The light bulb problem
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  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.
 Weiner, Matthew P,...
How many mathematical logicians does it take to replace a lightbulb??
None: They can't do it, but they can prove that it can be done.
How many numerical analysts does it take to replace a lightbulb??
3.9967: (after six iterations).
How many classical geometers does it take to replace a lightbulb??
None: You can't do it with a straight edge and a compass.
How many constructivist mathematicians does it take to replace a lightbulb??
None: They do not believe in infinitesimal rotations.
How many simulationists does it take to replace a lightbulb??
Infinity: Each one builds a fully validated model, but the light actually never goes on.
How many topologists does it take to screw in a lightbulb??
Just one. But what will you do with the doughnut?
How many analysts does it take to screw in a lightbulb??
Three: One to prove existence, one to prove uniqueness and one to derive a nonconstructive algorithm to do it.
How many Bourbakists does it take to replace a lightbulb: ?
Changing a lightbulb is a special case of a more general theorem concerning the maintain and repair of an electrical system. To establish upper and lower bounds for the number of personnel required, we must determine whether the sufficient conditions of Lemma 2.1 (Availability of personnel) and those of Corollary 2.3.55 (Motivation of personnel) apply. Iff these conditions are met, we derive the result by an application of the theorems in Section 3.1123. The resulting upper bound is, of course, a result in an abstract measure space, in the weak-* topology.
How many professors does it take to replace a lightbulb??
One: With eight research students, two programmers, three post-docs and a secretary to help him.
How many university lecturers does it take to replace a lightbulb??
Four: One to do it and three to co-author the paper.
How many graduate students does it take to replace a lightbulb??
Only one: But it takes nine years.
How many math department administrators does it take to replace a lightbulb?
None: What was wrong with the old one then???