Arithmetica

Arithmetica, commonly known as Diophantus's Arithmetica, is a 3rd-century treatise on algebra attributed to the Greek mathematician Diophantus of Alexandria. It is a systematic collection of problems and solutions focused on solving equations with integer or rational solutions, now called Diophantine equations. The work is traditionally divided into thirteen books, each addressing different classes of equations and techniques.

The problems are presented in a concise, practical style and often solved through a sequence of logical steps rather than abstract theory. Diophantus introduces early forms of symbolic notation for unknown quantities and their powers, and he develops methods for reducing complex equations to simpler ones. The emphasis is on finding specific solutions rather than proving general theorems, and many problems involve creative constructions, auxiliary variables, and balancing techniques.

Arithmetica is regarded as one of the foundational works in the history of algebra. It marks a transition from rhetorical, verb-based problem solving to a more systematic, rule-based approach to equations. The term “Diophantine equations” derives from the book’s focus and its enduring association with integer solutions.

The surviving textual tradition of Arithmetica is fragmentary in its original Greek form. Much of what is known about the work comes from later Arabic and Latin translations and quotations by medieval scholars. Modern scholarship relies on critical editions and commentaries that assemble the surviving portions and contextualize Diophantus’s methods within the broader development of algebra.