Some jokes are based on stereotypes of mathematicians tending to think in complicated, abstract terms, causing them to lose touch with the "real world".
Many of these jokes compare mathematicians to other professions, typically physicists, engineers, or the "soft" sciences in a form similar to those which begin "An Englishman, an Irishman and a Scotsman…" or the like. The joke generally shows the other scientist doing something practical, while the mathematician does something less useful such as making the necessary calculation but not performing the implied action.
Examples:
- A mathematician and his best friend, an engineer, attend a public lecture on geometry in thirteen-dimensional space. "How did you like it?" the mathematician wants to know after the talk. "My head's spinning," the engineer confesses. "How can you develop any intuition for thirteen-dimensional space?" "Well, it's not even difficult. All I do is visualize the situation in n-dimensional space and then set n = 13."
- A mathematician, a biologist and a physicist are sitting in a street café watching people entering and leaving the house on the other side of the street. First they see two people entering the house. Time passes. After a while they notice three people leaving the house. The physicist says, "The measurement wasn't accurate." The biologist says, "They must have reproduced." The mathematician says, "If one more person enters the house then it will be empty."
An example of a joke relying on mathematicians' propensity for not taking the implied action is as follows:
- A mathematician, an engineer and a chemist are at a conference. They are staying in adjoining rooms. One evening they are downstairs in the bar. The mathematician goes to bed first. The chemist goes next, followed a minute or two later by the engineer. The chemist notices that in the corridor outside their rooms a rubbish bin is ablaze. There is a bucket of water nearby. The chemist starts concocting a means of generating carbon dioxide in order to create a makeshift extinguisher but before he can do so the engineer arrives, dumps the water on the fire and puts it out. The next morning the chemist and engineer tell the mathematician about the fire. He admits he saw it. They ask him why he didn't put it out. He replies contemptuously "there was a fire and a bucket of water: a solution obviously existed."
Mathematicians are also shown as averse to making sweeping generalizations from a small amount of data, preferring instead to state only that which can be logically deduced from the given information – even if some form of generalization seems plausible:
- An astronomer, a physicist and a mathematician are on a train in Scotland. The astronomer looks out of the window, sees a black sheep standing in a field, and remarks, "How odd. Scottish sheep are black." "No, no, no!" says the physicist. "Only some Scottish sheep are black." The mathematician rolls his eyes at his companions' muddled thinking and says, "In Scotland, there is at least one field, containing at least one sheep, at least one side of which appears black from here."
A variant has the punchline "No," says the mathematician, "all we can say is that there is at least half of a black sheep in Scotland." Another variant with cows was featured in the book The Curious Incident of the Dog in the Night-time by Mark Haddon.
Pure mathematicians are mainly concerned with the properties of the abstract systems under study, not their actual applications. However, such applications are sometimes found in mathematics itself, resulting in new insights as old problems are cast in new light. In striving not to miss such connections, mathematicians often see problems in novel (but theoretically valid) ways, which unfortunately are not always as illuminating as one could wish for:
- A sociologist, a physicist and a mathematician are all given equal amounts of fencing, and are asked to enclose the greatest area. The sociologist pauses for a moment and decides to enclose a square area with his fence. The physicist, realizing he can fence off a greater amount of land with the same amount of fencing, promptly sets his fence in the form of a circle, and smiles. "I'd like to see you beat that!" he says to the mathematician. The mathematician, in response, takes a very small piece of his own fencing, and wraps it around himself, proclaiming, "I define my location to be outside of the fence!"
A small set of jokes involves only mathematicians, such as the following involving statisticians:
- Three statisticians go duck hunting. Their dog chases out a duck and it starts to fly. The first statistician aims and takes his shot, and it misses a foot too high. The second statistician aims and takes his shot, and it misses a foot too low. The third statistician says, "We got him!"
The humor there is derived from the fact that the average of the shots hits the duck, and so it is dead.
- An engineer and a physicist are in a hot-air balloon. After a few hours they lose track of where they are and descend to get directions. They yell to a jogger, "Hey, can you tell us where we're at?" After a few moments the jogger responds, "You're in a hot-air balloon." The engineer says, "You must be a mathematician." The jogger, shocked, responds, "yeah, how did you know I was a mathematician?" "Because, it took you far too long to come up with your answer, it was 100% correct, and it was completely useless."
