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A physicist represents the scientific link between the operational perspective of an engineer and the theoretical inclination of the mathematician. This is illustrated by the following story (which makes fun of mathematicians, if not all three) that I have heard for as long as I have been in mathematics.
An engineer, a physicist, and a mathematician each notices (in separate places) a fire.
The engineer immediately runs a large bucket of water and pours it on the fire extinguishing it completely.
The physicist examines the fire, does some calculations, measures a precise amount of water, and pours it on the fire extinguishing it without a drop to spare.
The mathematician looks at the fire and says, "There exists a solution." and walks on.
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