Diophantus

Diophantus of Alexandria was a Greek mathematician who worked in the city of Alexandria during the 3rd century AD. Little is known about his life, and the dates of his birth and death are uncertain. He is traditionally regarded as a major early figure in algebra and is sometimes called the father of algebra.

Diophantus is best known for his treatise Arithmetica, a comprehensive collection on solving algebraic equations. The work, originally organized into thirteen books, focuses on finding numerical solutions, especially integer or rational solutions, to problems posed with multiple unknowns. Diophantus treats linear and quadratic equations, and in some passages more complex equations, using methods of algebra that involve setting up relationships between variables and solving by substitution, balancing, and proportion. He often presents problems as short statements and then provides a step-by-step solution, illustrating techniques that resemble modern solving of equations without symbolized notation. The treatise helped introduce the idea of indeterminate equations and pioneered systematic problem solving in algebra.

Because the original Arithmetica survives only in later manuscripts and through translations, our understanding comes largely from medieval Arabic scholars and later Latin commentators. The work influenced later mathematicians in both the Islamic world and medieval Europe, contributing to the development of number theory and the study of Diophantine equations, where attention is given to integer solutions. The modern term "Diophantine equations" reflects this legacy, and Diophantine methods influenced later techniques such as infinite descent and various numerical methods used by number theorists.

Although Diophantus's life remains poorly documented, his influence on algebra and number theory is widely recognized. His Arithmetica provided one of the earliest systematic treatments of solving algebraic problems and inspired centuries of mathematical work, even as the notation and rigor of his era differ from modern practice.