Tuesday, May 03, 2005

Diophantus of Alexandria

When Fermat made his famous note in the margin, he was making a comment on a problem from Diophantus of Alexandria. While Fermat is today considered the father of number theory, he would probably have given this title to Diophantus.

Not much is known about Diophantus's life. He was a Hellenized Babylonian who lived in Alexandria, Egypt. He was born around 200 AD and he died around 284 AD.

His classic work is the Arithmetica which consists of 130 problems in 13 books. Today, only 6 of the books survive. It was written around 240 AD.

He focused on problems that have a positive rational number as a solution (a rational number is any fraction made from two whole numbers). He considered negative numbers and irrational numbers to be "useless," "meaningless," and "absurd."

When he spoke about quadratic equations, he only offered one solution. It is not clear if he knew that all quadratic equations have two solutions.

Diophantus is considered to be the father of algebra. Diophantine equations are named after him.

Much of what we know about him comes from the words written on his tombstone, which is itself an algebra problem for determining his age:

This tomb hold Diophantus. Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father's life, the chill grave took him. After consoling his grief by this science of numbers forfour years, he reached the end of his life.
This blog is based on the following sources: