丢番图生平Diophantus's personal life

84° Diophantus's personal life. Beyond the fact that Diophantus flourished at Alexandria, nothing certain is known about his life. There is, however, a problem in the Greek Anthology that purports to give us some details. The Greek, or Palatine, Anthology is a collection of forty-six number problems, in epigrammatic form, assembled about 500 A.D. by the grammarian Metrodorus. The problem concerning Diophantus appears as the following epitaphic summary: "Diophantus passed one sixth of his life in childhood, one twelfth in youth, and one seventh more as a bachelor. Five years after his marriage was born a son who died four years before his father, at half his father's age. [How old was Diophantus when he died?]"

If we interpret the phrase "at half his father's age" to mean "at half his father's final age," then, letting x denote Diophantus's age at death, we easily obtain the equation

x/6 + x/12 + x/7 + 5 + x/2 + 4 = x,

which gives x = 84. It then follows that Diophantus spent fourteen years in childhood, seven more in youth, and twelve more as a bachelor, thus marrying when he was thirty-three. Five years later, at the age of thirty-eight, he had a son who died at the age of forty-two when his father was eighty years old. If we should interpret the phrase "at half his father's age" to mean "when he was just half the age of his father," a different solution is obtained with the various episodes occurring at fractional years. Under this interpretation, Diophantus died when 65⅓ years old and his son when 30⅔ years old. Out of regard for Diophantus's love of integers, let us allow him and his son the longer spans of life.