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• How many analysts does it take to change a light bulb?
• Three. One to prove existence, one to prove uniqueness and one to derive a nonconstructive algorithm to do it.

"Once when lecturing in class he [Lord Kelvin] used the word 'mathematician' and then interrupting himself asked his class: 'Do you know what a mathematician is?' Stepping to his blackboard he wrote upon it: integral from - infinty to + infinity of exp(-x^2)dx = sqrt(pi). Then putting his finger on what he had written, he turned to his class and said, 'a mathematician is one to whom *that* is as obvious as that twice two makes four is to you.'"

--S. P. Thompson, Life of Lord Kelvin

—Peter Winch, 1968

The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

Two math professors are in a restaurant. One argues that the average person does not know any math beyond high school. The other argues that the average person knows some more advanced math.

Just then, the first one gets up to use the rest room. The second professor calls over his waitress and says:

"When you bring our food, I'm going to ask you a mathematical question. I want you to answer, 'One third x cubed.' Can you do that?"
The waitress says, "I don't know if I can remember that. One thurr... um..."
"One third x cubed," says the prof.
"One thir dex cue?," asks the waitress.
"One"
"One"
"Third"
"Third"
"X"
"X"
"Cubed"
"Cubed"
"One third X cubed"
"One third X cubed"
The waitress leaves, and the other professor comes back. They resume their conversation until a few minutes later when the waitress brings their food. The professor says to the waitress,

"Say, do you mind if I ask you something?"
"Not at all"
"Can you tell me what the integral of x squared dx is?"
The waitress pauses, then says, "One third x cubed."
As she walks away, she stops, turns, and adds, "Plus a constant!"

“[P]hilosophy can no more show a man what he should attach importance to than geometry can show a man where he should stand.”

—Peter Winch, 1968