Three mathematicians and three physicists are taking the train to go to a conference. The three physicist are first in the ticket line and buy three tickets; the mathematicians buy just one. The physicists ask: “What are you doing? The conductor is going to see that you only have one ticket and will surely throw two of you off the train.” The mathematicians reply, “don’t worry, we have a proven method.”
The train departs and the physicists take their seats, but do so strategically so as to observe the mathematicians’ method. They watch the mathematicians crowd into a single bathroom stall. When the conductor comes buy and knocks, the door is opened partway, a hand reaches out with a ticket, the conductor takes the ticket and all safely reach their destination.
On the way back from the conference, the physicist are again first in the ticket line, but this time they buy one ticket. The mathematicians buy none. The physicists ask: “What are you doing? Surely this way the conductor is going to throw all of you off the train.’ The mathematicians reply, “don’t worry, we have a proven method.”
When the train departs, the physicists and mathematicians crowd into separate bathroom stalls. Shortly before the conductor comes by, one of the mathematicians runs over the to the physicists’ stall and knocks. The door is opened partway, a hand with a ticket reaches out, the mathematician takes the ticket and returns to his stall.
Moral: if you are going to use mathematics, understand the method.