One plus one are two

Theorem: 1 + 1 = 2
Proof:
n(2n - 2) = n(2n - 2)
n(2n - 2) - n(2n - 2) = 0
(n - n)(2n - 2) = 0
2n(n - n) - 2(n - n) = 0
2n - 2 = 0
2n = 2
n + n = 2
or setting n = 1
1 + 1 = 2




Debate about the box
An engineer, a physicist, and a mathematician are trying to set up a fenced-in area for some sheep, but they have a limited amount of building material. The engineer gets up first and makes a square fence with the material, reasoning that it's a pretty good working solution. "No no," says the physicist, "there's a better way." He takes the fence and makes a circular pen, showing how it encompasses the maximum possible space with the given material.

Then the mathematician speaks up: "No, no, there's an even better way." To the others' amusement he proceeds to construct a little tiny fence around himself, then declares:

"I define myself to be on the outside."




Risk of plane bombs

A mathematician and a non-mathematician are sitting in an airport hall waiting for their flight to go. The non has terrible flight panic.

"Hey, don't worry, it's just every 10000th flight that crashes."

"1:10000? So much? Then it surely will be mine!"

"Well, there is an easy way out. Simply take the next plane. It's much more probable that you go from a crashing to a non-crashing plane than the other way round. So you are already at 1:10000 squared."




Two plus two is five

"First and above all he was a logician. At least thirty-five years of the half-century or so of his existence had been devoted exclusively to proving that two and two always equal four, except in unusual cases, where they equal three or five, as the case may be." -- Jacques Futrelle, "The Problem of Cell 13"

Most mathematicians are familiar with -- or have at least seen references in the literature to -- the equation 2 + 2 = 4. However, the less well known equation 2 + 2 = 5 also has a rich, complex history behind it. Like any other complex quantitiy, this history has a real part and an imaginary part; we shall deal exclusively with the latter here.

Many cultures, in their early mathematical development, discovered the equation 2 + 2 = 5. For example, consider the Bolb tribe, descended from the Incas of South America. The Bolbs counted by tying knots in ropes. They quickly realized that when a 2-knot rope is put together with another 2-knot rope, a 5-knot rope results.

Recent findings indicate that the Pythagorean Brotherhood discovered a proof that 2 + 2 = 5, but the proof never got written up. Contrary to what one might expect, the proof's nonappearance was not caused by a cover-up such as the Pythagoreans attempted with the irrationality of the square root of two. Rather, they simply could not pay for the necessary scribe service. They had lost their grant money due to the protests of an oxen-rights activist who objected to the Brotherhood's method of celebrating the discovery of theorems. Thus it was that only the equation 2 + 2 = 4 was used in Euclid's "Elements," and nothing more was heard of 2 + 2 = 5 for several centuries.

Around A.D. 1200 Leonardo of Pisa (Fibonacci) discovered that a few weeks after putting 2 male rabbits plus 2 female rabbits in the same cage, he ended up with considerably more than 4 rabbits. Fearing that too strong a challenge to the value 4 given in Euclid would meet with opposition, Leonardo conservatively stated, "2 + 2 is more like 5 than 4." Even this cautious rendition of his data was roundly condemned and earned Leonardo the nickname "Blockhead." By the way, his practice of underestimating the number of rabbits persisted; his celebrated model of rabbit populations had each birth consisting of only two babies, a gross underestimate if ever there was one.

Some 400 years later, the thread was picked up once more, this time by the French mathematicians. Descartes announced, "I think 2 + 2 = 5; therefore it does." However, others objected t