Already Solved

One day a mathematician decides that he is sick of math. So, he walks down to
the fire department and announces that he wants to become a fireman.
The fire chief says, "Well, you look like a good guy. I'd be glad to hire you,
but first I have to give you a little test."
The fire chief takes the mathematician to the alley behind the fire department
which contains a dumpster, a spigot, and a hose. The chief then says, "OK,
you're walking in the alley and you see the dumpster here is on fire. What do
you do?"
The mathematician replies, "Well, I hook up the hose to the spigot, turn the
water on, and put out the fire."
The chief says, "That's great... perfect. Now I have to ask you just one more
question. What do you do if you're walking down the alley and you see the
dumpster is not on fire?"
The mathematician puzzles over the question for a while and he finally says,
"I light the dumpster on fire."
The chief yells, "What? That's horrible! Why would you light the dumpster on
fire?"
The mathematician replies, "Well, that way I reduce the problem to one I've
already solved."