Diophantus

Diophantus has been called the "Father of Algebra." He lived during the period from 250 to 350 A.D., "a silver age in mathematics." His text the Arithmetica was composed of 13 books and 189 problems.

The problems he worked on were mostly linear systems of equations with a few quadratics. He included strong hints to make the questions easier to solve. One of these problems uses his age as a solution, so he apparently lived to at least 84.

Diophantus introduced symbols for subtraction, for an unknown, and for the degree of the variable. Although there were several solutions to some of his problems, he only looked for one positive integer solution. Now we call an equation to be solved in integers a diophantine equation. For example, Diophantus considered the equations

ax + by = c

where the variables x and y are positive integers. This equation is solvable if and only if the greatest common divisor of a and b divides c. We can find the solution to these equations using a modified Euclidean Algorithm.

This entry edited from a contribution by Jimmy Goodman.