An engineer is working at his desk in his office. His cigarette falls off the desk into the wastebasket, causing the papers within to burst into flames. The engineer looks around, sees a fire extinguisher, grabs it, puts out the flames, and goes back to work.

A physicist is working at his desk in another office and the same thing happens. He looks at the fire, looks at the fire extinguisher, and thinks “Fire requires fuel plus oxygen plus heat. The fire extinguisher will remove both the oxygen and the heat in the wastebasket. Ergo, no fire.” He grabs the extinguisher, puts out the flames, and goes back to work.

A mathematician is working at his desk in another office and the same thing happens. He looks at the fire, looks at the fire extinguisher, and thinks for a minute, says “Ah! A solution exists!” and goes back to work.