Diophantos of
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
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
Further
information on the Diophantine equation:
http://de.wikipedia.org/wiki/Diophantische_Gleichung