The Prototype:

How many Californians does it take to replace a lightbulb (1)?
Six: one to replace the bulb and five to share in the life experience.

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How many mathematicians does it take to replace a lightbulb (1)?
Ten: One to do it and eight to watch.

How many mathematicians does it take to replace a lightbulb (2)?
One: He gives it to six Californians, thereby solves the problem by
reducing it to a previous joke.

How many mathematicians does it take to replace a lightbulb (3)?
The answer is intuitively obvious.

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 change 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 functions does it take to replace a lightbulb?
The integral of f: But that's not definite.

How many real functions does it take to replace a lightbulb: None: It's too
complex for them.

How many Bourbakists does it take to replace a lightbulb:
Changing a lightbulb is a special case of a more general theorem concerning
the maintainence 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 maths department administrators does it take to replace a
lightbulb?
None: What was wrong with the old one then???

How many Dick Askeys does it take to replace a lightbulb?
Six: One (Dick Askey) to check if Ramanujan had already done it. One (Dick
Askey) to understand Ramanujan's proof. One (Dick Askey) to check if the
proof already appears in the letters between Stieltjes and Hermite. One
(Dick Askey) to consult the Norwegian literature. One (Liz Askey) to
replace the lightbulb. One (Dick Askey) to have a satisfying nap after all
this toil.

How many IMA types does it take to replace a lightbulb?
None: They are incapable of replacing a lightbulb, but they charge �1000
for it.
[This of course refers to the British IMA, not to the Minnesota one which
(1) doesn't overcharge; and (2) does it in dollars.]