DHIOPHANTUS, THE FATHER OF ALGEBRA

Diophantus of Alexandria, who lived in the fourth century A.D., is generally credited with being the originator of algebra. He was the first to use letters to represent numbers and symbols to represent operations. Although some of his writings have survived, the lay unheeded for twelve hundred years and were not fully appreciated until Fermat worked on some of his problems in the seventeenth century.

Since good notation in a mathematical problem is a valuable tool, the improvements in notation which Diophantus made were of great significance. He not only introduced letters as generalized symbols for numbers, but he also made beginning in expressing powers of a number with exponents.

When you come to work with quadratic equations you will discover the phrase “square half the coefficient of x”. This phrase comes from Diophantus, who made a thorough study af such equations. He also worked with some third ad fourth degree equations. Since negative numbers were unknown at that time, he was limited to solutions involving positive integers and fractions. He spoke of the impossibility of solving 4=4x+20; he even called it an absurd equation.

Diophantus was so thorough in his treatment of indeterminate equations that even today they are known as Diophantus equations. An indeterminate equation involves the solution in integers of common fractions of a single equation in two or more variables.

Diophantus also posed the problem of breaking up a square into the sum or two others squares, again limiting the solutions to whole numbers or common fractions. A simple illustration of a problem involving Diophantine equations is the following puzzle: Admission prices for an entertainment were men, $1.00; women, $.50; children, $.25. 100 persons attend and the receipts were $50.00. how many men, women, and children were in the audience? A complete theory for the solution of Diophantive equations was completed about 100 years ago by H. J. S. Smith.