Diophantus of Alexandria (Ancient Greek: Διόφαντος, romanized: Diophantos) (/daɪoʊˈfæntəs/; fl. 250 CE) was a Greek mathematician who was the author of the Arithmetica in thirteen books, ten of which are still extant, made up of arithmetical problems that are solved through algebraic equations.

Although Joseph-Louis Lagrange called Diophantus "the inventor of algebra" he did not invent it; however, his exposition became the standard within the Neoplatonic schools of Late antiquity, and its translation into Arabic in the 9th century AD and had influence in the development of later algebra: Diophantus' method of solution matches medieval Arabic algebra in its concepts and overall procedure. The 1621 edition of Arithmetica by Bachet gained fame after Pierre de Fermat wrote his famous "Last Theorem" in the margins of his copy.

In modern use, Diophantine equations are algebraic equations with integer coefficients for which integer solutions are sought. Diophantine geometry and Diophantine approximations are two other subareas of number theory that are named after him. Some problems from the Arithmetica have inspired modern work in both abstract algebra and number theory.

The exact details of Diophantus' life are obscure. Although he probably flourished in the third century CE, he may have lived anywhere between 170 BCE, roughly contemporaneous with Hypsicles, the latest author he quotes from, and 350 CE, when Theon of Alexandria quotes from him. Paul Tannery suggested that a reference to an "Anatolius" as a student of Diophantus in the works of Michael Psellos may refer to the early Christian bishop Anatolius of Alexandria, who may possibly the same Anatolius mentioned by Eunapius as a teacher of the pagan Neopythagorean philosopher Iamblichus, either of which would place him in the 3rd century CE.

The only definitive piece of information about his life is derived from a set of mathematical puzzles attributed to the 5th or 6th century CE grammarian Metrodorus preserved in book 14 of the Greek Anthology. One of the problems (sometimes called Diophantus' epitaph) states:

Here lies Diophantus, the wonder behold. Through art algebraic, the stone tells how old: 'God gave him his boyhood one-sixth of his life, One twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage After attaining half the measure of his father's life chill fate took him. After consoling his fate by the science of numbers for four years, he ended his life.'

This puzzle implies that Diophantus' age x can be expressed as

which gives x a value of 84 years. However, the accuracy of the information cannot be confirmed.