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How do letters near the beginning of the alphabet represent known 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).

In algebra, the convention of using letters near the beginning of the alphabet (a, b, c, ...) to represent known quantities originated with the 17th-century French thinker René Descartes.1

These letters are typically used to denote values that are known but arbitrary within the context of a specific problem. In contrast, letters near the end of the alphabet, such as x, y, and z, are reserved to represent unknown quantities or variables.12

This distinction is frequently seen in polynomial equations, such as the quadratic equation $a x^{2} + b x + c = 0$ . In this expression, x is the variable to be solved for, while a, b, and c serve as coefficients—fixed, known values that must be specified to solve the equation. This flexible system of symbolic representation is a fundamental characteristic that provides algebra with its great utility in solving mathematical problems.21