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Why are x, y, and z commonly used for unknown quantities in algebra?

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Map of the Greco-Roman world highlighting the birthplaces of notable ancient mathematicians, marked with the pi symbol and labeled with their names. Cities such as Athens, Alexandria, Syracuse, and Miletus are shown around the Mediterranean, with modern country boundaries outlined. An inset provides detail for the region of Greece and western Anatolia. — algebra This map spans a millennium of prominent Greco-Roman mathematicians, from Thales of Miletus (c. 600 bce) to Hypatia of Alexandria (c. 400 ce).

The convention of using x, y, and z to represent unknown quantities in algebra originated with the 17th-century French philosopher and mathematician René Descartes.31

In his influential 1637 work, La Géométrie, Descartes established a systematic notation that distinguished between different types of values. He proposed using letters from the end of the alphabet—specifically x, y, and z—to denote unknown quantities or variables. Conversely, he used letters from the beginning of the alphabet (a, b, c) to represent known, arbitrary numbers or parameters.123

This notation replaced earlier systems, such as that of the mathematician François Viète, who had used capital vowels to denote variables and consonants for parameters. Descartes's system provided greater flexibility for symbolic manipulation and became a foundational element of analytic geometry, allowing for the clear representation of equations and their corresponding geometric curves.231