Let a and b each be equal to 1. Since a and b are equal,

*b ^{2}=ab *(eq.1)

Since a equals itself, it is obvious that

*a ^{2}= a^{2 }*(eq.2)

Subtract equation1 from equation 2. This yields

*a ^{2}– b^{2}= a^{2}-ab *(eq.3)

We can factor both sides of the equation; a^{2}-ab equals a(a-b). Likewise, a^{2}– b^{2} equals (a+b)(a-b). (Nothing fishy is going on here. The statement is perfectly true. Plug in mubers and see for yourself!) Substituting into equation 3, we get

*(a+b)(a-b)=a(a-b) *(eq.4)

So far, so good. Now divide both sides of the equation by (a-b) and we get

*a+b=a *(eq.5)

Subtract a from both sides and we get

*b=0 *(eq.6)

But we set b to 1 at the very beginning of this proof, so this means that

*1=0 *(eq.7)

This is an important result. Going further, we know that Winston Churchill has one head. But one equals zero by equation 7, so that means that Winston has no head. Likewise, Churchill has zero leafy tops, therefore he has one leafy top. Multiplying both sides of equation 7 by 2, we see that

*2=0 *(eq.8)

Churchill has two legs, therefore he has no legs. Churchill has two arms, therefore he has no arms. Now multiply equation 7 by Winston Churchill’s waist size in inches. This means that

*(Winston’s waist size)=0 *(eq.9)

This means that Winston Churchill tapers to a point. Now what colour is Winston Churchill? Take any beam of light that comes from him and select a photon. Multiply equation 7 by the wavelength, and we see that

*(Winston’s photon’s wavelength)=0* (eq.10)

But multiplying equation 7 by 640 nanometers, we see that

*640=0 *(eq.11)

Combining equations 10 and 11, we see that

*(Winston’s photon’s wavelength)= 640 nanometers*

This means that this photon – or any other photon that comes from Mr Churchill – is orange. Therefore, Winston Churchill is a bright shade of orange.

To sum up, we have proved, mathematically, that Winston Churchill has no arms and no legs; instead of a head, he has a leafy top; he tapers to a point; and he is bright orange. Clearly, Winston Churchill is a carrot. (There is a simpler way to prove this. Adding 1 to both sides of equation 7 gives the equation

*2=1*

(Winston Churchill and a carrot are two different things, therefore they are one thing. But that’s not nearly as satisfying.)

What is wrong with this proof? There is only one step that is flawed, and that is the one where we go from equation 4 to equation 5. We divide by a-b. But look out. Since a and b are both equal to 1, a-b=1-1=0.

We have divided by zero, and we get the ridiculous statement that 1=0. From there we can prove any statement in the universe, whether it is true or false. The whole framework of mathematics has exploded in our faces.

Used unwisely, zero has the power to destroy logic.

*From “Zero: The biography of a dangerous idea”; Charles Seife.*