Engineers think that equations approximate the real world. Scientists think that the real world approximates equations. Mathematicians are unable to make the connection.

A Mathematician, a Biologist, and a Physicist are in a street cafe watching people going in and coming out of a house across the street. First they see two people go in. Time passes...After a while they notice three people come out of the house. The Physicist: "The measurement was not accurate." The Biologists: "They have reproduced." The Mathematician: "Now if exactly one person enters the house, it will be empty again." 
A priest, a lawyer and an engineer are about to be guillotined. The priest puts his head on the block, they pull the rope, and nothing happens. The priest declares that he has been saved by God's intervention, and is set free. The lawyer is next, he puts his head on the block; and the blade doesn't release for a second time. He declares that he cannot be executed twice for the same crime and is set free. The executioner grabs the engineer and shoves his head in the guillotine. The engineer looks up and says, "Wait a minute, I see a problem with the release mechanism..." 
An engineer, a physicist, and a mathematician are shown a pasture with a herd of sheep, and told to put the herd inside the smallest possible fence. The engineer goes first. He herds the sheep into a tight circle and then he puts a fence around them. "A circle will use the least amount of fence for a given area, so it is the best solution." The physicist is next. She creates a circular fence of infinite radius around the sheep and then draws the fence tightly around the herd, declaring, "This will give the smallest circular fence around the herd. The mathematician is last. He waits a few moments, giving it some thought. He finally puts a small fence around himself and declares, "I define myself to be on the outside!" 
A programmer, a mechanical engineer, and a manager were on their way to a meeting. They were driving down a steep winding mountain road with many switchbacks. Suddenly the brakes failed. The car ran off the road, bounced down the mountain, rolled over a few times, bumped through some rocks, and finally came to a stop a few feet from the road below. Fortunately no one was hurt just a bit shaken, but they had a problem. They were on a mountain with a car without brakes. "Let's have a meeting," said the manager. "We'll propose a Vision, formulate a Mission Statement, define our goals, and by a process of Continuous Mission Improvement Focusing on our Core Business, find a solution to this Critical Problem." "No no no," exclaimed the engineer. "That never solved anything. I've got two shirt hangers, half a roll of duct tape, a highway flare, and a Swiss Army knife. Give me a few minutes, and the brakes will be good enough to get us to the nearest gas station." "Wait," said the programmer. "Before we do anything, I think we should push the car back up the road and see if it happens again."

Nun goes to see mother superior to say she's pregnant. "How can that be - have you ever been with a man?" "Well, there was only the bishop. He showed me something and said it was 'The Key to the Gates of Heaven', and that if he put it in my keyhole it would open the gates to the hereafter" "The bastard" said the mother superior "He told me it was Archangel Gabriel's horn, and I've been blowing it for 5 years."