To tell a difference between a mathematician and an engineer, perform
this experiment. Put an empty kettle in the middle of the kitchen
floor and tell your subjects to boil some water.

The engineer will fill the kettle with water, put it on the stove, and
turn the flame on. The mathematician will do the same thing.

Next, put the kettle already filled with water on the stove, and ask
the subjects to boil the water. The engineer will turn the flame on.
The mathematician will empty the kettle and put it in the middle of
the kitchen floor... thereby reducing the problem to one that has
already been solved!