Why is the problem called the ten martini problem? Sounds like an interesting name for people who drink.
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6$\begingroup$ Here Terry Tao says it is because Kac offered ten martinis for the solution: terrytao.wordpress.com/2014/08/12/… $\endgroup$– Sam HopkinsCommented Aug 14, 2014 at 5:01
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2$\begingroup$ Kac probably got the idea from participating in mathematicians' discussions in the famous Scottish Cafe when he was a student, and then a young researcher in Lwow before 1939. Quite often, a prize for solving a problem was a drink. See e.g. Problem 8 here: kielich.amu.edu.pl/Stefan_Banach/pdf/ks-szkocka/… $\endgroup$– Margaret FriedlandCommented Aug 14, 2014 at 15:29
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$\begingroup$ @MargaretFriedland --- very interesting! here's a photograph of the Scottish Book: en.wikipedia.org/wiki/Scottish_Book $\endgroup$– Carlo BeenakkerCommented Aug 14, 2014 at 18:01
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$\begingroup$ @Carlo-- the link I gave is to the typewritten English translation of the Scottish book. The portal has also complete reproductions of the Polish handwritten original and its typed version. $\endgroup$– Margaret FriedlandCommented Aug 14, 2014 at 18:29
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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.
answered Aug 14, 2014 at 7:10