Diophantus, Father of Algebra

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His Life

Diophantus was a Greek mathematician, famous for his work in algebra. What little is known of Diophantus' life is inferred from a letter of the 11th-century Byzantine scholar Michael Psellus. The only other information, which is uncertain, comes from the solution of an arithmetic epigram, which says that Diophantus married at 33 and had a son who died at age 42, four years before Diophantus' death at 84.

The Arithmetica, the treatise on which Diophantus' fame rests, purports to be in 13 books, but only 6 of the Greek manuscripts survive. Diophantus' work was doubtless influenced by traditions common to the Hellenistic and Roman world.

Diophantus' Riddle

Although little is known about Diophantus' life, his age at death is known because one of his admirers described his life in an algebraic riddle. See if you can solve it:

"Diophantus' youth lasted 1/6 of his life. He grew a beard after 1/12 more of his life. After 1/7 more of his life, Diophantus married. Five years later he had a son. The son lived exactly 1/2 as long as his father, and Diophantus died just four years after his son's death. All of this totals the years Diophantus lived."

Solution:

Let n represent the number of years Diophantus lived.

(1/6)n + (1/12)n + (1/7)n 5 + (1/2)n +4 = n

Simplify: (3/28)n = 9

n = 84 years old