Diophantus’ Arithmetica

Almost nothing is known of Diophantus’ life. He quotes Hypsicles, of the 2nd century BC, and is quoted by Theon of Alexandria in the 4th century AD; a link with Anatolius, an Alexandrian scholar who later became bishop of Laodicea, places him in the 3rd century, and he is usually said to have flourished around 250. A riddle in the Greek Anthology, if it can be trusted, says that he lived to the age of 84.

The Arithmetica is a collection of about 290 problems, most of them asking for numbers that satisfy given conditions; Diophantus sought positive rational solutions, often of equations with more than one unknown. Instead of writing every step out in words he used abbreviations for the unknown, its powers and some operations — the so-called syncopated notation, halfway between verbal and symbolic algebra. Six of the thirteen books survive in Greek, and four more were found in 1968 in an Arabic translation attributed to Qusta ibn Luqa.

Through Arabic mathematics and then Renaissance Europe the work shaped the development of algebra and number theory; Diophantus has been called the father of algebra, although he built on older methods. In his copy of Bachet’s Latin edition of 1621, Pierre de Fermat noted beside one of its problems that he had a marvellous proof which the margin was too narrow to contain — the conjecture known as Fermat’s Last Theorem, proved by Andrew Wiles only in 1994.