An engineer, physicist, and mathematician are all challenged with a problem: to fry an egg when there is a fire in the house.
The engineer just grabs a huge bucket of water, runs over to the fire, and puts it out.
The physicist thinks for a long while, and then measures a precise amount of water into a container. He takes it over to the fire, pours it on, and with the last drop the fire goes out.
The mathematician pores over pencil and paper. After a few minutes he goes "Aha! A solution exists!" and goes back to frying the egg.
Sequel: This time they are asked simply to fry an egg (no fire).
The engineer just does it, kludging along;
the physicist calculates carefully and produces a carefully cooked egg;
and the mathematician lights a fire in the corner, and says "I have reduced it to the previous problem."