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## Diophantus of Alexandria / die uh FAN tus /

###### Mathematics Ranking 37th of 46 What little is known of Diophantus of Alexandria’s life is inferred from a letter of the eleventh-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’s death at 84.

## The word “indeterminate” refers to a system of polynomial equations that has fewer equations than variables and “determinate” if the number of equations equals or exceeds the number of variables. Thus

x + y = a,  a constant,

xy = 1,

is a determinate system since there are an equal number of equations (2) and variables x and y make two as well. On the other hand:

x² + y² = z²

is indeterminate since there are three variables (x, y, and z) and only one equation. Note that polynomial equations in one variable, such as quadratic or cubic equations, are determinate.

The term “indeterminate” is most commonly applied to systems with fewer equations than variables for which integer or rational solutions are sought. Such systems, also called “Diophantine,” have been particularly influential in the development of algebra.(1) The fact that these indeterminate systems are also called “Diophantine” demonstrates the significance of Diophantus’s Arithmetica.

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(1) Isabella Bashmakova and Galina Smirnova, translated from the Russian by Abe Shenitzer, The Beginnings & Evolution of Algebra (Washington, D.C., 2000), p. xvi.

(2) C.C. Gillispie (Editor), Concise Dictionary of Scientific Biography (Chicago, 1980), p. 205.

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