Almost all we know of Diophantus's life comes from an algebra riddle
Lagrange called Diophantus the inventor of algebra, yet his dates could fall anywhere across five centuries. The one personal detail is a puzzle in the Greek Anthology describing his life in fractions, which works out to 84 years. It was in a copy of his book that Fermat scribbled his famous Last Theorem.
Diophantus of Alexandria probably flourished around 250 CE, but the evidence allows anything from about 170 BCE, when Hypsicles, the latest writer he quotes, was active, to 350 CE, when Theon of Alexandria quotes him. Paul Tannery linked a student named Anatolius, mentioned by Michael Psellos, to a 3rd-century bishop of Alexandria, which would fit the usual dating.
The riddle, attributed to the grammarian Metrodorus of the 5th or 6th century, divides his life into stages: a sixth as a boy, a twelfth more as a youth, a seventh before marriage, a son five years later who lived half his father's span, and four final years of grief. Solving the resulting equation gives 84, though nobody can confirm it.
His masterpiece, the Arithmetica, gathered 290 problems solved with algebraic equations, some with single answers and many with several. It filled thirteen books; six survive in Greek, and four more turned up in Arabic in 1968, corresponding to books four to seven. It is the oldest surviving work to solve arithmetic problems by algebra, though Diophantus did not invent the method, which practitioners had long passed on by word of mouth. He introduced shorthand for common operations and for an unknown and its powers, but had no symbols for equality or exponents, placed coefficients after variables and showed addition by setting terms side by side.
His influence was long. The work became standard in the Neoplatonic schools of late antiquity, was translated into Arabic in the 9th century, and closely matches medieval Arabic algebra in method. Claude Bachet's 1621 edition gained fame through Fermat's marginal note. Today Diophantine equations, those with whole-number coefficients seeking whole-number solutions, along with Diophantine geometry and approximation, keep his name alive in number theory.
Source: Diophantus
