Arithmetica

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Arithmetica

work by Diophantus

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June 18, 2026

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Arithmetica is a seminal work by the Greek mathematician Diophantus, who flourished around 250 CE. This treatise is renowned for its pioneering use of algebraic symbolism and its significant contributions to the field of number theory.1

The Arithmetica is primarily a collection of problems with solutions, approximately 260 in its extant form. Diophantus introduced symbols for unknowns and their powers, laying the groundwork for modern algebraic notation. His problems often involve indeterminate equations, meaning they have multiple solutions. A key focus is on finding positive rational solutions that make given algebraic expressions numerical squares or cubes.1

This work inspired later mathematicians, including those in the Islamic world and Pierre de Fermat, who famously used its margins to develop his own theories, including the famous Fermat's Last Theorem. Equations that seek integer solutions are now known as Diophantine equations in his honor.123

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Diophantus
…of Diophantus reposes, is his Arithmetica. Its historical importance is twofold: it is the first known work to employ algebra in a modern style, and it inspired the rebirth of number theory.
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…of Diophantus reposes, is his Arithmetica. Its historical importance is twofold: it is the first known work to employ algebra in a modern style, and it inspired the rebirth of number theory.
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Lagrange’s four-square theorem
…of Alexandria in his treatise Arithmetica (3rd century ce). Credit for the first proof is given to the 17th-century French amateur mathematician Pierre de Fermat. (Although he did not publish this proof, his study of Diophantus led to Fermat’s last theorem.) The first published proof of the four-square theorem was…
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…of Alexandria in his treatise Arithmetica (3rd century ce). Credit for the first proof is given to the 17th-century French amateur mathematician Pierre de Fermat. (Although he did not publish this proof, his study of Diophantus led to Fermat’s last theorem.) The first published proof of the four-square theorem was…
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mathematics
Number theory
His writing, the Arithmetica, originally in 13 books (six survive in Greek, another four in medieval Arabic translation), sets out hundreds of arithmetic problems with their solutions. For example, Book II, problem 8, seeks to express a given square number as the sum of two square numbers (here…
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His writing, the Arithmetica, originally in 13 books (six survive in Greek, another four in medieval Arabic translation), sets out hundreds of arithmetic problems with their solutions. For example, Book II, problem 8, seeks to express a given square number as the sum of two square numbers (here…
Read More

number theory
Diophantus
250), author of Arithmetica. This book features a host of problems, the most significant of which have come to be called Diophantine equations. These are equations whose solutions must be whole numbers. For example, Diophantus asked for two numbers, one a square and the other a cube, such…
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250), author of Arithmetica. This book features a host of problems, the most significant of which have come to be called Diophantine equations. These are equations whose solutions must be whole numbers. For example, Diophantus asked for two numbers, one a square and the other a cube, such…
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Waring’s problem
…Diophantus of Alexandria’s publication of Arithmetica.) The general assertion concerning f(n) was proved by the German mathematician David Hilbert in 1909. In 1912 the German mathematicians Arthur Wieferich and Aubrey Kempner proved that f(3) = 9. In 1986 three mathematicians, Ramachandran Balasubramanian of India and Jean-Marc Deshouillers and François Dress…
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…Diophantus of Alexandria’s publication of Arithmetica.) The general assertion concerning f(n) was proved by the German mathematician David Hilbert in 1909. In 1912 the German mathematicians Arthur Wieferich and Aubrey Kempner proved that f(3) = 9. In 1986 three mathematicians, Ramachandran Balasubramanian of India and Jean-Marc Deshouillers and François Dress…
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