Q: How many mathematicians does it take to screw in a light bulb?
A1: None. It's left to the reader as an exercise.
A2: None. A mathematician can't screw in a light bulb, but he can easily prove the work can be done.
A3: One. He gives it to four programmers, thereby reducing the problem to the already solved (ask a programmer, how)
A4: The answer is intuitively obvious
A5: Just one, once you've managed to present the problem in terms he/she is familiar with.
A6: In earlier work, Wiener [1] has shown that one mathematician can change a light bulb.
If k mathematicians can change a light bulb, and if one more simply watches them do it, then k+1 mathematicians will have changed the light bulb.
Therefore, by induction, for all n in the positive integers, n mathematicians can change a light bulb.