Diophantus
Greek mathematician, author of Arithmetica, often called the father of algebra.
Diophantus of Alexandria was a Greek mathematician, likely active in the third century CE, though his life is poorly documented. He is best known as the author of the *Arithmetica*, a major work originally in thirteen books, of which ten survive (six in Greek and four in Arabic, the latter rediscovered in 1968). This collection contains 290 arithmetic problems solved through algebraic equations, making it the earliest extant work to treat arithmetic problems algebraically. Diophantus did not invent algebra, which existed before him as an oral practice, but he systematized its techniques for solving problems. His method involved naming an unknown, setting up an equation, simplifying it to a standard form, and then solving it—a procedure matching medieval Arabic algebra in concept and overall steps. Joseph-Louis Lagrange later called Diophantus "the inventor of algebra," and his exposition became standard in Neoplatonic schools of Late antiquity. Translated into Arabic in the 9th century, it influenced later algebra. The 1621 Latin edition by Bachet gained fame when Pierre de Fermat wrote his "Last Theorem" in its margins. Diophantus introduced an algebraic symbolism with abbreviations for the unknown and its powers, though lacking modern symbols for operations and relations. His problems often seek integer solutions to equations with integer coefficients, now called Diophantine equations, and most lead to quadratic equations. He noted that numbers of the form \(4n+3\) cannot be sums of two squares and appears to have known that every number is a sum of four squares. The only biographical detail comes from a puzzle in the *Greek Anthology*, which gives his age as 84 years.
- born
- Unknown
- died
- Unknown
- field
- Mathematics
- nationality
- Greek
- known_for
- Arithmetica, Diophantine equations, Diophantine analysis
Lore & Background
Joseph-Louis Lagrange called Diophantus 'the inventor of algebra'; his exposition became the standard within the Neoplatonic schools of Late antiquity, and its translation into Arabic in the 9th century AD 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. As a result of his work, he has sometimes been referred to as the father of algebra.
Reader's Guide
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 be 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 x = x/6 + x/12 + x/7 + 5 + x/2 + 4, which gives x a value of 84 years. However, the accuracy of the information cannot be confirmed.
Did You Know?
- Arithmetica was originally written in thirteen books, but only six of them survive in Greek, while another four books survive in Arabic, which were discovered in 1968.
- The books in Arabic correspond to books 4 to 7 of the original treatise, while the Greek books correspond to books 1 to 3 and 8 to 10.
Notable Quotes (Wikiquote)
"The 16th century Italian mathematician Rafael Bombelli, L’Algebra, published in 1572." — Diophantus "Florian Cajori, A History of Mathematics (1893)." — Diophantus "In this work [Arithmetica] is introduced the idea of an algebraic equation expressed in algebraic symbols. His treatment is purely analytical and completely divorced from geometrical methods." — Diophantus "Florian Cajori, A History of Mathematics (1893)." — Diophantus
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