In the year 235 A.D., Diophantus of Alexandria was thirty-five years old and the only prominent mathematician alive.  At this time, he had been married for two years, but not much else is known about his personal life.  Diophantus had a son that died about four years before himself in 280 A.D.
For Diophantus, the most important topics in mathematics were algebra and number theory.  His greatest work was a set of thirteen books called "Arithmetica."  All the translations of this work, including the early Arabic ones, contain only six of the books.  Historians believe this is evidence that the other books were lost soon after Diophantus’ death.  In "Arithmetica," Diophantus solves 130 determinate and indeterminate equations, some being of fourth and sixth degree.  Unlike many earlier mathematicians who required that equations have whole number solutions, Diophantus did not refrain from giving rational solutions to the problems.  Interestingly, he did not include negative solutions to the equations.  Diophantus was first to use symbols in algebra in Greek mathematics.  He also introduced the idea of a variable, which he labels as "arithmos."  The other important feature of "Arithmetica" is several propositions in number theory.  One example is that no number of the form 8n-7, where n is a non-negative integer, could be rewritten as the sum of three squares.  150 years later the famous female mathematician Hypatia wrote a commentary on Diophantus’ "Arithmetica."  (See 400 A.D.)

Author: Tim Lucas

References:
Mac Tutor History of Mathematics Archive
 http://www-history.mcs.st-and.ac.uk:/history Mathematicians/Diophantus.html

Diophantus of Alexandria
http://www.csc.vic.edu.au/cscWeb/MathWEB/encyc/d/Diophantus.htm