Fermat's Last Theorem
(This article draws on the excellent paperback, Fermat's Enigma" by Simon Singh.)
I begin with a riddle:

Three Navajo women sit side by side on the ground. The first woman, who is sitting on a buffalo skin, has a son who weighs 70 pounds. The second woman, who is sitting on a deer skin, has a son who weighs 80 pounds. The third woman who weighs 150 pounds is sitting on a hippopotamus skin.
The moral: the squaw of the hippopotamus is equal to the sons of the squaws of the other two hides.

If you were paying attention in the 8th grade, you know that the square of the hypotenuse equals the sum of the squares of the other two sides. Z^2=x^2 +y^2

Fermat's Last Theorem states that for z^n=x^n +y^n, there are no whole number solutions for n>2. He wrote in the margin of his copy of Diophantus' "Arithmetica" , originally published around 300 AD, 6 of the original volumes survived the Dark Ages; Fermat was using a French translation published in 1621.

He made a marginal note, circa 1637, when he was 36: "I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain." Fermat was known among mathematicians as a tease. At least one of his puzzlers was proven wrong. For those striving for cultural awareness, not mere dilettantes, his full name is Pierre de Fermat, the de denoting royalty not widowhood.

There are an infinite number of solutions for the case n=2, e.g. 3, 4, 5 and 5, 12, 13. You can generate your own by selecting any two whole numbers p and q, where p> q. p^2+q^2, p^2 q^2, and 2pq are Pythagorean triples.

Let's do some cubing. Try 7, 6, and 5. 7 cubed is 49x7=343. 6 cubed is 216 and 5 cubed is 125, which total 341, not 343. Come on, you say, isn't that close enough, an error of less than 1%. NO.

Infinity is a mathematical term meaning for a set which is equivalent to a proper subset of itself. The even numbers are a proper subset of the natural numbers. Infinity is not all the grains of sand at all the beaches in the world, not all the hydrogen atoms in all the world's water molecules, not how many times I've told you to clean up your room. Computers have confirmed Fermat's theorem for all n up to 4 million. Nothing in this world is infinite. The word you should use is googol, a 1 followed by 100 zeros .The founders of Google are good at sorting, not at spelling. Their corporate headquarters is known however, as the Googolplex, which is 10 raised to the googol power

• 1
• 2
• next page >>

---

Add your voice

Know something about Fermat's last theorem?
We want to hear your view. Write now!