Diophantus

Diophantus was an ancient Greek mathematician whose surviving work, especially the Arithmetica, studies equations and problems seeking rational or integer solutions.

Arithmetica: An ancient Greek mathematical work by Diophantus, presenting problems solved through algebraic procedures. This surviving text contains most of the work that made Diophantus known.
Syncopated algebra: An algebraic notation system that abbreviates some operations while expressing others in words. Diophantus used abbreviations for powers, subtraction, and equality rather than modern symbolic notation.
Hypatia: A late-antique Alexandrian philosopher and mathematician who taught and wrote on mathematical works. The Suda associates Hypatia with commentary on Diophantus, linking their scholarly traditions.
Fermat's Last Theorem: The claim that no positive integers satisfy xⁿ + yⁿ = zⁿ for any integer n greater than two. Fermat's famous marginal note was written in his copy of Diophantus's Arithmetica.
Diophantine equation: A polynomial equation whose solutions are sought among integers or other specified number systems. Modern terminology honors Diophantus for his attention to equations with constrained solutions.
Indeterminate equation: An equation with multiple unknowns that admits more than one solution under the chosen number system. Many Arithmetica problems ask for a suitable solution among numerous possible values.
Pappus of Alexandria: A Greek mathematician of late antiquity known for the Mathematical Collection. Pappus is a nearby witness to the later Greek mathematical culture that preserved earlier works.
Pierre de Fermat: A seventeenth-century French mathematician known for number theory and contributions to analytic geometry. Fermat annotated a Latin translation of Diophantus and drew inspiration from its problems.
Rational number: A number expressible as the ratio of two integers with a nonzero denominator. Many problems in the Arithmetica seek rational, not exclusively integer, solutions.
Diophantine analysis: The study of integer or rational solutions to polynomial equations. Later mathematics grouped related equation-solving problems under a name derived from Diophantus.

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