Diophantus
# Diophantus of Alexandria

### Born: about 200
in Alexandria, Egypt

Died: about 284
in Alexandria, Egypt

**Diophantus** worked during the middle of the 3rd century and is best known for his Arithmetica , a work on the theory of numbers.

Little is known of Diophantus's life. The most details we have (and these may not be accurate) say that he married at the age of 33 and had a son who died at the age of 42, 4 years before Diophantus himself died aged 84. Based on this information we have given him a life span of 84 years despite having no more than a very rough guide to the dates of his birth and death.
The Arithmetica is a collection of 130 problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations. The method for solving the latter is now known as Diophantine analysis. Only 6 of the original 13 books survive and the others must have been lost quite soon after they were written since there are many Arabic translations, for example by Abu'l-Wafa, but they only contain material from these 6 books. The most famous Latin translation is due to Bachet.

Diophantus was always satisfied with a rational solution and did not require a whole number. He did not deal in negative solutions and one solution was all he required to a quadratic equation. In fact most of the Arithmetica problems lead to quadratic equations.

Although he did not use sophisticated algebraic notation, he did introduce an algebraic symbolism that used an abbreviation for the unknown.

Fragments of another of Diophantus' books on polygonal numbers has survived and Diophantus himself refers to a collection of theorems called The Porisms but this book is entirely lost.

**References (20 books/articles)**

**Some pages from works by Diophantus:**

The title page from the translation by Bachet of *Arithmetica* (1670)

and another page showing the transcription of Fermat's marginal note

**References elsewhere in this archive:**

A curious fact about Diophantus's Arithmetica

There is a **Crater Diophantus** on the moon. There is also a **Rima Diophantus**. You can see a list of lunar features named after mathematicians.

**Other Web sites:**

University of Virginia, USA

JOC/EFR December 1996