A mathematician and a physicist were arguing over whose field of study was better.
They decided to settle the argument by posing questions. The mathematician went first, and posed a complicated mathematical problem. With a great deal of effort, several books of mathematical tables and techniques, and a few hours, the physicist gave the solved problem to the mathematician, who was duly impressed.
“All right, my turn. Here’s the problem: you have a pot of water on the stove, at 60 F. You want to heat it up to 70 F. What do you do?”
The mathematician replied, “Oh, that’s easy. You turn the stove on. Fourier’s equations govern how heat transfers from the stove to the pot, and you can solve them numerically to find out how long it takes for the water to reach 70 F.”
The physicist then asks, “All right, so what if the water is at 65 F?”
“Oh, that’s even easier. You take the pot of water, stick it in the refrigerator until it cools down to 60 F, and then it simplifies to the previous problem!”
Tommy was sitting in math class when suddenly his teacher asked him
“Tommy, How much is 2 + 2?”
Tommy, caught off guard, begins counting his fingers under the table mumbling to himself: “1…2…3…4,” before happily exclaiming “The answer is four!”
“That’s correct,” answered his teacher, “but I saw you counting your fingers instead of doing the math in your head. So I want you to put your hands behind your back and tell me what do you get if you add 3 + 3?”
Tommy put his hands behind his back, but his teacher saw that he was still moving uncomfortably as if he were trying to count fingers. After a few moments he said uncertainly, “is the answer six?”
“You are correct,” she replied, “but I see you’re still counting fingers despite me asking you not to! Put your hands in your pant pockets and tell me what you get if you add 5 + 5.”
Tommy put his hands in his pants and his teacher saw him looking at his pants and moving his lips without uttering a word.
Finally the teacher became impatient and said: “I see what you’re doing there and I can tell you right now that the answer is not eleven!“
