AN ENGINEER, a physicist and a mathematician are staying in a hotel. In the middle of the night, the engineer wakes up and smells smoke. He goes out into the hallway and sees a fire burning, so he grabs a rubbish bin from his room, fills it with water and tips the water on the fire to put it out. Then he goes back to bed.
Later, the physicist wakes up and smells smoke.
Opening his door, he sees a fire burning in the hallway. But at the other end of the hall he spots a firehose, so after calculating the distance from the hose to the fire, the intensity of the flames, the water pressure and trajectory, he extinguishes the fire with the hose using the minimum possible amount of water and energy expenditure.
Still later that evening, the mathematician wakes up and smells smoke. He goes out into the hall, sees a fire and a firehose, thinks for a few moments, and declares: “Aha, there is a solution.” Then he goes back to bed.