Diophantus
Diophantus of Alexandria (
Greek: circa
200/
214 – circa
284/
298) was a
Hellenistic mathematician. Little is known of his life except that he lived in
Alexandria,
Egypt and worked in the
Greek tradition of mathematics, principally on arithmetic and number theory.
He was known for his study of
equations with
variables which take on
rational values and these
Diophantine equations are named after him. Diophantus is sometimes known as the "father of
Algebra" perhaps because his unusual syncopated notation seems reminiscent of the fully symbolic algebra that
al-Khwarizmi would develop much later. His most famous work is the
Arithmetica — originally thirteen Greek books, of which only six survive today in extant Greek manuscripts. Some Diophantine problems from these books have been found in Arabic sources. An additional four books of the
Arithmetica, apparently from the lost Greek books, have been discovered in an Arabic manuscript in 1968. Diophantus also wrote a treatise on
polygonal numbers, of which part survives.
The
editio princeps of Diophantus was published in 1575 by
Xylander, and editions of
Arithmetica exerted a profound influence on the development of algebra in Europe in the late sixteenth and through the seventeenth and eighteenth centuries.
|
Problem II.8 in the Arithmetica (edition of 1670), annotated with Fermat's comment which became Fermat's last theorem. |
In
1637, while reviewing his copy of Diophantus'
Arithmetica Pierre de Fermat wrote his famous "
Last Theorem" in the margins of his copy of
Bachet's 1621 edition of the
Arithmetica. Although this original copy is lost today, Fermat's son edited the next edition of Diophantus, published in 1670. Although the text is otherwise inferior to the 1621 edition, Fermat's annotations - were printed in this version. Fermat was not the first mathematician so moved to write: in his own marginal notes (
scholia) to Diophantus on the same problem (II.8), the Byzantine mathematician
Maximus Planudes had written "Thy soul, Diophantus, be with Satan because of the difficulty of your other theorems, and of this one in particular".
Little is known about life of Diophantus. Some biographical information can be computed from a 5th and 6th century math puzzle involving Diophantus' age and styled as his epitaph (see links below).
"This tomb holds 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 for four years, he reached the end of his life."
*
*A. Allard, "Les scolies aux arithmétiques de Diophante d'Alexandrie dans le Matritensis Bibl. Nat. 4678 et les Vaticani gr. 191 et 304,"
Byzantion 53. Brussels, 1983: 682-710.
*P. Ver Eecke,
Diophante d'Alexandrie: Les Six Livres Arithmétiques et le Livre des Nombres Polygones, Bruges: Desclée, De Brouwer, 1926.
*T. L. Heath,
Diophantos of Alexandria: A Study in the History of Greek Algebra, Cambridge: Cambridge University Press, 1885, 1910.
*D. C. Robinson and Luke Hodgkin.
History of Mathematics,
King's College London, 2003.
*P. L. Tannery,
Diophanti Alexandrini Opera omnia: cum Graecis commentariis, Lipsiae: In aedibus B.G. Teubneri, 1893-1895.
*Jacques Sesiano,
Books IV to VII of Diophantus' Arithmetica in the Arabic translation attributed to Qusṭā ibn Lūqā, Heidelberg: Springer-Verlag,
1982. ISBN 0387906908.
