Q: How do you tell an engineer, a physicist, and a mathematician apart?
A: Put them, one at a time, in a room with an empty bucket on a table, a sink, a stove, and curtains behind the stove which have caught fire.
- The engineer will run to the table, grab the bucket, fill it with water, throw the water on the flames, douse the fire, and leave a mess.
- The physicist will do some rough order of magnitude calculations, fill the bucket one third of the way up with water, throw the water on the fire, douse the flames, and think himself clever for solving what would have been a messy problem elegantly.
- The mathematician will walk in the room, observe the fire, observe the bucket and the sink, and comment, "The solution is trivial," then walk out, leaving the proof as an exercise to the student.
Q: If you are still not sure, how can you tell them apart?
A: Place them each, one at a time, in a room with a bucket filled with water on a table, a sink, a stove, and curtains behind the stove which have caught fire.
- The engineer will douse the fire with the water in the bucket, leaving a mess.
- The physicist will do some calculations, throw 1/3 of the water on the flames, and douse the fire.
- The mathematician will empty the water from the bucket into the sink, place the bucket back on the table, then announce, "The problem is now reduced to one previously solved."
Was the fire Gas or grease or electric? the solution will depend upon the initial source, unless just putting out the flames on the curtains is the goal.
I do agree with the comment about the Mathematician and it is trival and let the student prove it.