Diophantus of Alexandria
210-290
Greek Mathematician
The work of Diophantus is particularly remarkable in light of the time in which it took place. By his era, in the third century A.D., the Roman Empire—of which his hometown, the Greek city of Alexandria in Egypt, was a part—had long since entered its slow decline. Little in the way of original mathematical work took place during this period, yet in his Arithmetica, Diophantus explored the frontiers of mathematics. This new, abstract arithmetic involved the use of special symbols, and centuries later it would come to be known as algebra.
From a sixth century Greek collection of brainteasers comes this one, concerning Diophantus: "...his boyhood lasted 1/6th of his life; he married after 1/7th more; his beard grew after 1/12th more; and his son was born five years later; the son lived to half his father's age, and the father died 4 years after the son." Unraveling the puzzle yields the information that Diophantus married at age 26 and became a father at 31, and that his son died at age 42, four years before Diophantus died at the age of 84.
As for his Arithmetica, this consisted of 130 problems in 13 books, of which only six survive. The book offers numerical solutions to determinate equations, or ones with a single solution, and seems to have been largely concerned with equations that have rational integer solutions. Apparently Diophantus, perhaps drawing on the influence of the ancient Pythagorean school, believed that irrational solutions (i.e., solutions that resulted in numbers that cannot be expressed as a fraction) were impossible.
More important than his beliefs about irrationals was Diophantus's use of the first symbolic notation, including abbreviations for an unknown and its powers. Prior to that time, mathematicians had simply written out all elements of the problem. Most significant of all, however, was the nature of the problems themselves: for instance, "...a sixfold number increased by twelve, which is divided by the difference by which the square of the number exceeds three." Such a problem would have been difficult indeed to solve with the limited notation Diophantus introduced; by contrast, mathematicians today would write (12 + 6n)/(n2 - 3). Obviously Diophantus had gone past the realm of arithmetic, but not until al-Khwarizmi (c. 780-c. 750)—from whose Kitab al-jabr the word "algebra" is drawn—did the implications of this become clear.
It is not correct to refer to Diophantus as the "father of algebra," because some of the concepts he used go back to the Babylonians; but it is obvious that he greatly advanced the mathematics of unknowns, and was first to give form to their study. In addition to his other achievements, Diophantus seems to have been the first mathematician to treat fractions as numbers. Centuries later, his work would attracted the admiration of such luminaries as Regiomontanus (1436-1476) and Pierre de Fermat (1601-1665).
This is the complete article, containing 471 words
(approx. 2 pages at 300 words per page).
