Diophantus
"Father of algebra"
c. 250 C.E.

The "Silver Age" of Alexandria, also known as the Later Alexandrian Age, was about 250 - 350 C.E. Diophantus, a Greek algebraist of this era, was thought to belong to this time period, but there is some uncertainty to the exact time frame of his life. Little is known of his personal life except for an algebraic puzzle rhyme determining his age from Anthologia Palatina which is a collection of problems dating from the 5th and 6th centuries.

"Here lies Diophantus." The wonder behold- Through art algebraic, the stone tells how old: "God gave him his boyhood one-sixth of his life, One-twelfth more as youth while whiskers grew rife; And then yet one-seventh eve marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage Met fate at just half his dad's final age. Four years yet his studies gave solace from grief; Then leaving scenes earthly he, too found relief."
Did you solve the puzzle? The answer is 84 years old.

Diophantus studied at the University of Alexandria in Egypt. His major contribution to mathematics is a collection of 13 books called Arithmetica, in which only 6 survived through the centuries, and exhibit a high degree of math skills and ingenuity. His series of books, a collection of approximately 150 problems, was devoted to the exact solution of equations, but lacked finding a method of determining general solutions. His books are thought to be a problem collection in the application of algebra and not an algebra textbook.

In the historical development of algebra, three stages exist: rhetorical (everything written out in words), syncopated (some representative symbols used), and symbolic. Diophantus introduced the syncopated style of algebraic writing, in which he could write polynomials in a single unknown. The major difference between Diophantine syncopated method and modern algebraic notation is the absence of special symbols for operations, relations, and exponential notations.

An example of a problem from his works: Find 2 numbers such that the sum is 20 and the sum of the squares is 208. In terms of modern notation, the variables are (10 + x) and (10 - x); therefore,

(10 + x)2 + (10 - x)2 = 208;
and x = 2, so the numbers are 8 and 12.

Some claim that Diophantus should not be called the "Father of Algebra" since his work contained mainly solutions to exact problems with no general solutions proposed. If we are to consider only the advancement of algebraic notation, then he was truly the "Father of Algebra".

Contributed by Judy Lasater

References:

  1. Boyer, C. B. (1991). A History of Mathematics, 2nd Edition. New York: John Wiley, pp. 178-183.
  2. Historical Topics for the Mathematics Classroom, 31st Yearbook. (1969). Washington, DC: The National Council of Teachers of Mathematics, pp.240-241.

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