This thread seems to have a remarkable deficiency of "Mathematician, Physicist, and Engineer" jokes. I guess I'll have to fix that.
A mathematician, a physicist, and and engineer are attending a convention together, and decide to share a hotel room to split the cost. After a long day, the three of them get back to their room and all promptly fall asleep.
Around midnight, a fire breaks out in the wastebasket. The physicist wakes up, looks at the fire, and says "Problem exists." He then promptly falls back asleep.
Next the mathematician wakes up. He looks at the fire, and says "Problem exists." He looks around and sees a bucket in the corner, and the faucet in the bathroom. He says "Solution exists." and goes back to sleep.
A minute later, the engineer wakes up, fills the bucket from the faucet, puts out the fire, and then goes back to bed.
A mathematician, a physicist, and an engineer are riding a train through Scotland, when they see a black sheep through the window.
"Look, the sheep in Scotland are black!" says the engineer.
"You mean, ONE sheep in Scotland is black" corrects the physicist.
The mathematician cuts in, "No, no, no. All we can say with certainty is that in Scotland, there exists at least one sheep, at least one SIDE of which is black."
A psychologist decides to perform a study on the differences in how various professionals think. She recruits a mathematician (a topologist, to be precise), a physicist, and an engineer for her study, and locks each one in a room with one can of food, but no can opener. The next day, she comes around and checks each of the rooms to see how its occupant is doing.
First, she checks on the engineer. The walls of his room are covered with dents, and he is happily scraping the last of the food from the can. When questioned, he explained, "I'm a materials guy. I knew the material of the can wouldn't hold up to repeated stress, so I threw it against the wall until it broke open."
The psychologist then goes to the physicist's room. Equations are scribbled all over the walls, there is a single enormous dent in one wall, and the physicist is happily scraping the last of the food from his can. He explains, "I computed the optimal angle and velocity for the can to break upon collision with the wall. I then threw the can at the wall in such a was as to achieve those, and broke it open."
Finally, she goes to the mathematician's room. There are equations scribbled over every bit of the walls. The can is sitting in the middle of the room, unopened. The mathematician is nowhere to be seen. However, there are some strange noises coming from inside the can. So the psychologist gets her can opener and opens the can. The mathematician crawls out, looks around at his equations on the walls, and says,
"Hmmm... I must have gotten a sign wrong somewhere."