The Hotel Fire
An engineer, a mathematician, and a physicist are staying for the night in a hotel. Fortunately for this joke, a small fire breaks out in each room.
The physicist awakes, sees the fire, makes some careful observations, and on the back of the hotel's wine list does some quick calculations. Grabbing the fire extinguisher, he puts out the fire with one, short, well placed burst, and then crawls back into bed and goes back to sleep.
The engineer awakes, sees the fire, makes some careful observations, and on the back of the hotel's room service list (pizza menu) does some quick calculations. Grabbing the fire extinguisher (and adding a factor of safety of 5), he puts out the fire by hosing down the entire room several times over, and then crawls into his soggy bed and goes back to sleep.
The mathematician awakes, sees the fire, makes some careful observations, and on a blackboard installed in the room, does some quick calculations. Jubliant, he exclaims "A solution exists!", and crawls into his dry bed and goes back to sleep.
......
The Farmer's Fence
Mathematician, Physicist, Engineer walking through a field come upon a farmer.
The farmer asks what is the best way to construct a fence that will contain his livestock (ie., most area for least perimeter). The physicist does some calculus and concludes that the best way to do this is a square fence. The engineer looks at him and laughs. "No, the best way is a circle". The physicist concedes and they start building the fence.
The mathematician just sits there for a while and eventually stands up, puts a small piece around himself and says "I declare myself to be outside".