually, Kac said "has all
  its gaps there", so perhaps one should solve instead:
The Ten Martini Problem: (Strong Form, or should it be Dry Form)...
[*] Marc Kac, public communication at 1981 AMS Annual Meeting.