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Diophantos of Alexandria

Diophantos of Alexandria

 

 

Diophantus, often known as the 'father of algebra', is best known for his publication “Arithmetica”, a work on the solution of algebraic equations and on the theory of numbers.

It is the oldest known publication to focus on algebra. It contains 13 books consisting of 130 problems giving numerical solutions to determinate equations (with unique solutions) and indeterminate equations. His used method became known as Diophantine analysis.

 

Only 6 of originally 13 books have survived and scholars who have studied his work came to the conclusion that Diophantos was always satisfied with rational numbers not requiring a whole number. He did not deal with negative solutions and only required one solution to a quadratic equation, which was what most of the Arithmetica problems led to. Brahmagupta was the first to give the general solution of the linear Diophantine equation:

 

ax + by = c

 

In his publication he did not use sophisticated algebraic notation but he introduced an algebraic symbolism that used an abbreviation for the unknown he was solving for. His algebraic methods of solving mathematical problems had lasting effects and great benefits for the studies of algebra and number theory.

 

However, essentially nothing is known of his life and there has been much debate regarding the date at which he lived. Historians have approximated his birth to be at about 200 A.D. in Alexandria, Egypt and his death at -censored- A.D. in Alexandria as well. Diophantus married at the age of -censored- and had a son who later died at -censored-, only 4 years before Diophantus' death at -censored-.

 

à In his epitaph there is no age marked but a brain-teaser to find out the age on your own:

 

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 she 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.

 

German translation:

 

Hier das Grabmal deckt Diophantos - ein Wunder zu schauen:

Durch arithmetische Kunst lehret sein Alter der Stein.

Knabe zu bleiben verlieh ein Sechstel des Lebens ein Gott ihm;

Fügend das Zwölftel hinzu, ließ er ihm sprossen die Wang;

Steckte ihm drauf auch an in dem Siebtel die Fackel der Hochzeit,

Und fünf Jahre nachher teilt er ein Söhnlein ihm zu.

Weh! Unglückliches Kind, so geliebt! Halb hat es des Vaters

Alter erreicht, da nahm's Hades, der schaurige, auf.

Noch vier Jahre den Schmerz durch Kunde der Zahlen besänft'gend,

Langte am Ziele des Seins endlich er selber auch an.

 

 

Check here if you have dissolved the brain-teaser!

 

 

 

 

 

Reference for the contents above and further information of Diophantus’ live:

 

http://www.schepart.ch/mho/Wissenschaft/Wissenschaftsseite.htm

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Diophantus.html

Ziegenbalg J.: Algorithmen, von Hammurapi bis Gödel; Spektrum Akademischer Verlag Heidelberg, Berlin 1996

 

 

Further information on the Diophantine equation:

 

http://de.wikipedia.org/wiki/Diophantische_Gleichung