Here are my favorites!

A Mathematician, a Biologist and a Physicist are sitting in a street cafe watching people going in and coming out of the house on the other side of the street.
First they see two people going into the house. Time passes. After a while they notice three persons coming out of the house.
The Physicist: "The measurement wasn't accurate.”
The Biologists conclusion: "They have reproduced."
The Mathematician: "If now exactly one person enters the house then it will be empty again."

An engineer, a physicist, and a mathematician were on a train heading north, and had just crossed the border into Scotland.
The engineer looked out of the window and said "Look! Scottish sheep are black!"
The physicist said, "No, no. Some Scottish sheep are black."
The mathematician looked irritated. "There is at least one field, containing at least one sheep, of which at least one side is black."

An engineer, a chemist and a mathematician are staying in three adjoining cabins at an old motel. First the engineer's coffee maker catches fire. He smells the smoke, wakes up, unplugs the coffee maker, throws it out the window, and goes back to sleep.
Later that night the chemist smells smoke too. He wakes up and sees that a cigarette butt has set the trash can on fire. He says to himself, "Hmm. How does one put out a fire? One can reduce the temperature of the fuel below the flash point; isolate the burning material from oxygen, or both. This could be accomplished by applying water." So he picks up the trash can, puts it in the shower stall, turns on the water, and, when the fire is out, goes back to sleep.
The mathematician, of course, has been watching all this out the window. So later, when he finds that his pipe ashes have set the bed sheet on fire, he is not in the least taken aback. He says: "Aha! A solution exists!" and goes back to sleep.

Aleph-null bottles of beer on the wall,
Aleph-null bottles of beer,
You take one down, and pass it around,
Aleph-null bottles of beer on the wall.

An engineer, a physicist, and a mathematician are shown a pasture with a herd of sheep, and told to put them inside the smallest possible amount of fence.
The engineer is first. He herds the sheep into a circle and then puts the fence around them, declaring, "A circle will use the least fence for a given area, so this is the best solution."
The physicist is next. He straightens the fence, declares it to be endless, and thus encircles half the globe.
The mathematician is last. After giving the problem a little thought, he puts a small fence around himself and then declares, "I define myself to be on the outside."

I remember that one from Caltech, and I still never get tired of sharing it with those of my comrades who are smart enough to get it, but I think that it's funnier in its original version, where it's a *chemist* who is so unscientific as to jump to the initial broad conclusion.

Kindly note that I correctly punctuated both my itses above. No one punctuates like a mathematician!!

--jonathan